url stringlengths 6 1.61k | fetch_time int64 1,368,856,904B 1,726,893,854B | content_mime_type stringclasses 3 values | warc_filename stringlengths 108 138 | warc_record_offset int32 9.6k 1.74B | warc_record_length int32 664 793k | text stringlengths 45 1.04M | token_count int32 22 711k | char_count int32 45 1.04M | metadata stringlengths 439 443 | score float64 2.52 5.09 | int_score int64 3 5 | crawl stringclasses 93 values | snapshot_type stringclasses 2 values | language stringclasses 1 value | language_score float64 0.06 1 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
https://www.teachoo.com/13076/502/Ex-3.5--1-ii/category/Ex-3.5/ | 1,726,095,328,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651405.61/warc/CC-MAIN-20240911215612-20240912005612-00749.warc.gz | 948,413,541 | 22,090 | Cross Multiplication Method
Chapter 3 Class 10 Pair of Linear Equations in Two Variables
Serial order wise
### Transcript
Ex 3.5 ,1 Which of the following pairs of linear equations has unique solution, no solution, or infinitely many solutions. In case there is a unique solution, find it by using cross multiplication method (ii) 2x + y = 5 3x + 2y = 8 2x + y = 5 3x + 2y = 8 2x + y = 5 2x + 1y – 5 = 0 Comparing with a1x + b1y + c1 = 0 ∴ a1 = 2, b1 = 1, c1 = –5 3x + 2y = 8 3x + 2y – 8 = 0 Comparing with a2x + b2y + c2 = 0 ∴ a2 = 3, b2 = 2, c2 = –8 a1 = 2, b1 = 1, c1 = –5 & a2 = 3, b2 = 2, c2 = –8 𝒂𝟏/𝒂𝟐 𝑎1/𝑎2 = 2/3 𝒃𝟏/𝒃𝟐 𝑏1/𝑏2 = 1/2 𝒄𝟏/𝒄𝟐 𝑐1/𝑐2 = (−5)/(−8) 𝑐1/𝑐2 = 5/8 Since 𝑎1/𝑎2 ≠ 𝑏1/𝑏2 We have a unique solution Solving 2x + y = 5 …(1) 3x + 2y = 8 …(2) For cross-multiplication 2x + y – 5 = 0 3x + 2y – 8 = 0 𝑥/(1×(−8) − 2 ×(−5) ) 𝑥/((−8) + 10 ) 𝑥/(2 ) = 𝑦/(3 ×(−5) − 2 × (−8) ) = 𝑦/(−15 + 16) = 𝑦/(1 ) = 1/(2 × 2 − 3 × 1 ) = 1/(4 − 3 ) = 1/1 Now, 𝒙/𝟐 = 𝟏/𝟏 x = 2 × 1 ∴ x = 2 𝒚/𝟏 = 𝟏/𝟏 y = 1 × 1 ∴ y = 1 Therefore, x = 2, y = 1 is the solution of our equation | 615 | 1,070 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.65625 | 5 | CC-MAIN-2024-38 | latest | en | 0.755951 |
https://e-eduanswers.com/mathematics/question18578015 | 1,638,701,779,000,000,000 | text/html | crawl-data/CC-MAIN-2021-49/segments/1637964363157.32/warc/CC-MAIN-20211205100135-20211205130135-00073.warc.gz | 292,322,825 | 16,308 | Madison’s plant was 10 7/8 inches tall. She trimmed off 2 1/4 inches. How tall is her plant now? thx edited
, 22.10.2020 22:01, tylermorse3775
# Madison’s plant was 10 7/8 inches tall. She trimmed off 2 1/4 inches. How tall is her plant now? thx edited
### Other questions on the subject: Mathematics
Mathematics, 20.06.2019 18:04, stephanieanaya7
111 thirty dollars is to be divided among three girls and two boys so that each of the girls receives twice as much as each of the boys. how much does each receive? | 159 | 517 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.875 | 3 | CC-MAIN-2021-49 | latest | en | 0.962591 |
https://www.iam.uni-bonn.de/afa/teaching/12w/derivation-of-macroscopic-evolution-models | 1,722,756,673,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722640393185.10/warc/CC-MAIN-20240804071743-20240804101743-00588.warc.gz | 658,155,239 | 5,637 | ## Derivation of macroscopic evolution models from deterministic microscopic equations
Winter 2012/2013
Lecture course "Advanced Topics in PDE and Mathematical Models" V5B3
Prof. Dr. J. J. L. Velázquez
Lectures Monday 12-14 and Friday 10-12, Room N0.003 (Endenicher Allee 60)
### Synopsis
In Mathematical Physics and Applied Mathematics there are many problems of systems composed of many particles, which interact by means of deterministic microscopic rules but for which the dynamics of some macroscopic particle densities can be defined by means of a system of Partial Differential Equations or some kinetic model. In some cases it is possible to use Mean-Field Approximations in which the dynamics of individual particles can be approximated by the sum of the effects of many small contributions of many other particles (cf. for instance [2,6]). In other cases a given particle interacts only with a small number of neighbouring particles, but – either because the microscopic dynamics drives the system very fast towards "local equilibrium'' configurations or because the interactions between particles are rare – it is possible to derive an effective set of equations for a set of macroscopic quantities which describe some important properties of the system. One of the most relevant examples is the Boltzmann Equation that was rigorously obtained as the limit of a many particle system in [4].
A common feature of most of the systems considered in this course is that their microscopic dynamics are described by a system of Ordinary Differential Equations, i. e. no stochastic behaviour is present in the microscopic evolution. In many interesting examples, the microscopic equations describing the evolution of the system are reversible in time, but the effective macroscopic equations which describe the collective behaviour of the particle system have dissipative properties, increasing entropies and similar properties. The solutions of the microscopic equations which exhibit such type of irreversible behaviour must be chosen usually according to suitable probability distributions that ensure that the solutions of the microscopic system mimic the behaviour of a random system. Such randomness of the distribution of particles must be preserved along the evolution. One of the main goals is to study the conditions on the microscopic distributions of particles in the currently available rigorous results which guarantee the dissipative behaviour of the macroscopic problem.
The course addresses students interested in Differential Equations with some background in basic Probability Theory. At the beginning, some examples of rigorous derivations of Mean Field Theories will be described in detail and some open problems will be discussed. The second part of the course will consist of the detailed study of the derivation by O. E. Lanford of the Boltzmann Equation, taking as starting point an uncorrelated system of particles.
### References
1. L. A. Buniwovich and Y. G. Sinai. Statistical Properties of Lorentz gas with periodic configuration of scatterers. Comm. Math. Phys. 78, 479–497, 1980/81.
2. W. Braun and K. Hepp. The Vlasov Dynamics and Its Fluctuations in the 1/N Limit of Interacting Classical Particles. Comm. Math. Phys. 56, 125–146, 1977.
3. F. Golse. The Mean-Field Limit for the Dynamics of Large Particle Systems. Journées Équations aux dérivées partielles, Forges-les-Eaux, 2-6 juin 2003, GDR 2434 (CNRS).
4. O. E. Lanford III. Time evolution of large classical systems. Dynamical systems, theory and applications (Rencontres, Battelle Res. Inst., Seattle, Wash., 1974), pp. 1–111. Lecture Notes in Phys., Vol. 38, Springer, Berlin, 1975.
5. B. Niethammer and J. J. L. Velázquez. Homogenization in coarsening systems II. Stochastic case. Math. Methods Mod. Appl. Sci. 14(8), 1401–1424, 2004.
6. K. Oelschläger. Large systems of interacting particles and the porous medium equation. Journal of Differential Equations, 88(2), 294–346, 1990.
7. H. Spohn. Kinetic equations from Hamiltonian dynamics: Markovian limits. Review of Modern Physics 53, 569–615, 1980.
## News
Prof. Dr. Lisa Sauermann has been honored with the von Kaven Award 2023 for her outstanding scientific achievements. (16.11.2023)
Prof. Dr. Angkana Rüland has been awarded a New Horizons in Mathematics Prize 2024 for her contributions to applied analysis (press release). (14.09.2023)
Prof. Dr. Angkana Rüland has been awarded the Calderon Prize that is awarded every two years by the Inverse Problems International Association. (06.09.2023)
Prof. Dr. Karl-Theodor Sturm has been elected into the Academia Europaea. (28.06.2022)
Florian Schweiger erhielt den Hausdorff-Gedächtnispreis 2021 der Fachgruppe Mathematik für die beste Dissertation. Er fertigte die Dissertation unter der Betreuung von Prof. Stefan Müller an. Unter anderen wurde Vanessa Ryborz mit einem Preis der Bonner Mathematischen Gesellschaft für ihre von Prof. Sergio Conti betreute Bachelorarbeit ausgezeichnet. (18.01.2022)
Contact
Managing Director: Prof. Dr. Juan J. L. Velázquez
Chief Administrator: Dr. B. Doerffel
geschaeftsfuehrung@iam.uni-bonn.de
Imprint | Datenschutzerklärung
Mailing address
Institute for Applied Mathematics
University of Bonn
Endenicher Allee 60
D-53115 Bonn / Germany | 1,239 | 5,293 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.625 | 3 | CC-MAIN-2024-33 | latest | en | 0.92103 |
https://community.secondlife.com/forums/topic/52863-what-level-of-math/ | 1,685,820,166,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224649302.35/warc/CC-MAIN-20230603165228-20230603195228-00456.warc.gz | 194,069,241 | 23,226 | What Level of Math....
Please take a moment to consider if this thread is worth bumping.
Recommended Posts
I'm curious, as I've began my studies again on the importance of Math in SL. As I'd say so far I've seen Algebra I being the highest level so far of what I've 'seen'. Or am I missing something?
Eins.
Share on other sites
depends on what you are doing. geometry and trig are very useful in scripting, calculus doesn't see much use (though it sees some) and is less useful than an understanding of discrete math and alternate bases. anything else is just special purpose.
Share on other sites
Addition and subtraction are very useful, but usually not yer understood by the average resident or builder.
Alla dem prim's iz gots number-thingies on em, ad up teh numberz roight an yeh can'z gows rong.
And yet there is still rampant accidental encroachment, or items build in random haphazard layout causing portions to overlap and flicker...
1 + 1 = 2, but in SL it more often = 1.97.
Share on other sites
What it really boils down to is that much of second life is mathematics based, as is much of the world around you in real life as well. Everything from building to scripting in second life uses mathematics, even the point at which you stand is a number that can be taken, manipulated, and output however you wish. I think the only limits to mathematics is with the functions and operators we can use, and really those 'limits' aren't very limited at all. We can add, subtract, multiply, divide, and even use more complex functions like and, or, xor. We can apply these mathematics to everything from color to prim size to simple calculations and outputs. Basically, if you can think it, it can be done! I have seen everything from Group theory to Order theory (linked parts), Combinatronics, Geometry, Trigenometry, Topology of course is a huge part of second life, Measurement theory alongside it, I could go on and on.
1 + 1 = 11.
Very simple.
Share on other sites
no,
1+1=10
(it's a computer after all)
I'd recomend at least up to geometry for builders, at least up to trigonometry for scripters, and everybody else can get away with basic math. to be ahead of the game I'd recommend trig, calc, and algebra respectively, with extra attention to number theory for scripters.
topology, set theory and other advanced topics are mostly special use within SL and not really required to understand or achieve most things in SL and formulas and instruction for achieving goals that use them are available at a more basic level for the most part.
Share on other sites
Void Singer wrote:
no,
1+1=10
(it's a computer after all)
I'm using the Abacus...
Share on other sites
I had to drag a lot of my high school trig out of deep memory for SL building. Working out the length of the long side of a triangular prim and such, and angles for constructing polygons. Basic algebra is handy for scripting, because handling expressions with variables is more or less what algebra does. Boolean algebra helps in understanding conditional statements.
Knowing what a radian is and how they make angles easier to calculate is a huge help for scripting (2*pi = 1 full circle).
Binary comes up less in SL scripting than you'd think, but it's still handy to know.
Vectors are big in scripting. Most tasks with them you can handle by just imagining them as three variables stored in one, or as an x-y-z coordinate, but trickier stuff comes up with unit vectors, magintudes and when you need to combine them as dot products and cross products.
Slightly trickier are quaternions for 3D rotations; I still don't have those down yet.
Share on other sites
the abacus can do binary too
Share on other sites
it's easier to ignore the internal math for rotations and just learn the formulas ( the big thing is that order is important)
binary isn't a requirement, but if you can do boolean algebra, you're really already there (it's just multiple booleans)
Share on other sites
Void Singer wrote:
it's easier to ignore the internal math for rotations and just learn the formulas ( the big thing is that order is important)
binary isn't a requirement, but if you can do boolean algebra, you're really already there (it's just multiple booleans)
Yes, that's the line I take whenever rotations come up. I just about know enough to make them work now, without really being sure about the detailed maths.
Share on other sites
For building and sculpting I can't see where you need anything more than basic skills. I build and sculpt and the most I use is my desktop calculator because I suck at basic math. I have yet to need to use any formula or geometry to build in second life, although I do know them. Scripting might be a different story depending on what you are scripting. I don't really script so I couldn't say for sure. But most of the ones I know that script it seems prior knowledge of programming and coding helps. Although I guess sl scripting is not quite like regular programming. You have to sort of learn as you go from what I hear. I myself gave up on it, I just get friends to do it for me now that why I know it will be done right lol. That being said if you had prior coding or programming skills you would already have the required math skills to go with it. But for building and sculpting a basic calculator is all you need, if that even. I only use it to figure out how many vertices I might need when I divide stuff up or something. | 1,206 | 5,477 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.96875 | 3 | CC-MAIN-2023-23 | latest | en | 0.958054 |
http://math.stackexchange.com/questions/455193/for-f-continuous-show-lim-n-to-infty-n-int-01-fxxn-dx-f1 | 1,469,337,899,000,000,000 | text/html | crawl-data/CC-MAIN-2016-30/segments/1469257823947.97/warc/CC-MAIN-20160723071023-00126-ip-10-185-27-174.ec2.internal.warc.gz | 155,196,434 | 24,921 | # For $f$ continuous, show $\lim_{n\to\infty} n\int_0^1 f(x)x^n\,dx = f(1).$
Suppose $f:[0,1]\to \mathbb{R}$ is continuous. Show that
$$\lim_{n\to\infty} n\int_0^1 f(x)x^n\,dx = f(1).$$
My answer so far: First I want to assume that $f\in C^1$. Then
$$n\int_0^1f(x)x^n\,dx = \left[\frac{n}{n+1}x^{n+1}f(x)\right]_0^1 - \frac{n}{n+1}\int_0^1 x^{n+1}f'(x)\, dx\\ \frac{n}{n+1}f(1) - \frac{n}{n+1}\int_0^1 x^{n+1}f'(x)\, dx,$$
which goes to $f(1)$ because the last integral goes to zero.
But approximating $f$ by $\phi\in C^1$ won't necessarily work, because $\phi(1)$ may not equal $f(1)$... how can we finish the argument?
-
I don't think you could argue by proving it in the case when $f$ is continuously differentiable and then somehow using that to prove it when $f$ is just continuous - you'd have to argue via other methods. – Andrew D Jul 29 '13 at 22:06
Hint: $f(1)=(n+1)\int_{0}^{1} f(1)x^n dx$. – Amitesh Datta Jul 29 '13 at 22:09
For a different approach, see the first answer here. – David Mitra Jul 29 '13 at 22:09
You can simplify your part of the argument: Only polynomials, rather than arbitrary $C^1$ functions, need to be considered. This case is trivial, as we only need to argue for monomials $x^k$, and everything is explicit here. The uniform convergence argument as in the answer below then goes unchanged. – Andrés E. Caicedo Jul 29 '13 at 22:25
We can finish the argument as follows. (Note: We'll assume that the limit in question exists for $f$ and establish that it's equal to $f(1)$. Technically, we should prove that this limit exists as Peter Tamaroff notes below (thanks!). A minor modification of the following argument simultaneously establishes the existence of the limit and its value but we'll leave that as an exercise to the reader.) Let $\epsilon>0$. Choose $\phi\in C^1$ such that $\left|f(x)-\phi(x)\right|<\epsilon$ for all $x\in [0,1]$. You've proven that $$\lim_{n\to\infty} n\int_{0}^{1} \phi(x)x^n=\phi(1).$$ Therefore,
\begin{align}\left|\lim_{n\to\infty} n\int_{0}^{1} f(x)x^n dx -\lim_{n\to\infty} n\int_{0}^{1} \phi(x)x^n dx\right|&=\left|\lim_{n\to\infty} n\int_{0}^{1} (f(x)-\phi(x))x^n dx\right|\\ &\leq \lim_{n\to\infty} n\int_{0}^{1} \left|(f(x)-\phi(x))x^n\right| dx\\ &< \lim_{n\to\infty} n\int_{0}^{1} \epsilon x^n dx\\ &=\lim_{n\to\infty} \epsilon \frac{n}{n+1}\\ &=\epsilon\end{align}
Therefore,
\begin{align}\left|\lim_{n\to\infty} n\int_{0}^{1} f(x)x^n dx - f(1)\right|\leq \left|\lim_{n\to\infty} n\int_{0}^{1} f(x)x^n dx - \phi(1)\right| + \left|\phi(1)-f(1)\right|&<\epsilon + \epsilon\\&=2\epsilon\end{align}
Since $\epsilon>0$ was arbitrary, we conclude that $$\lim\limits_{n\to\infty} n\int_{0}^{1} f(x)x^n dx=f(1)$$ for all continuous functions $f:[0,1]\to \mathbb{R}$.
-
Why'd there exist such $\varphi \in C^1$? – Kunnysan Jul 29 '13 at 22:22
@Kunnysan I'm not sure which tools you'd like to use but this follows, e.g., from the Stone-Weierstrass theorem. – Amitesh Datta Jul 29 '13 at 22:27
Yeah of course. You could have chosen even a polynomial. – Kunnysan Jul 29 '13 at 22:32
I was writing exactly same solution. Discarded it seeing yours, so +1 instead, :) – Kunnysan Jul 29 '13 at 22:36
Thanks @Kunnysan and I'm really sorry that you had to discard your answer! (The same thing happens to me sometimes. In a few years when there are more users on this website, it will hardly be possible to read the question, I suspect, before someone posts an answer!) – Amitesh Datta Jul 29 '13 at 22:39
Here is a more elementary method than you proposed:
First, note that if $f$ is continuous on $[0,1]$, then it is necessarily bounded on $[0,1]$; say $\lvert f(x)\rvert\leq M$ for all $x\in[0,1]$. If we define $\delta_n:=\frac{1}{\sqrt{n}}$, then $$\left\lvert n\int_0^{1-\delta_n}f(x)x^n\,dx\right\rvert\leq Mn\int_0^{1-\delta_n}x^n\,dx=\frac{n}{n+1}\left(1-\frac{1}{\sqrt{n}}\right)^{n+1}\rightarrow0\text{ as }n\rightarrow\infty.$$ Now, let $\epsilon>0$ be given. Continuity of $f$ at $1$ implies that there exists $\delta>0$ such that $\lvert 1-x\rvert<\delta$ implies $\lvert f(x)-f(1)\rvert<\epsilon$. Choose $N\in\mathbb{N}$ such that $0<\delta_n<\delta$ for all $n\geq N$. Then for $n\geq N$, $$n\int_{1-\delta_n}^1(f(1)-\epsilon)x^n\,dx\leq n\int_{1-\delta_n}^1 f(x)x^n\,dx\leq n\int_{1-\delta_n}^{1}(f(1)+\epsilon)x^n\,dx.$$ Computing the left integral $$\frac{n}{n+1}\left(1-\left(1-\frac{1}{\sqrt{n}}\right)^{n+1}\right)\left(f(1)-\epsilon\right)\rightarrow f(1)-\epsilon\text{ as }n\rightarrow\infty;$$ the right integral yields the same, except with $f(1)+\epsilon$. Then $$f(1)-\epsilon\leq\liminf_{n\rightarrow\infty}\ n\int_0^1f(x)x^n\,dx\leq\limsup_{n\rightarrow\infty}\ n\int_0^1 f(x)x^n\,dx\leq f(1)+\epsilon.$$ But, this holds for any $\epsilon>0$; so, letting $\epsilon\rightarrow0$, we get the desired result.
-
This is a great answer, Nicholas. Thanks for your contribution! (I would upvote it except that I've exhausted my daily upvote quota (sorry!). I'll return here in a couple of hours and upvote!) – Amitesh Datta Jul 29 '13 at 22:36
First, note that $$\int_0^1 x^n f(x)dx\to 0$$
since $f$ is bounded, so we can prove that $$(n+1)\int_0^1 x^n f(x)dx\to f(1)$$
But note $$\left( {n + 1} \right)\int_0^1 {x^n}f (1)dx = f(1).$$ so it suffices to consider the case $f(1)=0$.
THM Suppose that $f:[0,1]\to \Bbb R$ is continuous and $f(1)=0$. Then $$\mathop {\lim }\limits_{n \to \infty } \left( {n + 1} \right)\int_0^1 f (x){x^n}dx = 0$$
P Let $\epsilon >0$ be given. By continuity, there exists a neighborhood $[1-\delta,1]$ such that $$|f(x)|<\frac\varepsilon2$$ whenever $x\in[1-\delta,1]$. Write $$\left( {n + 1} \right)\left| {\int_0^1 f (x){x^n} dx} \right| \leqslant \left( {n + 1} \right)\left| {\int_0^{1 - \delta } f (x){x^n} dx} \right| + \left( {n + 1} \right)\left| {\int_{1 - \delta }^1 f (x){x^n} dx} \right|$$ so that $$\left( {n + 1} \right)\left| {\int_{1 - \delta }^1 {f\left( x \right){x^n} dx} } \right| \leqslant \left( {n + 1} \right)\frac{\varepsilon }{2}\int_{1 - \delta }^1 {{x^n} dx} \leqslant \left( {n + 1} \right)\frac{\varepsilon }{2}\int_0^1 {{x^n} dx} = \frac{\varepsilon }{2}$$
On the other hand, $|f|$ attains a maximum on $[0,1-\delta]$ and we have $$\left( {n + 1} \right)\left| {\int_0^{1 - \delta } {f\left( x \right){x^n}{\mkern 1mu} dx} } \right| \leqslant \left( {n + 1} \right)\int_0^{1 - \delta } {\left| {f\left( x \right)} \right|{x^n}{\mkern 1mu} dx} \leqslant M\left( {n + 1} \right)\int_0^{1 - \delta } {{x^n}{\mkern 1mu} dx} \leqslant M{\left( {1 - \delta } \right)^{n + 1}}$$
Since $1-\delta <1$, this goes to $0$; so the claim follows. Note we could have also used that $(n+1)x^n$ converges to zero uniformly on $[0,1-\delta]$ for any $0<\delta <1$ $\blacktriangle$
OBS Note how the proof works: $x^n$ crunches everything away from $1$, and continuity of $f$ plus $f(1)=0$ crunches everything near $1$.
-
Thanks @Peter for this excellent contribution! (In general, your fantastic contributions to this website have had an enormous positive impact! So, thanks for all of your contributions!) It's great to see that so many different approaches to the question are being posted. (I would certainly upvote this except that I've exhausted my daily quota of upvotes. I'm sorry but I'll definitely return here in a couple of hours to upvote!) – Amitesh Datta Jul 29 '13 at 22:44
@AmiteshDatta Thank you for those kind words! =) – Pedro Tamaroff Jul 29 '13 at 22:45
I did it :-) ${}$ – leo Jul 29 '13 at 22:46
@leo Ah? ${}{}{}{}{}$ – Pedro Tamaroff Jul 29 '13 at 22:46
I did upvote this – leo Jul 29 '13 at 23:07
First, note that $$(n+1)\color{#C00000}{\int_0^ax^n\,\mathrm{d}x}=a^{n+1}\tag{1}$$ and $$(n+1)\color{#00A000}{\int_0^1x^n\,\mathrm{d}x}=1\tag{2}$$ Pick an $\epsilon>0$. Since $f$ is continuous, there is a $\delta>0$ so that for all $x\in[1-\delta,1]$, we have $|f(x)-f(1)|\le\epsilon$. Since $f$ is continuous on $[0,1]$, there is an $M$ so that $|f(x)|\le M$ for $x\in[0,1]$. Furthermore, there is an $N$ so that for $n\ge N$, we have $2M(1-\delta)^{n+1}\le\epsilon$.
Thus, for $n\ge N$ \begin{align} &\left|f(1)-(n+1)\int_0^1x^nf(x)\,\mathrm{d}x\right|\\ &=(n+1)\left|\int_0^1x^n(f(1)-f(x))\,\mathrm{d}x\right|\\ &=(n+1)\left|\color{#C00000}{\int_0^{1-\delta}x^n(f(1)-f(x))\,\mathrm{d}x} +\color{#00A000}{\int_{1-\delta}^1x^n(f(1)-f(x))\,\mathrm{d}x}\right|\\ &\le\color{#C00000}{2M(1-\delta)^{n+1}}+\color{#00A000}{\epsilon}\\ &\le2\epsilon\tag{3} \end{align} Thus, $$\lim_{n\to\infty}(n+1)\int_0^1x^nf(x)\,\mathrm{d}x=f(1)\tag{4}$$ Since $\lim\limits_{n\to\infty}\dfrac n{n+1}=1$, we get $$\lim_{n\to\infty}n\int_0^1x^nf(x)\,\mathrm{d}x=f(1)\tag{5}$$
-
Nice, but it can be written a bit easier: $$\lim\limits_{n\to+\infty}n\int_0^1x^nf(x)dx =\lim\limits_{\delta\to 0^{+}}\lim\limits_{n\to+\infty}n\int_0^{1-\delta}x^nf(x)dx +\lim\limits_{\delta\to 0^{+}}\lim\limits_{n\to+\infty}n\int_{1-\delta}^1x^nf(x)dx$$ For any $\delta\in (0,1] \lim\limits_{n\to+\infty}n\int_0^{1-\delta}x^nf(x)dx=0$ while $$\inf\{f(x):x\in[1-\delta,1]\}\leqslant\lim\limits_{n\to+\infty}n\int_{1-\delta}^1x^nf(x)dx\leqslant\sup\{f(x):x\in[1-\delta,1]\}$$ so, when $\delta\to 0^+$ then $$\lim\limits_{\delta\to 0^+}\lim\limits_{n\to+\infty}n\int_{1-\delta}^1x^nf(x)dx=f(1)$$ – Darius Jun 23 '14 at 6:53
By changing the variable, let $x=t^{\frac{1}{n}}$ and we have $$n\int_0^1 x^n f(x)dx=\int_0^1 f\left(t^{\frac{1}{n}}\right)t^{\frac{1}{n}}dt,$$
and by dominated convergence theorem we conclude: $$\lim_n n\int_0^1 x^n f(x)dx=f(1).$$
-
Thought I'd write out the polynomial method @Kunnysan mentioned in the comments.
Consider an arbitrary polynomial $p(x) = a_0 + a_1x + \dots + a_kx^k$. We can calculate \begin{align} \lim_{n \rightarrow \infty} n \int_0^1 p(x)x^n \, dx &= \lim_{n \rightarrow \infty} n \int_0^1 a_0x^n + a_1x^{n+1} + \dots + a_kx^{n+k} \, dx \\ &= \lim_{n \rightarrow \infty} \left( \frac{n}{n+1} a_0 + \frac{n}{n+2} a_1 + \dots + \frac{n}{n+k} a_k \right) \\ &= a_0 + a_1 + \dots + a_k \\ &= p(1) \end{align}
By the Weierstrass approximation theorem there exists a sequence of polynomials $\{p_m\}$ such that $p_m(x) \rightarrow f(x)$ uniformly.
We then write \begin{align} \lim_{n \rightarrow \infty} n\int_0^1 f(x)x_n \, dx &= \lim_{n \rightarrow \infty} n \int_0^1 \lim_{m \rightarrow \infty} p_m(x)) x^n \, dx \\ &= \lim_{n\rightarrow n} n \int_0^1 \lim_{m \rightarrow \infty} p_m(x)x^n \, dx \\ &= \lim_{n \rightarrow \infty} \lim_{m \rightarrow \infty} \int_0^1 p_m(x)x^n \, dx \end{align} where the interchanging of the limit and the integral is valid because the sequence $p_m(x)x^n$ converges uniformly to $f(x)x^n$.
Since $p_m(x)$ is a polynomial, we can use our preliminary work to write $$\lim_{n \rightarrow \infty} \lim_{m \rightarrow \infty} \int_0^1 p_m(x)x^n \, dx = \lim_{n \rightarrow \infty} \lim_{m \rightarrow \infty} \left( \frac{n}{n+1} a_0 + \frac{n}{n+2} a_1 + \dots + \frac{n}{n+k} a_k \right)$$ where $a_i$ are the coefficients of the polynomial $p_m(x)$.
Lastly we interchange limits again, first taking the limit as $n \rightarrow \infty$:
$$\lim_{n \rightarrow \infty} \lim_{m \rightarrow \infty} \left( \frac{n}{n+1} a_0 + \frac{n}{n+2} a_1 + \dots + \frac{n}{n+k} a_k \right) = \lim_{m \rightarrow \infty} p_m(1) = f(1)$$
-
Hint: Try $f(x)=x^k$, then a polynomial, and then a general continuous function.
-
Since $f$ is continuous, it is bounded on the compact interval $[0,1]$, say $|f(x)|<M$ for all $x\in[0,1]$. Also, for any $\epsilon>0$, we find delta such that $|f(x)-f(1)|<\epsilon$ for all $x>1-\delta$. Then $$\int_0^1 x^nf(x)\,dx = \int_0^{1-\delta} x^n f(x)\,dx+\int_{1-\delta}^1 x^n f(1)\,dx+\int_{1-\delta}^1 x^n (f(x)-f(1))\,dx$$ The first summand can be estimated by $$\left|\int_0^{1-\delta} x^n f(x)\,dx\right|\le \int_0^{1-\delta}\left| x^n f(x)\right|\,dx\le M\int_0^{1-\delta}x^n\,dx=\frac1{n+1} M(1-\delta)^{n+1}.$$ The second is just $$\int_{1-\delta}^1 x^n f(1)\,dx=\frac{f(1)}{n+1}\cdot(1-(1-\delta)^{n+1}).$$ The last can be estimated as $$\left|\int_{1-\delta}^1 x^n (f(x)-f(1))\,dx\right|\le \int_{1-\delta}^1 \left|x^n (f(x)-f(1))\right|\,dx\\\le\epsilon\int_{1-\delta}^1x^n=\frac\epsilon{n+1}\cdot(1-(1-\delta)^{n+1}).$$ As $n\to\infty$, we have $(1-\delta)^{n+1}\to 0$. If you stick these results together, you'll find that $$\lim_{n\to\infty}n\int_0^1x^nf(x)\,dx=f(1).$$
- | 4,916 | 12,324 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 5, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.890625 | 4 | CC-MAIN-2016-30 | latest | en | 0.854444 |
https://www.aqua-calc.com/calculate/volume-to-weight/substance/nickel-blank-monoxide | 1,606,458,987,000,000,000 | text/html | crawl-data/CC-MAIN-2020-50/segments/1606141189141.23/warc/CC-MAIN-20201127044624-20201127074624-00576.warc.gz | 570,669,496 | 8,602 | # Weight of Nickel monoxide
## nickel monoxide: convert volume to weight
### Weight of 1 cubic centimeter of Nickel monoxide
carat 33.6 ounce 0.24 gram 6.72 pound 0.01 kilogram 0.01 tonne 6.72 × 10-6 milligram 6 720
#### How many moles in 1 cubic centimeter of Nickel monoxide?
There are 89.97 millimoles in 1 cubic centimeter of Nickel monoxide
### The entered volume of Nickel monoxide in various units of volume
centimeter³ 1 milliliter 1 foot³ 3.53 × 10-5 oil barrel 6.29 × 10-6 Imperial gallon 0 US cup 0 inch³ 0.06 US fluid ounce 0.03 liter 0 US gallon 0 meter³ 1 × 10-6 US pint 0 metric cup 0 US quart 0 metric tablespoon 0.07 US tablespoon 0.07 metric teaspoon 0.2 US teaspoon 0.2
• For instance, calculate how many ounces, pounds, milligrams, grams, kilograms or tonnes of a selected substance in a liter, gallon, fluid ounce, cubic centimeter or in a cubic inch. This page computes weight of the substance per given volume, and answers the question: How much the substance weighs per volume.
#### Foods, Nutrients and Calories
DELI-STYLE BEEF and PORK FRANKS, UPC: 030771095080 contain(s) 280 calories per 100 grams or ≈3.527 ounces [ price ]
#### Gravels, Substances and Oils
Gravel, Regular weighs 1 346 kg/m³ (84.02803 lb/ft³) with specific gravity of 1.346 relative to pure water. Calculate how much of this gravel is required to attain a specific depth in a cylindricalquarter cylindrical or in a rectangular shaped aquarium or pond [ weight to volume | volume to weight | price ]
Lutetium [Lu] weighs 9 840 kg/m³ (614.29113 lb/ft³) [ weight to volume | volume to weight | price | mole to volume and weight | mass and molar concentration | density ]
Volume to weightweight to volume and cost conversions for Refrigerant R-437A, liquid (R437A) with temperature in the range of -40°C (-40°F) to 60°C (140°F)
#### Weights and Measurements
A decipoise (dP) is a non-SI (non-System International) measurement unit of dynamic viscosity in the centimeter gram second (CGS) system of units
Electric car energy economy, i.e. energy or fuel economy of an electric vehicle is used to estimate mileage and electricity cost associated with and usage of the vehicle.
st/ml to short tn/ft³ conversion table, st/ml to short tn/ft³ unit converter or convert between all units of density measurement.
#### Calculators
Estimate daily calories using height, weight, age, gender, activity | 655 | 2,408 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.109375 | 3 | CC-MAIN-2020-50 | latest | en | 0.680774 |
http://www.carrawaydavie.com/liters-to-ounces-calculator/ | 1,571,193,066,000,000,000 | text/html | crawl-data/CC-MAIN-2019-43/segments/1570986661296.12/warc/CC-MAIN-20191016014439-20191016041939-00488.warc.gz | 239,483,864 | 8,748 | ## What is a liters to ounces calculator
What is a liters to ounces calculator as well as the US?
We will consider many other values needed in everyday life, such as liters to ounces calculator, how many ounces in a gallon, gallons to an unce and many others.
There are 1000 milliliters in a liter (1000 mL in 1 liter).
Liters to fluid flows (fl oz) volume units conversion factors are listed below. To find out how much the liter is in the x liters, multiply the liter by the conversion factor.
1 Liter = 33.814022 US Fluid Ounces
1 Liter = 35.195079 Imperial Fluid Ounces
So, liters to ounces calculator!
## What is a liquid ounce (fl oz) liters to ounces calculator
A liquid ounce is an imperial as well as US customary measurement system volume unit. 1 US fluid ounce equals to 29.5735 mL and 1 royal (UK) fluid ounce equals to 28.4131 mL. So, liters to ounces calculator?
There are 33.8140226 ounces in a liter because one liter (liter) is defined as the volume of 1 kilogram of water and there are 33.814 fluid ounces in the same volume of water.
There are 35.195079 imperial (UK) fl. ounces in a liter, because 1 fl. an ounce is 1.04084 imperial fl. ounce, and that makes 1.04084 * 33.814 (US fl oz in a liter)= 35.195079 imperial fl. oz in a liter. liters to ounces calculator
## We need to know liters to ounces calculator
1 gal is equal to 128 oz
Convert fluid formula to this formula:
pints = fluid ounces × 0.0625
1 Gallon (US, Fluid) = 128 Ounces (US, Fluid)
1 Gallon (UK, Fluid) = 160 Ounces (UK, Fluid)
liters to ounces calculator
In Summary :.
1 gallon = 4 quarts = 8 pints = 16 mugs = 128 fluid ounces.
liters to ounces calculator | 454 | 1,653 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.1875 | 3 | CC-MAIN-2019-43 | latest | en | 0.88734 |
https://www.teacherspayteachers.com/Product/Number-Bond-Worksheets-886141 | 1,524,475,849,000,000,000 | text/html | crawl-data/CC-MAIN-2018-17/segments/1524125945940.14/warc/CC-MAIN-20180423085920-20180423105920-00191.warc.gz | 885,472,667 | 17,241 | Total:
\$0.00
Number Bond Worksheets
Subject
Resource Type
Product Rating
File Type
Presentation (Powerpoint) File
Be sure that you have an application to open this file type before downloading and/or purchasing.
5 MB|50 pages
Share
Product Description
Number bonds are a crucial component in the Singapore math pedagogy. They provide a pictorial representation of the part-part-whole concept of numbers.
The worksheets in this product are aligned with the first grade CCSS 1.OA.8 and the second grade CCSS 2.OA.2. The activities will promote students’ understanding that there is a relationship between addition and subtraction and will enhance their fluency for addition and subtraction within 20.
This packet includes 50 worksheets that require students to work with number bonds. The worksheets offer a variety of task including:
Writing number sentences based on a number bond.
Determining the whole part of a number bond.
Determining a part of the whole in a number bond.
Writing and solving a real-world math problem based on a number bond.
Click on links below to view other number bond products.
Story Problems: Number Bond and Pictorial Worksheets - Addition to 10
Number Bonds: Addition and Subtraction Facts to 10
Number Bonds: Addition and Subtraction Facts to 20
Number Bonds: Addition and Subtraction Facts up to 99
Number Bonds and Fact Families: Addition and Subtraction Facts to 10
Number Bonds and Fact Families: Addition and Subtraction Facts to 20
Number Bond Posters and Flash Cards
Halloween Number Bond Worksheets
Thanksgiving Number Bond Worksheets
Christmas Number Bond Worksheets
Valentine Day Number Bond Worksheets
Total Pages
50 pages
N/A
Teaching Duration
N/A
Report this Resource
Teachers Pay Teachers is an online marketplace where teachers buy and sell original educational materials. | 382 | 1,839 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.65625 | 3 | CC-MAIN-2018-17 | latest | en | 0.870099 |
https://www.greaterwrong.com/tag/formal-proof | 1,708,898,109,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947474643.29/warc/CC-MAIN-20240225203035-20240225233035-00441.warc.gz | 812,530,957 | 9,404 | # Formal Proof
TagLast edit: 26 Sep 2021 22:04 UTC by
A Formal Proof is a finite sequence of steps from axiom(s) or previous derived proof(s) which strictly follow the allowed rules of inference of the mathematical system in which it exists. They are used to establish statements as true within a mathematical framework in a way which can be independently verified with extremely high certainty, with the most reliable flavor of proof being machine-checked proofs generated by proof assistants since they have even less room for human error.
# Proofs, Implications, and Models
30 Oct 2012 13:02 UTC
126 points
# [talk] Osbert Bastani—Interpretable Machine Learning via Program Synthesis—IPAM at UCLA
13 Jan 2023 1:38 UTC
9 points
# List of links: Formal Methods, Embedded Agency, 3d world models, and some tools
23 Jan 2023 18:21 UTC
16 points
# A List of things I might do with a Proof Oracle
5 Feb 2023 18:14 UTC
−14 points
# [Question] What Programming Language Characteristics Would Allow Provably Safe AI?
28 Aug 2019 10:46 UTC
4 points
# Eleuther releases Llemma: An Open Language Model For Mathematics
17 Oct 2023 20:03 UTC
22 points
(blog.eleuther.ai)
# Squeezing foundations research assistance out of formal logic narrow AI.
8 Mar 2023 9:38 UTC
16 points
# Infra-Domain Proofs 2
28 Mar 2021 9:15 UTC
13 points
# Allowing a formal proof system to self improve while avoiding Lobian obstacles.
23 Jan 2019 23:04 UTC
6 points
# [Math] Towards Proof Writing as a Skill In Itself
13 Jun 2018 4:39 UTC
25 points
# The value of learning mathematical proof
2 Jun 2015 3:15 UTC
7 points
# An Illustrated Proof of the No Free Lunch Theorem
8 Jun 2020 1:54 UTC
19 points
(mlu.red)
# An example of self-fulfilling spurious proofs in UDT
25 Mar 2012 11:47 UTC
33 points
# Weak HCH accesses EXP
22 Jul 2020 22:36 UTC
16 points
# Alignment proposals and complexity classes
16 Jul 2020 0:27 UTC
40 points
# LBIT Proofs 5: Propositions 29-38
16 Dec 2020 3:35 UTC
8 points
# LBIT Proofs 1: Propositions 1-9
16 Dec 2020 3:48 UTC
7 points
# LBIT Proofs 6: Propositions 39-47
16 Dec 2020 3:33 UTC
7 points
# LBIT Proofs 2: Propositions 10-18
16 Dec 2020 3:45 UTC
7 points
# Proofs Section 2.3 (Updates, Decision Theory)
27 Aug 2020 7:49 UTC
8 points
# Proofs Section 2.2 (Isomorphism to Expectations)
27 Aug 2020 7:52 UTC
8 points
# A proof of Löb’s theorem in Haskell
19 Sep 2014 13:01 UTC
52 points
# Counterfactual Induction (Algorithm Sketch, Fixpoint proof)
17 Dec 2019 5:04 UTC
5 points
# Social Choice Theory and Logical Handshakes
29 Dec 2023 3:49 UTC
14 points
# Formalized math: dream vs reality
9 Jul 2009 20:51 UTC
19 points
# Progress on automated mathematical theorem proving?
3 Jul 2013 18:40 UTC
26 points
# Proofs Section 1.1 (Initial results to LF-duality)
27 Aug 2020 7:59 UTC
8 points
# Proofs Section 1.2 (Mixtures, Updates, Pushforwards)
27 Aug 2020 7:57 UTC
8 points
# Proofs Section 2.1 (Theorem 1, Lemmas)
27 Aug 2020 7:54 UTC
8 points
# LBIT Proofs 4: Propositions 22-28
16 Dec 2020 3:38 UTC
7 points
# LBIT Proofs 7: Propositions 48-52
16 Dec 2020 3:31 UTC
7 points
# LBIT Proofs 8: Propositions 53-58
16 Dec 2020 3:29 UTC
7 points
# LBIT Proofs 3: Propositions 19-22
16 Dec 2020 3:40 UTC
8 points
# Question/Issue with the 5/10 Problem
29 Nov 2021 10:45 UTC
6 points
# Interview Daniel Murfet on Universal Phenomena in Learning Machines
6 Feb 2023 0:00 UTC
43 points
# Speedrunning 4 mistakes you make when your alignment strategy is based on formal proof
16 Feb 2023 1:13 UTC
62 points
# Logical inductor limits are dense under pointwise convergence
6 Oct 2016 8:07 UTC
5 points
# Planning to build a cryptographic box with perfect secrecy
31 Dec 2023 9:31 UTC
37 points
# Davidad’s Bold Plan for Alignment: An In-Depth Explanation
19 Apr 2023 16:09 UTC
153 points
# Roadmap for a collaborative prototype of an Open Agency Architecture
10 May 2023 17:41 UTC
30 points
# I bet \$500 on AI winning the IMO gold medal by 2026
11 May 2023 14:46 UTC
37 points | 1,555 | 4,221 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.578125 | 3 | CC-MAIN-2024-10 | latest | en | 0.782349 |
https://www.scribd.com/document/426204615/Lecture-Notes-1 | 1,580,273,063,000,000,000 | text/html | crawl-data/CC-MAIN-2020-05/segments/1579251788528.85/warc/CC-MAIN-20200129041149-20200129071149-00283.warc.gz | 1,063,960,743 | 74,057 | You are on page 1of 8
# CE-112
## Engineering Drawing for Civil
Engineers
Lecture Notes by:
Office: CE: B109
## Department of Civil Engineering, University of Engineering and
Technology, Peshawar
Course Outlines
Drawing Instruments and their Uses
Lines, Lettering and Dimensioning
Geometrical Construction
Engineering Curves, Parabola, Ellipse, Hyperbola
Projection of points, Lines, Plans and Solids
Sectional Views of Solids
Isometric Views
Building Drawings
1
Course Books
Engineering Drawing by N. D. Bhatt
Essential of Drafting by James D. Bethune
Programmed Technical Drawing by Cooper and Mullin
A first Year Engineering Drawing by A. C. Parkinson
## What is Technical Drawing?
Drawing is the universal language of graphics, having its
rules of grammar (ANSI, ISO), to communicate information
about the shape, size and features of a physical object
2
Course Objectives
After taking this course the student shall be able:
z Not only to express his ideas and design findings on drawing paper in
the universal language of drafting
z But also to understand drawings developed by another persons
Drawing Instruments
Drawing board
Drawing papers/sheets
Tee square and Set squares
Protractor
Compass and divider
Divider
Scales
French curves
Pencil, Eraser, Pen/pointer
3
Drawing Board
Available in different sizes depending on the size of drawing
paper.
Usually made from well seasoned wood with fairly smooth
surface.
At least one edge is straight called working edge.
Sizes of the board according to BS 308 are:
z Quarter Imperial : (16 x 12 in)
z Half Imperial : (23 x 16 in)
z Imperial : (32 x 23 in)
z Double Elephant : (42 x 32 in)
z Antiquarian : (54 x 32 in)
Drawing Papers/Sheets
ISO ANSI
A0 E
(840 x 1188) (34″ x 44″)
A1 D
(594 x 840) (22″ x 34″)
A2 C
(420 x 594) (17″ x 22″)
A3 B
(297 x 420) (11″ x 17″)
A4 (210 x A
297) (8.5″ x 11″)
4
Tee square
at right angle
The stock is made to slide along the working edge of board
and the blade moves on board.
The working edge of T-square is used to draw horizontal lines
and acts as a guide for set squares
Shall never be used to draw vertical lines directly
The working edge shall be checked for straightness
Set Squares
Triangular in shape and made usually with
plastic
Available in pair; 45o set square and 30-60o
set square
Used to draw lines at 30o, 45o, 60o and 90o
The may be combined to draw angles a 15o,
75o and 105o
They are also used to draw parallel lines
Shall be checked for accuracy of 90o
5
Protractor
Available in semi-circle shape
Used to draw and measures angles
To divide a circle
## Compass and Divider
Compass
z Used to draw circles and arcs of circles
z The needle side is kept about 1.0 mm longer than the lead
point
z The compass should kept slightly inclined in the direction
of rotation
z It is desirable to used slightly softer lead in compass than
the pencils used to draw straight lines
Divider
z Used to divide curves or straight lines into desired number
of equal parts
z To transfer dimension from one part of drawing to other
z To set-off given distances from scale to the drawing
6
French Curves
Used to draw curves which cannot be drawn
with compass
Available in various shapes
Pencils
Good quality pencils should be used to draw lines of uniform shade and
thickness
Available in various grades like (from soft to hard) 6B, 5B, 4B, 3B, 2B,
B, HB, F, H, 2H, 3H, to 9H
Softer pencils are used for sketching than those for line work
Chisel-point is used to geometry and machine drawings and Conical-point
is used for hand sketching and lettering
Beginning of drawing should be made with H or 2H pencils used very
lightly
Fair work may be done with harder pencils, e.g. 3H or harder
H and HB are used for letting an dimensioning | 1,039 | 3,837 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.96875 | 3 | CC-MAIN-2020-05 | latest | en | 0.864025 |
https://freud.readthedocs.io/en/stable/gettingstarted/examples/module_intros/order.Nematic.html | 1,686,189,545,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224654031.92/warc/CC-MAIN-20230608003500-20230608033500-00744.warc.gz | 293,772,370 | 12,459 | # freud.order.Nematic#
## Nematic Order Parameter#
The freud.order module provids the tools to calculate various order parameters that can be used to identify phase transitions. This notebook demonstrates the nematic order parameter, which can be used to identify systems with strong orientational ordering but no translational ordering. For this example, we’ll start with a set of random positions in a 3D system, each with a fixed, assigned orientation. Then, we will show how deviations from these orientations are exhibited in the order parameter.
[1]:
import freud
import matplotlib.pyplot as plt
import numpy as np
from mpl_toolkits.mplot3d import Axes3D
In order to work with orientations in freud, we need to do some math with quaternions. If you are unfamiliar with quaternions, you can read more about their definition and how they can be used to represent rotations. For the purpose of this tutorial, just consider them as 4D vectors, and know that the set of normalized (i.e. unit norm) 4D vectors can be used to represent rotations in 3D. In fact, there is a 1-1 mapping between normalize quaternions and 3x3 rotation matrices. Quaternions are more computationally convenient, however, because they only require storing 4 numbers rather than 9, and they can be much more easily chained together. For our purposes, you can largely ignore the contents of the next cell, other than to note that this is how we perform rotations of vectors using quaternions instead of matrices.
[2]:
# Random positions are fine for this. Order is measured
# in terms of similarity of orientations, not positions.
L = 10
N = 100
box, points = freud.data.make_random_system(L, N, seed=0)
orientations = np.array([[1, 0, 0, 0]] * N)
[3]:
# To show orientations, we use arrows rotated by the quaternions.
arrowheads = rowan.rotate(orientations, [1, 0, 0])
fig = plt.figure()
ax.quiver3D(
points[:, 0],
points[:, 1],
points[:, 2],
)
ax.set_title("Orientations", fontsize=16);
The nematic order parameter provides a measure of how much of the system is aligned with respect to some provided reference vector. As a result, we can now compute the order parameter for a few simple cases. Since our original system is oriented along the x-axis, we can immediately test for that, as well as orientation along any of the other coordinate axes.
[4]:
nop = freud.order.Nematic([1, 0, 0])
nop.compute(orientations)
print(f"The value of the order parameter is {nop.order}.")
The value of the order parameter is 1.0.
In general, the nematic order parameter is defined as the eigenvalue corresponding to the largest eigenvector of the nematic tensor, which is also computed by this class and provides an average over the orientations of all particles in the system. As a result, we can also look at the intermediate results of our calculation and see how they are related. To do so, let’s consider a more interesting system with random orientations.
[5]:
# We rotate identity quaternions slightly, in a random direction
np.random.seed(0)
interpolate_amount = 0.3
identity_quats = np.array([[1, 0, 0, 0]] * N)
orientations = rowan.interpolate.slerp(
identity_quats, rowan.random.rand(N), interpolate_amount
)
[6]:
# To show orientations, we use arrows rotated by the quaternions.
arrowheads = rowan.rotate(orientations, [1, 0, 0])
fig = plt.figure()
ax.quiver3D(
points[:, 0],
points[:, 1],
points[:, 2],
)
ax.set_title("Orientations", fontsize=16);
First, we see that for this nontrivial system the order parameter now depends on the choice of director.
[7]:
axes = [[1, 0, 0], [0, 1, 0], [0, 0, 1], [1, 1, 0], [1, 0, 1], [0, 1, 1], [1, 1, 1]]
for ax in axes:
nop = freud.order.Nematic(ax)
nop.compute(orientations)
print(f"For axis {ax}, the value of the order parameter is {nop.order:0.3f}.")
For axis [1, 0, 0], the value of the order parameter is 0.600.
For axis [0, 1, 0], the value of the order parameter is 0.586.
For axis [0, 0, 1], the value of the order parameter is 0.587.
For axis [1, 1, 0], the value of the order parameter is 0.591.
For axis [1, 0, 1], the value of the order parameter is 0.589.
For axis [0, 1, 1], the value of the order parameter is 0.573.
For axis [1, 1, 1], the value of the order parameter is 0.578.
Furthermore, increasing the amount of variance in the orientations depresses the value of the order parameter even further.
[8]:
interpolate_amount = 0.4
orientations = rowan.interpolate.slerp(
identity_quats, rowan.random.rand(N), interpolate_amount
)
arrowheads = rowan.rotate(orientations, [1, 0, 0])
fig = plt.figure()
ax.quiver3D(
points[:, 0],
points[:, 1],
points[:, 2],
)
ax.set_title("Orientations", fontsize=16)
axes = [[1, 0, 0], [0, 1, 0], [0, 0, 1], [1, 1, 0], [1, 0, 1], [0, 1, 1], [1, 1, 1]]
for ax in axes:
nop = freud.order.Nematic(ax)
nop.compute(orientations)
print(f"For axis {ax}, the value of the order parameter is {nop.order:0.3f}.")
For axis [1, 0, 0], the value of the order parameter is 0.451.
For axis [0, 1, 0], the value of the order parameter is 0.351.
For axis [0, 0, 1], the value of the order parameter is 0.342.
For axis [1, 1, 0], the value of the order parameter is 0.374.
For axis [1, 0, 1], the value of the order parameter is 0.391.
For axis [0, 1, 1], the value of the order parameter is 0.316.
For axis [1, 1, 1], the value of the order parameter is 0.344.
Finally, we can look at the per-particle quantities and build them up to get the actual value of the order parameter.
[9]:
# The per-particle values averaged give the nematic tensor
print(np.allclose(np.mean(nop.particle_tensor, axis=0), nop.nematic_tensor))
print("The nematic tensor:")
print(nop.nematic_tensor)
eig = np.linalg.eig(nop.nematic_tensor)
print("The eigenvalues of the nematic tensor:")
print(eig[0])
print("The eigenvectors of the nematic tensor:")
print(eig[1])
# The largest eigenvalue
print(
"The largest eigenvalue, {:0.3f}, is equal to the order parameter {:0.3f}.".format(
np.max(eig[0]), nop.order
)
)
True
The nematic tensor:
[[ 0.0115407 0.21569438 0.14729623]
[ 0.21569438 0.02040018 0.14309749]
[ 0.14729623 0.14309748 -0.03194092]]
The eigenvalues of the nematic tensor:
[ 0.34387365 -0.20013455 -0.14373913]
The eigenvectors of the nematic tensor:
[[ 0.6173224 0.73592573 -0.27807635]
[ 0.6237324 -0.6732561 -0.3970945 ]
[ 0.47944868 -0.07169023 0.87463677]]
The largest eigenvalue, 0.344, is equal to the order parameter 0.344. | 1,882 | 6,420 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.53125 | 4 | CC-MAIN-2023-23 | longest | en | 0.848915 |
https://docslib.org/doc/5736347/chapter-7-kinetic-energy-potential-energy-work-i | 1,708,933,907,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947474653.81/warc/CC-MAIN-20240226062606-20240226092606-00224.warc.gz | 213,491,852 | 14,119 | <<
Chapter 7 – Kinetic , energy, I. . II. Work. III. Work - Kinetic energy theorem. IV. Work done by a constant : Gravitational force V. Work done by a variable force. - force. - General: 1D, 3D, Work-Kinetic Energy Theorem VI. VII. Energy of configuration VIII. Work and potential energy IX. Conservative / Non-conservative X. Determining potential energy values: energy, elastic potential energy Energy: quantity associated with a state (or condition) of one or more objects. I. Kinetic energy 1 Energy associated with the state of of an object. K mv2 (7.1) 2 Units: 1 = 1J = 1 kgm2/s2 = N m II. Work Energy transferred “to” or “from” an object by means of a force acting on the object. To +W From -W
- Constant force: Fx max v2 v2 v2 v2 2a d a 0 0 x x 2d 1 1 1 F ma m(v2 v2 ) ma d m(v2 v2 ) x x 2 0 d x 2 0 1 Work done by the force = Energy m(v2 v2 ) K K F d W F d 2 0 f i x x transfer due to the force. - To calculate the work done on an object by a force during a , we use only the force component along the object’s displacement. The force component perpendicular to the displacement does zero work. F cos φ W Fxd F cos d F d (7.3) d
- Assumptions: 1) F=cte, 2) Object -like. 90 W 180 90 W Units: 1 Joule = 1J = 1 kgm2/s2 90 0 A force does +W when it has a vector component in the same direction as the displacement, and –W when it has a vector component in the opposite direction. W=0 when it has no such vector component.
Net work done by several forces = Sum of works done by individual forces.
Calculation: 1) Wnet= W1+W2+W3+…
2) Fnet Wnet=Fnet d II. Work-Kinetic Energy Theorem
K K f Ki W (7.4)
Change in the kinetic energy of the particle = Net work done on the particle
III. Work done by a constant force
- Gravitational force: W F d mgd cos (7.5)
Rising object: W= mgd cos180º = -mgd Fg transfers mgd energy from the object’s kinetic energy.
Falling object: W= mgd cos 0º = +mgd Fg transfers mgd energy to the object’s kinetic energy. - External applied force + Gravitational force:
K K f Ki Wa Wg (7.6)
Object stationary before and after the lift: Wa+Wg=0 The applied force transfers the same amount of energy to the object as the gravitational force transfers from the object.
IV. Work done by a variable force - Spring force: F kd (7.7)
Hooke’s law
k = spring constant measures spring’s stiffness. Units: N/m Hooke’s law
1D Fx kx
Work done by a spring force:
- Assumptions: • Spring is massless mspring << mblock • Ideal spring obeys Hooke’s law exactly. • Contact between the block and floor is frictionless. • Block is particle-like. Fx
- Calculation: xi ∆x x f x
1) The block displacement must be divided into Fj many segments of width, ∆x.
2) F(x) ≈ cte within each short ∆x segment. x f x f Ws Fjx x 0 Ws F dx (kx) dx xi xi
x f 1 2 x f 1 2 2 WS k x dx k x x k (x f xi ) x i i 2 2
1 2 1 2 W =0 If Block ends up at x =x . W k x k x s f i s 2 i 2 f
1 W k x2 if x 0 s 2 f i
Work done by an applied force + spring force: K K f Ki Wa Ws
Block stationary before and after the displacement: ∆K=0 Wa=-Ws The work done by the applied force displacing the block is the negative of the work done by the spring force. Work done by a general variable force:
1D-Analysis
Wj Fj,avg x
W Wj Fj,avg x better approximation more x, x 0
x f W F x W F(x)dx (7.10) lim j,avg x0 xi
Geometrically: Work is the between the curve F(x) and the x-axis. 3D-Analysis ˆ ˆ ˆ F Fxi Fy j Fzk ; Fx F(x), Fy F(y), Fz F(z)
dr dx iˆ dy ˆj dz kˆ r x y z f f f f dW F dr Fxdx Fydy Fzdz W dW Fxdx Fydy Fzdz
ri xi yi zi
Work-Kinetic Energy Theorem - Variable force
x f x f W F(x)dx ma dx xi xi dv dv ma dx m dx m v dx mvdv dt dx
dv dv dx dv v dt dx dt dx
v f v f 1 2 1 2 W mv dv m v dv mv f mvi K f Ki K 2 2 vi vi V. Power
Time at which the applied force does work.
- Average power: amount of work done in an amount of ∆t by a force. W P (7.12) avg t
- Instantaneous power: instantaneous time rate of doing work.
dW P (7.13) F dt φ x dW F cos dx dx P F cos Fv cos F v (7.14) dt dt dt
Units: 1Watt=1W=1J/s
1 kilowatt-hour = 1 kW·h = 3.60 x 106 J=3.6MJ 54. In the figure (a) below a 2N force is applied to a 4kg block at a downward θ as the block moves rightward through 1m across a frictionless floor. Find
an expression for the vf at the end of that if the block’s initial is: (a) 0 and (b) 1m/s to the right. (c) The situation in (b) is similar in that the block is initially moving at 1m/s to the right, but now the 2N force is directed downward to the left. Find an expression for the speed of the block at the end of the 1m distance. W F d (F cos )d N F 2 2 x N W K 0.5m(v f v0 ) Fx 2 (a) v0 0 K 0.5mv f mg mg F Fy y 2 (2N)cos 0.5(4kg)v f
v f cos m / s
2 2 2 (b) v0 1m / s K 0.5mv f 0.5(4kg)(1m / s) (c) v0 1m / s K 0.5mv f 2J 2 2 (2N)cos 0.5(4kg)v f 2J (2N)cos 0.5(4kg)v f 2J v 1 cos m / s f v f 1 cos m / s 18. In the figure below a horizontal force Fa of magnitude 20N is applied to a 3kg psychology book, as the book slides a distance of d=0.5m up a frictionless ramp.
(a) During the displacement, what is the net work done on the book by Fa,the gravitational force on the book and the normal force on the book? (b) If the book has zero kinetic energy at the start of the displacement, what is the speed at the end of the displacement? N d W 0 y Only F , F do work x gx ax N (a) W WFa WFg or Wnet Fnet d Fgx x x F mg gy Fnet Fax Fg x 20cos30 mg sin 30
Wnet (17.32N 14.7N)0.5m 1.31J
(b) K0 0 W K K f 2 W 1.31J 0.5mv f v f 0.93m / s 55. A 2kg lunchbox is sent over a frictionless surface, in the positive direction of an x axis along the surface. Beginning at t=0, a steady pushes on the lunchbox in the negative direction of x, Fig. below. Estimate the kinetic energy of the lunchbox at (a) t=1s, (b) t=5s. (c) How much work does the force from the wind do on the lunch box from t=1s to t=5s?
Motion concave downward parabola 1 x t(10 t) 10
dx 2 v 1 t dt 10 dv 2 a 0.2m / s2 dt 10
F cte ma (2kg)(0.2m / s2 ) 0.4N (b) t 5s v f 0 W F x (0.4N)(t 0.1t 2 ) K f 0J
(a) t 1s v f 0.8m / s (c) W K K f (5s) K f (1s) K 0.5(2kg)(0.8m / s)2 0.64J f W 0 0.64 0.64J 74. (a) Find the work done on the particle by the force represented in the graph below as the particle moves from x=1 to x=3m. (b) The curve is given by F=a/x2, with a=9Nm2. Calculate the work using integration
(a) W Area under curve W (11.5squares)(0.5m)(1N) 5.75J
3 3 9 1 1 (b) W dx 9 9( 1) 6J 2 1 x x1 3
73. An elevator has a of 4500kg and can carry a maximum load of 1800kg. If the cab is moving upward at full load at 3.8m/s, what power is required of the force moving the cab to maintain that speed?
F m 4500kg 1800kg 6300kg a total P F v (61.74kN)(3.8m / s) Fa mg Fnet 0 Fa Fg 0 P 234.61kW 2 Fa mg (6300kg)(9.8m / s ) 61.74kN mg A single force acts on a body that moves along an x-axis. The figure below shows the velocity component versus time for the body. For each of the intervals AB, BC, CD, and DE, give the sign (plus or minus) of the work done by the force, or state that the work is zero.
1 W K K K mv2 v2 v f 0 2 f 0
BC AB vB vA W 0 D A t BC vC vB W 0 E
CD vD vC W 0
DE vE 0, vD 0 W 0 50. A 250g block is dropped onto a relaxed vertical spring that has a spring constant of k=2.5N/cm. The block becomes attached to the spring and compresses the spring 12 cm before momentarily stopping. While the spring is being compressed, what work is done on the block by (a) the gravitational force on it and (b) the spring force? (c) What is the speed of the block just before it hits the spring? ( negligible) (d) If the speed at is doubled, what is the maximum compression of the spring?
2 (a) WFg Fg d mgd (0.25kg)(9.8m / s )(0.12m) 0.29J
1 2 2 (b) Ws kd 0.5(250N / m)(0.12m) 1.8J mg 2 F 2 2 s (c) Wnet K 0.5mv f 0.5mvi d mg 2 v f 0 K f 0 K Ki 0.5mvi WFg Ws 2 0.29J 1.8J 0.5(0.25kg)vi
vi 3.47m / s
(d) If vi ' 6.95m / s Maximum spring compressio n ?v f 0 2 2 Wnet mgd '0.5kd ' K 0.5mvi ' d' 0.23m 62. In the figure below, a cord runs around two massless, frictionless pulleys; a canister with mass m=20kg hangs from one pulley; and you exert a force F on the free end of the cord. (a) What must be the magnitude of F if you are to lift the canister at a constant speed? (b) To lift the canister by 2cm, how far must you pull the free end of the cord? During that lift, what is the work done on the canister by (c) your force (via the cord) and (d) the gravitational force on the canister?
(a) Pulley 1: v cte Fnet 0 2T mg 0 T 98N mg Hand cord : T F 0 F 98N P2 2 (b) To rise “m” 0.02m, two segments of the cord must T be shorten by that amount. Thus, the amount of the T T string pulled down at the left end is: 0.04m
P1 (c) WF F d (98N )(0.04m) 3.92J mg 2 (d) WFg mgd (0.02m)(20kg)(9.8m / s ) 3.92J
WF+WFg=0 There is no change in kinetic energy. I. Potential energy
Energy associated with the arrangement of a system of objects that exe forces on one another. Units: J Examples:
- Gravitational potential energy: associated with the state of separation between objects which can attract one another via the gravitational for - Elastic potential energy: associated with the state of compression/extension of an elastic object. II. Work and potential energy If tomato rises gravitational force transfers energy “from” tomato’s kinetic energy “to” the gravitational potential energy of the tomato- system.
If tomato falls down gravitational force transfers energy “from” the gravitational potential energy “to” the tomato’s kinetic energy. U W Also valid for elastic potential energy
Spring compression
Spring force does –W on block energy fs transfer from kinetic energy of the block to potential of the spring.
Spring extension
f Spring force does +W on block s energy transfer from potential energy of the spring to kinetic energy of the block.
General:
- System of two or more objects.
- A force acts between a particle in the system and the rest of the system. - When system configuration changes force does work on the
object (W1) transferring energy between KE of the object and some other form of energy of the system.
- When the configuration change is reversed force reverses the energy
transfer, doing W2.
III. Conservative / Nonconservative forces
- If W1=W2 always . Examples: Gravitational force and spring force associated potential .
- If W1≠W2 nonconservative force. Examples: force, frictional force KE transferred into . Non-reversible process.
- Thermal energy: Energy associated with the random movement of and molecules. This is not a potential energy. - Conservative force: The net work it does on a particle moving around every closed path, from an initial point and then back to that point is zero. - The net work it does on a particle moving between two points does not depend on the particle’s path.
Conservative force Wab,1= Wab,2 Proof:
Wab,1+ Wba,2=0 Wab,1= -Wba,2
Wab,2= - Wba,2 Wab,2= Wab,1 IV. Determining potential energy values
x W f F(x)dx U Force F is conservative xi
Gravitational potential energy: Change in the gravitational y y U f (mg)dy mgy f mg(y y ) mgy potential energy of the y yi f i i particle-Earth system. Ui 0, yi 0 U(y) mgy Reference configuration
The gravitational potential energy associated with particle-Earth system depends only on particle’s vertical “y” relative to the reference position y=0, not on the horizontal position.
x k x f 1 1 Elastic potential energy: U f (kx)dx x2 kx2 kx2 x xi f i i 2 2 2 Change in the elastic potential energy of the spring-block system.
Reference configuration when the spring is at its relaxed length and th
block is at xi=0. 1 U 0, x 0 U(x) kx2 i i 2 Remember! Potential energy is always associated with a system. V. Conservation of Mechanical energy of a system: Sum of its potential (U) and kinetic (K) energies. Emec=U+K Assumptions: - Only conservative forces cause energy transfer within the system. - The system is isolated from its No external force from an object outside the system causes energy changes inside the system. W K K U 0 (K2 K1) (U2 U1) 0 K2 U2 K1 U1 W U
∆Emec= ∆K+∆U=0
- In an where only conservative forces cause energy changes, the kinetic energy and potential energy can change, but their sum, the mechanical energy of the system cannot change.
- When the mechanical energy of a system is conserved, we can relate the sum of kinetic energy and potential energy at one instant to that at another instant without considering the intermediate motion and without finding the work done by the forces involved. y Emec= constant x
Emec K U 0
K2 U2 K1 U1
Potential energy curves
Finding the force analytically:
dU(x) U (x) W F(x)x F(x) (1D motion) dx
- The force is the negative of the of the curve U(x) versus x.
- The particle’s kinetic energy is: K(x) = Emec –U(x) Turning point: a point x at which the particle reverses its motion (K=0).
K always ≥0 (K=0.5mv2 ≥0)
Examples:
x= x1 Emec= 5J=5J+K K=0
x5J+K K<0 impossible
Equilibrium points: where the slope of the U(x) curve is zero F(x)=0 ∆U = -F(x) dx ∆U/dx = -F(x) ∆U(x)/dx = -F(x) Slope
Equilibrium points Emec,1
Emec,2
Emec,3
Example: x ≥ x5 Emec,1= 4J=4J+K K=0 and also F=0 x5 neutral equilibrium
x2>x>x1, x5>x>x4 Emec,2= 3J= 3J+K K=0 Turning points
x3 K=0, F=0 particle stationary Unstable equilibrium
x4 Emec,3=1J=1J+K K=0, F=0, it cannot move to x>x4 or x
W=-∆U
- The zero is arbitrary Only potential energy differences have physical meaning.
- The potential energy is a scalar function of the position.
- The force (1D) is given by: F = -dU/dx P1. The force between two atoms in a can be represented by the following potential energy function:
12 6 a a where U and a are constants. U (x) U0 2 0 x x
11 5 dU (x) a a a a i) Calculate the force Fx F(x) U 0 12 2 2 2 6 dx x x x x 13 7 12 13 6 7 12U 0 a a U 0 12a x 12a x a x x ii) Minimum value of U(x).
13 7 dU (x) 12U 0 a a U (x)min if F(x) 0 0 dx a x x
x a U (a) U 0 1 2 U 0
U0 is approx. the energy necessary to dissociate the two atoms. | 6,581 | 15,132 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.1875 | 4 | CC-MAIN-2024-10 | latest | en | 0.787133 |
http://nrich.maths.org/public/leg.php?code=71&cl=3&cldcmpid=543 | 1,506,443,601,000,000,000 | text/html | crawl-data/CC-MAIN-2017-39/segments/1505818696653.69/warc/CC-MAIN-20170926160416-20170926180416-00126.warc.gz | 242,484,001 | 10,149 | # Search by Topic
#### Resources tagged with Mathematical reasoning & proof similar to System Speak:
Filter by: Content type:
Stage:
Challenge level:
### There are 176 results
Broad Topics > Using, Applying and Reasoning about Mathematics > Mathematical reasoning & proof
### Janine's Conjecture
##### Stage: 4 Challenge Level:
Janine noticed, while studying some cube numbers, that if you take three consecutive whole numbers and multiply them together and then add the middle number of the three, you get the middle number. . . .
### Leonardo's Problem
##### Stage: 4 and 5 Challenge Level:
A, B & C own a half, a third and a sixth of a coin collection. Each grab some coins, return some, then share equally what they had put back, finishing with their own share. How rich are they?
### Multiplication Square
##### Stage: 4 Challenge Level:
Pick a square within a multiplication square and add the numbers on each diagonal. What do you notice?
### Unit Interval
##### Stage: 4 and 5 Challenge Level:
Take any two numbers between 0 and 1. Prove that the sum of the numbers is always less than one plus their product?
### Common Divisor
##### Stage: 4 Challenge Level:
Find the largest integer which divides every member of the following sequence: 1^5-1, 2^5-2, 3^5-3, ... n^5-n.
### Square Mean
##### Stage: 4 Challenge Level:
Is the mean of the squares of two numbers greater than, or less than, the square of their means?
### Zig Zag
##### Stage: 4 Challenge Level:
Four identical right angled triangles are drawn on the sides of a square. Two face out, two face in. Why do the four vertices marked with dots lie on one line?
### Pareq Exists
##### Stage: 4 Challenge Level:
Prove that, given any three parallel lines, an equilateral triangle always exists with one vertex on each of the three lines.
##### Stage: 4 Challenge Level:
Four jewellers share their stock. Can you work out the relative values of their gems?
### Never Prime
##### Stage: 4 Challenge Level:
If a two digit number has its digits reversed and the smaller of the two numbers is subtracted from the larger, prove the difference can never be prime.
### Lens Angle
##### Stage: 4 Challenge Level:
Find the missing angle between the two secants to the circle when the two angles at the centre subtended by the arcs created by the intersections of the secants and the circle are 50 and 120 degrees.
### Number Rules - OK
##### Stage: 4 Challenge Level:
Can you convince me of each of the following: If a square number is multiplied by a square number the product is ALWAYS a square number...
### Magic Squares II
##### Stage: 4 and 5
An article which gives an account of some properties of magic squares.
### To Prove or Not to Prove
##### Stage: 4 and 5
A serious but easily readable discussion of proof in mathematics with some amusing stories and some interesting examples.
### Proof Sorter - Quadratic Equation
##### Stage: 4 and 5 Challenge Level:
This is an interactivity in which you have to sort the steps in the completion of the square into the correct order to prove the formula for the solutions of quadratic equations.
### Mouhefanggai
##### Stage: 4
Imagine two identical cylindrical pipes meeting at right angles and think about the shape of the space which belongs to both pipes. Early Chinese mathematicians call this shape the mouhefanggai.
### AMGM
##### Stage: 4 Challenge Level:
Can you use the diagram to prove the AM-GM inequality?
### Mediant
##### Stage: 4 Challenge Level:
If you take two tests and get a marks out of a maximum b in the first and c marks out of d in the second, does the mediant (a+c)/(b+d)lie between the results for the two tests separately.
### Composite Notions
##### Stage: 4 Challenge Level:
A composite number is one that is neither prime nor 1. Show that 10201 is composite in any base.
### Whole Number Dynamics III
##### Stage: 4 and 5
In this third of five articles we prove that whatever whole number we start with for the Happy Number sequence we will always end up with some set of numbers being repeated over and over again.
### Diophantine N-tuples
##### Stage: 4 Challenge Level:
Can you explain why a sequence of operations always gives you perfect squares?
### Towering Trapeziums
##### Stage: 4 Challenge Level:
Can you find the areas of the trapezia in this sequence?
### Pythagoras Proofs
##### Stage: 4 Challenge Level:
Can you make sense of these three proofs of Pythagoras' Theorem?
### Geometric Parabola
##### Stage: 4 Challenge Level:
Explore what happens when you draw graphs of quadratic equations with coefficients based on a geometric sequence.
### L-triominoes
##### Stage: 4 Challenge Level:
L triominoes can fit together to make larger versions of themselves. Is every size possible to make in this way?
### Advent Calendar 2011 - Secondary
##### Stage: 3, 4 and 5 Challenge Level:
Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.
### A Long Time at the Till
##### Stage: 4 and 5 Challenge Level:
Try to solve this very difficult problem and then study our two suggested solutions. How would you use your knowledge to try to solve variants on the original problem?
### Always Perfect
##### Stage: 4 Challenge Level:
Show that if you add 1 to the product of four consecutive numbers the answer is ALWAYS a perfect square.
### Iffy Logic
##### Stage: 4 and 5 Challenge Level:
Can you rearrange the cards to make a series of correct mathematical statements?
### Perfectly Square
##### Stage: 4 Challenge Level:
The sums of the squares of three related numbers is also a perfect square - can you explain why?
### Find the Fake
##### Stage: 4 Challenge Level:
There are 12 identical looking coins, one of which is a fake. The counterfeit coin is of a different weight to the rest. What is the minimum number of weighings needed to locate the fake coin?
### Some Circuits in Graph or Network Theory
##### Stage: 4 and 5
Eulerian and Hamiltonian circuits are defined with some simple examples and a couple of puzzles to illustrate Hamiltonian circuits.
### Whole Number Dynamics II
##### Stage: 4 and 5
This article extends the discussions in "Whole number dynamics I". Continuing the proof that, for all starting points, the Happy Number sequence goes into a loop or homes in on a fixed point.
### The Great Weights Puzzle
##### Stage: 4 Challenge Level:
You have twelve weights, one of which is different from the rest. Using just 3 weighings, can you identify which weight is the odd one out, and whether it is heavier or lighter than the rest?
### Postage
##### Stage: 4 Challenge Level:
The country Sixtania prints postage stamps with only three values 6 lucres, 10 lucres and 15 lucres (where the currency is in lucres).Which values cannot be made up with combinations of these postage. . . .
### Long Short
##### Stage: 4 Challenge Level:
What can you say about the lengths of the sides of a quadrilateral whose vertices are on a unit circle?
### Sixational
##### Stage: 4 and 5 Challenge Level:
The nth term of a sequence is given by the formula n^3 + 11n . Find the first four terms of the sequence given by this formula and the first term of the sequence which is bigger than one million. . . .
### A Biggy
##### Stage: 4 Challenge Level:
Find the smallest positive integer N such that N/2 is a perfect cube, N/3 is a perfect fifth power and N/5 is a perfect seventh power.
### Cosines Rule
##### Stage: 4 Challenge Level:
Three points A, B and C lie in this order on a line, and P is any point in the plane. Use the Cosine Rule to prove the following statement.
### Proof: A Brief Historical Survey
##### Stage: 4 and 5
If you think that mathematical proof is really clearcut and universal then you should read this article.
### Rotating Triangle
##### Stage: 3 and 4 Challenge Level:
What happens to the perimeter of triangle ABC as the two smaller circles change size and roll around inside the bigger circle?
### For What?
##### Stage: 4 Challenge Level:
Prove that if the integer n is divisible by 4 then it can be written as the difference of two squares.
### Picture Story
##### Stage: 4 Challenge Level:
Can you see how this picture illustrates the formula for the sum of the first six cube numbers?
### Natural Sum
##### Stage: 4 Challenge Level:
The picture illustrates the sum 1 + 2 + 3 + 4 = (4 x 5)/2. Prove the general formula for the sum of the first n natural numbers and the formula for the sum of the cubes of the first n natural. . . .
### DOTS Division
##### Stage: 4 Challenge Level:
Take any pair of two digit numbers x=ab and y=cd where, without loss of generality, ab > cd . Form two 4 digit numbers r=abcd and s=cdab and calculate: {r^2 - s^2} /{x^2 - y^2}.
### There's a Limit
##### Stage: 4 and 5 Challenge Level:
Explore the continued fraction: 2+3/(2+3/(2+3/2+...)) What do you notice when successive terms are taken? What happens to the terms if the fraction goes on indefinitely?
### Angle Trisection
##### Stage: 4 Challenge Level:
It is impossible to trisect an angle using only ruler and compasses but it can be done using a carpenter's square.
### Mod 3
##### Stage: 4 Challenge Level:
Prove that if a^2+b^2 is a multiple of 3 then both a and b are multiples of 3.
### The Triangle Game
##### Stage: 3 and 4 Challenge Level:
Can you discover whether this is a fair game?
### Sprouts Explained
##### Stage: 2, 3, 4 and 5
This article invites you to get familiar with a strategic game called "sprouts". The game is simple enough for younger children to understand, and has also provided experienced mathematicians with. . . . | 2,267 | 9,706 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.875 | 4 | CC-MAIN-2017-39 | latest | en | 0.87775 |
http://math.stackexchange.com/questions/482653/all-sufficiently-large-squares-represented-as-sum-of-two-semiprimes | 1,467,298,161,000,000,000 | text/html | crawl-data/CC-MAIN-2016-26/segments/1466783398869.97/warc/CC-MAIN-20160624154958-00164-ip-10-164-35-72.ec2.internal.warc.gz | 192,130,910 | 16,558 | # All Sufficiently Large Squares, Represented as Sum of Two Semiprimes
Define a semiprime to be the product of two (not necessarily distinct) primes, $p_iq_i$.
Conjecture: All squares $\ge 4^2$ are representable as the sum of two distinct semiprimes.
Case 1: Squares of the form $4n^2$, $n \ge 2$.
Suppose $4n^2=p_1q_1+p_2q_2$. Allowing $p_1=p_2=2$ simplifies the relation to $2n^2=\left( q_1+q_2 \right)$. The LHS of the equation is an even number, and the RHS is a sum of two primes, which is equivalent to a weaker version of the Goldbach conjecture.
Case 2: Squares of the form $\left( 2n+1\right)^2$, $n \ge2.$
This is related to a theorem proposed by Meng. Meng proved that every sufficiently large odd integer is representable as the sum of three semiprimes. I am however only interested in the case of odd squares, and whether or not two semiprimes will suffice.
My question is whether or not this conjecture can be proven without assuming Goldbach's conjecture. I have checked squares up to $1519^2 \approx 10^{6.3}$ without finding any counterexamples. I am going to run a few more tests, hopefully up to $10^{10}$. In the meantime, does anyone have any input?
-
I just discovered a stronger conjecture that every sufficiently large integer is the sum of two semiprimes. It is apparently suspected to be true. oeis.org/A072966 – Ryan Sep 3 '13 at 3:03
I can't help but see the irony in me mulling over this problem. (I'm completely unrelated to the Meng mentioned in Case 2, just for the record) – Dennis Meng Sep 5 '13 at 21:48 | 447 | 1,546 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.265625 | 3 | CC-MAIN-2016-26 | latest | en | 0.921603 |
https://www.physicsforums.com/threads/finding-an-initial-speed-projectile-motion.337079/ | 1,532,160,622,000,000,000 | text/html | crawl-data/CC-MAIN-2018-30/segments/1531676592420.72/warc/CC-MAIN-20180721071046-20180721091046-00197.warc.gz | 977,978,132 | 14,701 | # Homework Help: Finding an initial speed (projectile motion)
1. Sep 13, 2009
### lilmul123
1. The problem statement, all variables and given/known data
A rock is thrown from the top of a 20-m high building at an angle of 53 degrees above the horizontal. If the horizontal range of the throw is equal to the height of the building, with what speed was the rock thrown? How long is it in the air?
Xf = 20, Xi = 0, Vxi = ?, t = ?, Yf = 0, Yi = 20, Vyi = ?, a = -9.81
2. Relevant equations
Xf = Xi + Vxi*t
Yf = Yi + Vyi*t + .5(a)(t)^2
3. The attempt at a solution
So first, I tried to find the time. I did this by doing 20 = 0 + Xcos(35)*t where X is initial speed and t is time. I then set t = 20/Xcos(35). I then plugged t back into my Yf equation which gives me 0 = 20 + Xsin(35)*(20/Xcos(35)) - 4.905(20/Xcos(35))^2. Solving this for x gives me about 2.7 m/s which is not right. The answer, according to the answer book, is 11 m/s.
Can anyone tell me where I'm going wrong?
Last edited: Sep 13, 2009
2. Sep 13, 2009
### rl.bhat
0 = Xsin(35)*(20/Xcos(35)) - 4.905(20/Xcos(35))^2.
In this equation you have not submitted initial y.
3. Sep 13, 2009
### lilmul123
Oops, pardon my typo. I have done it including the Vi in the equation, and 2.7 m/s is what i get. I have changed it above.
4. Sep 13, 2009
### rl.bhat
The angle is 53 degrees, not 35 degrees.
The equation becomes
0 = 20 + 20*tan53 - 4.9**20^2/vx^2cos^53.
Now solve.
Last edited: Sep 13, 2009
5. Sep 13, 2009
### lilmul123
I changed 35 to 53, but it is still incorrect. Is it possible that I am just inputting the formula into my calculator wrong? Maybe this isn't even the way I'm supposed to be solving it? I can't seem to get to 11 m/s no matter how I try.
6. Sep 13, 2009
### rl.bhat
I have edited the above post. Now try. You will get the answer.
7. Sep 13, 2009
### lilmul123
That equation can't possibly be correct. You must mean:
0 = 20 + 20*tan(53)Vxi - 4.9*20^2/Vxi^2*cos(53)^2
Regardless, this is still incorrect. I must be doing this problem incorrectly. Do you have any suggestions of another method I might take?
Just for reference, the next part of the problem asks "how long is the rock in the air?" The correct answer in this case is 3.1s, but I do not get this either, obviously.
8. Sep 13, 2009
### rl.bhat
[0 = 20 + 20*tan(53)Vxi - 4.9*20^2/Vxi^2*cos(53)^2]
It is only 20*tan53. There is no vxi there.
9. Sep 13, 2009
### lilmul123
Thank you very much for your patience with me. I finally got the correct answer. It seems the problem was me with my calculator. Thanks again! | 853 | 2,591 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.796875 | 4 | CC-MAIN-2018-30 | latest | en | 0.938847 |
https://www.coursehero.com/file/6438962/tables/ | 1,529,449,188,000,000,000 | text/html | crawl-data/CC-MAIN-2018-26/segments/1529267863206.9/warc/CC-MAIN-20180619212507-20180619232507-00090.warc.gz | 786,716,208 | 71,942 | tables
# tables - 1 Introduction and General Comments This document...
This preview shows pages 1–2. Sign up to view the full content.
1 Introduction and General Comments This document is intended for students who have heard the general language of probability applied to experimental data analysis and are in need only of formalism and detail. Material presented is non-linear and early sections may require understanding basics of concepts from latter sections. 1.1 Sections still needed Discarding data Significant Digits Statistical Process Control (Control Charts, UCL, LCL, assignable causes, ) Statistical Design of Experiments 1.2 Critical Rules 1. Always look critically at your data. Statistics applied blindly will yield meaningless results. Most analysis requires random uncorrelated errors – and certainly experimental mistakes will skew any analysis. 2. Garbage in Garbage Out holds. The last nine checks I wrote (and yes I still consider Pluto a planet) correlate extremely well with the relative masses of the planets in sequence from Mercury to Pluto. But I doubt that has diddly squat to do with anything. 3. Statistics help good experiments yield meaningful answers. Can’t do anything to help a hopeless or sloppy experiment. 1.3 Significant figures When no uncertainty is given in a numerical result, there is nonetheless an implied uncertainty from how the number is written. 3 . 141592654 implies that the value is accurate to the ninth decimal place. Similarly, writing v = 3 . 2284728372 implies significance to the last presented decimal position (which is typically ludicrous in experimental measurements). From Bevington, the number of significant figures in a result without a specific uncertainty is 1. The leftmost nonzero digit is the most significant digit 2. If there is no decimal point, the rightmost nonzero digit is the least significant digit 3. If there is a decimal point, the rightmost digit is the most significant digit even if it is a zero 4. All digits between the least and most significant digits are counted as significant digits. In cases of ambiguity (with large integers), it is preferable to go to scientific notation to express the value. For example, 73100 implies only three significant digits, but 7 . 310 × 10 4 implies four significant digits. When quoting uncertainty, there should never be more than two significant digits in the uncertainty, and then only if the first digit is a 1 (or sometimes a 2). The least significant digit of the result should be the same as the least significant digit of the uncertainty. For a measurement of 1 . 979, with an uncertainty of 0 . 012, the result could be presented as 1 . 979 ± 0 . 012 or 1 . 98 ± 0 . 01. If the uncertainty were 0 . 035, then the value should be reported as 1 . 98 ± 0 . 03. For rounding, the rules are 1. Above 0.5 round up, and below 0.5 round down 2. If exactly 0.5, round toward an even number The second rule ensures averaging of rounding for a large number of values. Both 1 . 275 and 1 . 285 become 1 . 28 after rounding.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up to access the rest of the document.
{[ snackBarMessage ]}
### What students are saying
• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.
Kiran Temple University Fox School of Business ‘17, Course Hero Intern
• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.
Dana University of Pennsylvania ‘17, Course Hero Intern
• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.
Jill Tulane University ‘16, Course Hero Intern | 914 | 4,192 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.875 | 4 | CC-MAIN-2018-26 | latest | en | 0.862017 |
http://blog.sina.com.cn/s/blog_94b2f1e50102vvcf.html | 1,639,017,112,000,000,000 | text/html | crawl-data/CC-MAIN-2021-49/segments/1637964363641.20/warc/CC-MAIN-20211209000407-20211209030407-00601.warc.gz | 10,451,730 | 12,457 | # 加载中...
-引力场-与-空间场
---zgygyzg
• 博客等级：
• 博客积分：0
• 博客访问：98,907
• 关注人气：124
• 获赠金笔：0支
• 赠出金笔：0支
• 荣誉徽章：
## "Dark energy" discussion
(2015-02-27 13:47:13)
### 三维空间
"Dark energy" discussion
Mingkun Yang 1，Yanxue Wang 2，Zhaoguo Yang 3
Email:ygyzg@126.com
Abstract
We live in "space" is a "three-dimensional space": if subjected to gravitational influence from the "fourth dimension", but also can be the "fourth dimension", "closed", the formation of a "four-dimensional space": "Ball cylinder.""Dark energy" only "fourth dimension gravitational effects", not what we in the "three-dimensional sphere", you can "find" and "physical reality" - is "invisible."The universe is not "expansion", is a Substance（celestial） body in this "fixed space" ("three-dimensional spherical") within the "diffusion".
Keywords
space closure; three-dimensional spherical; Dark energy
1. "cosmic space"
We live in "space" is a "three-dimensional space": if subjected to gravitational influence from the "fourth dimension", but also can be the "fourth dimension", "closed", the formation of a "four-dimensional space": "Ball cylinder."
Therefore, we can consider all of the "space" is a "special" "cylindrical space": the "three-dimensional sphere" for the border, that is the point P0 "event horizon" and "Ball cylinder": "underside radius Rs, height 2πRs (π is pi, Rs is the "fourth dimension of the center of mass Schwarzschild radius) of the 'cylindrical space' ', however, only the ends of the" cylindrical space "is coincident. ［1］
Figure 1
Figure 2
2. "dark energy"
2.1. "no See" "dark energy"
"High-dimensional" can be "low-dimensional space "were "closed." However, the "low-dimensional space" for the "high-dimensional", can only feel "high-dimensional" and "influence" but can not "see" the "high dimension in the matter."
For example, people living in a "three-dimensional sphere" on it, as "high-dimensional" - "fourth dimension" of the "quality" of "closed" this "three-dimensional sphere", the "" all on "material three-dimensional sphere "have the" same direction at the same speed "- all in the same direction (along the" geodesic "), are" speed of light "movement, and therefore considered to be a" full of space, increase the speed of expansion of the universe, "the "energy form", and is "isotropic, density is very small, in addition to any of the known gravitational interactions (i.e. electromagnetic, strong, weak interaction) does not react with ordinary matter." However, we can not see in this "three-dimensional sphere," actually, touched, measured, "the fourth dimension in the matter": that of "dark energy"!
Therefore, said: "dark energy" only "fourth dimension gravitational effects", not what we in the "three-dimensional sphere", you can "find" and "physical reality" - is "invisible."
2.2. "Visible" "dark energy"
As the "energy sphere" or "sphere of energy," "speed of light substance" force for the formation of spherical or ball outside, with its focus on the center of the sphere that the force was "equivalent." Ie "energy sphere" or "energy sphere" interaction on the outside of the sphere or ball is a "whole" presentation - the equivalent of all concentrated in the center of the sphere (discussed in another paper - the author note). ［2］
Figure 3
If the above in the "fourth dimension" and "energy substances", all evenly distributed in the "three-sphere" - "three-dimensional", it then these "energy substances" on the "three-sphere" - "three-dimensional space" "The role of substance", with all the focus on the "fourth dimension" - P0 point "action" is "equivalent." Therefore, the "three-dimensional sphere" - the "three-dimensional space," "special" "speed of light substances", you can also have a "dark energy effect."
So, too, can be considered: the above in the "fourth dimension" and "energy substances", in fact, in the "three-sphere" - "three-dimensional", it can make all the "substance", "three-dimensional sphere" on have the "same direction at the same speed" - all in the same direction (along the "geodesic"), are "speed of light" campaign, is a "full of space, increase the speed of expansion of the universe" and "forms of energy" and is "isotropic density is very small, in addition to any of the known gravitational interactions (ie, electromagnetic, strong and weak interactions) does not react with ordinary matter." Thus, the "dark energy" as a "special" "speed of light material" in our "three-dimensional space", it can "exist."
3. Not "cosmic expansion", but "mass diffusion"
Where we are, "space" - "three-dimensional" - "three-dimensional sphere" to meet "the same point at the same time, in the same direction at the same speed" conditions, so the movement of celestial bodies in line between "Hubble's Law", resulting in "Hubble constant effect. "
However, this is only temporary. Because the universe is "limited unbounded" and "ball cylinder", when age of the universe, "beyond the 'three-dimensional sphere' of the 'Equator' ', it will become increasingly apparent:" blue shift. "
So instead of the Universe "expansion" or "shrink", but the Substance (celestial) in this "fixed space" ("Three-dimensional sphere") within the "proliferation" or "gathering."
Figure 4
It should be noted that, in this "diffusion" or "gathering" in the process, with the continuation of the time due to the "point of departure", "substance" of the "across" and "space", has been in "gradually expanding "- so this" ordinary matter across space "would" have been swell. "Also, due to the "velocity component of the same size," as time reference point P and the "pole" of the distance r increases, then the "Hubble constant" H0 = v / r will be "more small ", will be changed to" negative "-" blue shift. "
4. "Lorentz factor"
Because of the speed of light c is the maximum speed, and the "big bang" in a "substance" and "in the same direction at the same speed" and "velocity component" is the "speed of light", so "radial velocity" v1 should be a component of the speed of light c, and at the same time on the "horizontal" (and "as the" vertical) also has a "weight", and its size is v0 =√c2-v12. This may be Lorentz factor 1 /√1- (v1/c) 2 resulting "root causes."
Figure 5
References
［1］产生 “哈勃常数”的“空间条件”．（作者的另一篇文章）．
［2］“光子球面”对“引力”的“屏蔽效应” ．（作者的另一篇文章）．
0
• 评论加载中，请稍候...
发评论
以上网友发言只代表其个人观点，不代表新浪网的观点或立场。
新浪BLOG意见反馈留言板 电话：4000520066 提示音后按1键（按当地市话标准计费） 欢迎批评指正
新浪公司 版权所有 | 1,745 | 6,440 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.609375 | 3 | CC-MAIN-2021-49 | latest | en | 0.815334 |
https://calculator-online.net/time/days-to-minutes/ | 1,713,505,421,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296817289.27/warc/CC-MAIN-20240419043820-20240419073820-00128.warc.gz | 138,441,101 | 101,076 | Uh Oh! It seems you’re using an Ad blocker!
We always struggled to serve you with the best online calculations, thus, there's a humble request to either disable the AD blocker or go with premium plans to use the AD-Free version for calculators.
Or
# Convert days to minutes (d to min)
From:
day (d)
To:
minute
Get the Widget!
Add Day to Minute converter to your website to use this unit converter directly. Feel hassle-free to account this widget as it is 100% free.
Available on App
Try Unit Converter App for your Mobile to get the ease of converting thousands of units. It’s 100% free with ample of features!
Convert Day to Other Time Units
Want to perform day to minute (min) conversions instantly? No doubt, these units of time conversions made easy with the above converter. Online days to minutes converter helps to convert the number of days into the equivalent number of minutes (min).
Well, in the above converter you just have to enter the number of days that you wish to turn into the equivalent minutes – the tool shows you the real-time conversions.
## Some Basics:
Days and minutes (min) both are the time measurements that used for the short-term. Simply calendars divide the weeks into days and this is the specific way that how you calculate date and important occasions. Minutes are the parameters that are there when you need to tell time during the day, or simply set a time for meetings in the future.
In order to determine how many minutes are in a day (manually step-by-step), then simply use the below-mentioned formula for time measurements.
• 1 day (d) is equal to 1440 minutes (min)
• 1 minute (min) is equal to 0.0006944444444444445 day (d)
## Days to minutes Formula:
The formula for is:
minutes = days x 1,440
## How do you convert days to minutes (d to min)?
Convert with:
• Online day to minute converter
• Formula (the below example helps you)
### Example of conversions between days and minutes:
Problem: Convert 12 days into minutes?
Solution:
Step 1 (Formula):
• minutes = days x 1,440
Step 2 (Put the Values):
• minutes = 12 x 1,440
Step 3 (Result):
• 17280 minutes (min)
Means, 12 days (d) is equal to 17280 minutes (min) | 517 | 2,200 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.703125 | 4 | CC-MAIN-2024-18 | longest | en | 0.864915 |
https://motls.blogspot.com/2010/10/arrow-of-time-part-101010.html?m=1 | 1,638,098,724,000,000,000 | text/html | crawl-data/CC-MAIN-2021-49/segments/1637964358520.50/warc/CC-MAIN-20211128103924-20211128133924-00611.warc.gz | 409,849,719 | 18,195 | ## Friday, October 08, 2010
### Arrow of time, part 101010
The past and the future play a fundamentally asymmetric role in logic. After more than 100 years, some people are still not getting it.
A backward guy is living his ordinary everyantiday backward life. Things get dramatic when he starts to antidrink and antieat. Some people still don't believe me but the events above don't naturally occur in the real world.
They imagine that to exchange the past and the future is as easy as to rotate a picture by 180°. But it's not.
This 101010th part of the neverending story will try to shrink the argument as much as possible.
Any evolution whose probability we want to calculate may be written as
Forward = A evolves into B
where "A" means that the physical system is found in one of the microstates (precisely determined positions and/or velocities of elementary particles, or whatever else can be maximally determined) A_1 or A_2 or A_3 ... or A_{N_a} where N_a is the number of microstates that we summarize as A.
Similarly, "B" means that the physical system is in one of the microstates B_1 or B_2 or B_3 ... or B_{N_b} where N_b is the number of microstates that we summarize as B.
The probability of evolution is calculated as
P(Forward) = 1/N_a Sum [i=1...N_a, j=1...N_b]
P(A_i evolves to B_j)
Note that to get the total probability, we're simply summing over possible final states B_j because the probability that "B_3 or B_5" appears as the final state is simply the sum of the partial probabilities for B_3 and B_5.
However, we're averaging over the initial states A_i. We know that one of the microstates A_i was realized in the initial state but we don't know which one. The sum of these "prior" probabilities of A_1, A_2, etc. has to equal one. Therefore, each of them has to be given the prior probability 1/N_a only. (We assume all the microstates to be equally likely, an assumption that can be relaxed if you need it.) The probability of the evolution from A_i is proportional to the prior probabilities of A_i, so we had to divide by N_a because the priors contain 1/N_a.
Now, assume that the physical system is T-reversal symmetric. And we also want to calculate the probability of the reverse process,
Backward = B evolves into A.
More generally, we should consider states A* and B* whose "velocities" are reverted relatively to A, B which is appropriate when the sign of time is inverted.
But for the sake of simplicity, let's assume that the velocities of both signs are equally represented in the ensemble A as well as B, so that the ensembles satisfy A=A*, B=B*. It wouldn't be hard to generalize the calculation for general states A, B.
What is the probability of the backward process? Well, it's given by the same formula as the forward process but A is exchanged with B:
P(Backward) = 1/N_b Sum [i=1...N_a, j=1...N_b]
P(B_j evolves to A_i)
Note that the coefficient in front of the sum is 1/N_b in this case rather than 1/N_a. So are the probabilities of forward and backward evolutions equal? Even if the microscopic laws are T-reversal-symmetric i.e. P(B_j evolves to A_i) is the same as P(A_i evolves to B_j), it's still true that
P(Backward) / P(Forward) = N_a/N_b.
Note that they are not equal if the numbers N_a, N_b differ. When we use the language of thermodynamics and the ensembles A, B are large, the numbers N_a, N_b are given by the entropies of the states A, B called S_a, S_b:
N_a = exp(S_a / k), N_b = exp(S_b / k)
where k is Boltzmann's constant which means that
P(Backward) / P(Forward) = exp[(S_a-S_b) / k].
If the entropy of B, S_b, is greater by 10^{26}*k than the entropy of A, which is typically the case in a macroscopic process (which adds a bit of entropy to each atom, and recall how large Avogadro's number is), then the backward probability is smaller than the forward probability by a factor of exp(10^{26}): for all practical (and most impractical) purposes, it is zero.
Note that I don't mean just 10^{26}: I mean exp(10^{26}) which is approximately the same thing as 10^{10^{26}}. This number quantifies the error that the people who don't understand the difference between the past and future are making in every single calculation of probability. A huge error, indeed.
This is no philosophy and there is no controversy here; it is an unquestionable conclusion of basic mathematical logic. A large entropy only increases the probability of a process if it is the final state that has a large entropy; because of the 1/N_a factor, a large entropy of the initial state is not favored by Nature in any way.
At any rate, there is a fundamental asymmetry between the initial states and the final states in mathematical logic that governs all calculations of probabilities that we ever perform in science, and outside science. Some naive "visualizations" of the Universe may look past-future symmetric but the full-fledged reality including all the required structure, including mathematical logic, is surely not past-future symmetric.
This asymmetry has nothing whatsoever to do with any assumptions about cosmology. It is a property of each cubic Planck length of space at each individual Planck time. The calculations above are valid anywhere and everywhere, whether or not there were many Big Bangs, one Big Bang, or no Big Bang.
I am completely convinced that every college freshman or sophomore who has gotten a grade better than F from mechanics, statistical physics, and quantum mechanics should feel absolutely certain about the rudimentary calculations above because the logical considerations needed to derive the conclusions above are needed in every portion of science.
And that's the memo.
1. All true within the limits E.t uncertainty and any theories of the 2T variety I guess. Comments?
2. My only comment is that your sequence of 15 words or so is too short to contain any useful information or insight, but long enough so that it can be seen that your ideas have nothing to do with the topic of this article.
3. I heard it attributed to Feynman that "time is what goes on when nothing else does."
4. But how come we have entropy increasing in a closed universe with unitary evolution? Putting in another way, how come the second law came into being? Or should we take it for granted?
5. Dear Fabio,
yes, you should definitely take the second law for granted and it's true. However, it hasn't fell from the skies or a religious text. It can be easily and universally proven, and if you carefully read this very text of mine, you will see one proof. If you haven't gotten it, read it twice, five times, ten times, 50 times, until you get this simple point because it is both trivial and paramount.
It's being proved that the probability that A evolves into B is much less (exp(-S/k) times) less likely than the probability from B to A if the evolution would decrease entropy. Consequently, processes with macroscopically decreasing entropy are impossible in practice as their probability is astronomically lower than the probability of the proper processes that increase the entropy.
The second law doesn't contradict unitarity. The entropy is not an "actual" objective property of the single microstate state (one that evolves unitarily). It is the logarithm of the number of microstates that are macroscopically indinstinguishable (given a convention for "indistinguishable", but the details of such a convention only make a very small impact) from the given microstate. This number of macroscopically indistinguishable states is not preserved by unitary evolution. And indeed, it increases all the time (unless one is already at equilibrium where it is constant).
Best wishes
Lubos | 1,778 | 7,685 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 1, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.640625 | 4 | CC-MAIN-2021-49 | latest | en | 0.957526 |
https://depedtambayan.net/grade-5-mathematics-module-dividing-whole-numbers-with-quotients-in-decimal-form/ | 1,713,274,000,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296817095.3/warc/CC-MAIN-20240416124708-20240416154708-00784.warc.gz | 179,518,474 | 27,703 | # Grade 5 Mathematics Module: Dividing Whole Numbers with Quotients in Decimal Form
This Self-Learning Module (SLM) is prepared so that you, our dear learners, can continue your studies and learn while at home. Activities, questions, directions, exercises, and discussions are carefully stated for you to understand each lesson.
Each SLM is composed of different parts. Each part shall guide you step-by-step as you discover and understand the lesson prepared for you.
Pre-tests are provided to measure your prior knowledge on lessons in each SLM. This will tell you if you need to proceed on completing this module or if you need to ask your facilitator or your teacher’s assistance for better understanding of the lesson. At the end of each module, you need to answer the post-test to self-check your learning. Answer keys are provided for each activity and test. We trust that you will be honest in using these.
Please use this module with care. Do not put unnecessary marks on any part of this SLM. Use a separate sheet of paper in answering the exercises and tests. And read the instructions carefully before performing each task.
If you have any questions in using this SLM or any difficulty in answering the tasks in this module, do not hesitate to consult your teacher or facilitator.
Good day, mathletes!
This module was designed to help you gain understanding and test your ability in dividing whole numbers with quotients in decimal form. Learning to divide whole numbers with quotients in decimal form is just as important as
any other lessons you have already taken from the previous modules for these can be of use in our everyday life situations.
After going through this module, you are expected to divide whole numbers with quotients in decimal form.
## Grade 5 Mathematics Quarter 2 Self-Learning Module: Dividing Whole Numbers with Quotients in Decimal Form
Math5_q2_mod12_DividingWholeNumbersWithQuotientsInDecimalForm_v2
## Can't Find What You'RE Looking For?
We are here to help - please use the search box below. | 424 | 2,049 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.78125 | 4 | CC-MAIN-2024-18 | latest | en | 0.919802 |
https://myelectrical.com/notes/entryid/167/international-system-of-units-si-system | 1,585,674,736,000,000,000 | text/html | crawl-data/CC-MAIN-2020-16/segments/1585370502513.35/warc/CC-MAIN-20200331150854-20200331180854-00316.warc.gz | 616,887,597 | 19,405 | International System of Units (SI System)
By on
The International System of Units (abbreviated SI) is the world's most widely used system of units. The system consists of a set of units and prefixes.
Note: this SI system is being revised to define the unit of mass in terms of fundamental constants. In addition the definitions ampere and kelvin will revised.
Several countries have only partially adopted the SI System; the United States being notable in this regard. A full list of SI units, a conversion calculator and conversion tables are maintained at:
Base Units
There are seven base units, from which all other units are derived. Each base unit is dimensionally independent.
Name Symbol Quantity
meter m The metre is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second.
kilogram kg The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram.
second s The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom.
ampere A The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 m apart in vacuum, would produce between these conductors a force equal to 2 x 10–7 newton per metre of length.
kelvin K The kelvin, unit of thermodynamic temperature, is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water.
mole mol The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12. When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles.
candela cd The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 x 1012 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian.
Prefixes
Factor Name Symbol Factor Name Symbol
101 deca da 10-1 deci d
102 hecto h 10-2 centi c
103 kilo k 10-3 mili m
106 mega M 10-6 micro μ
109 giga G 10-9 nano n
1012 tera T 10-12 pico p
1015 peta P 10-15 femto f
1018 exa E 10-18 atto a
1021 zetta Z 10-21 zepto z
1024 yotta Y 10-24 yocto y
Derived Units
Mechanical Units
Symbol SI Unit Base Units
Acceleration a m s-2 m s-2
Angular Momentum L kg m² s-1 kg m² s-1
Area A, S
Density ρ kg m-3 kg m-3
Energy E J (Joule) m² kg s-2
Force F N (Newton) m kg s-2
Frequency v, f Hz (Hertz) s-1
Momentum p kg m s-1 kg m s-1
Moment of Inertia I, J kg m² kg m²
Pressure P Pa (Pascal) m-1 kg s-2
Power P W (Watt) m² kg s-3
Speed, linear u m s-1 m s-1
Stress p Pa m-1 kg s-2
Surface Tension λ N m-1 kg s-2
Torque T N m-1 kg s-2
Velocity u, v m s-1 m s-1
Viscosity: kinematic m2 s-1 m2 s-1
Viscosity: dynamic μ, v Pa s m-1 kg s-1
Work We J m² kg s-2
Electrical & Magnetic Units
Symbol SI Unit Base Units
Admittance Y S (Siemens) m-2 kg-1 s³ A²
Capacitance C F (Farad) m-2 kg-1 s4
Charge Q C (Coulomb) s A
Charge density, area ρ C m-3 m-3 s A
Conductance G S (Siemens) m-2 kg-1 s³ A²
Conductivity σ S m-1 m-3 kg-1 s³ A²
Current (base unit) I, I A (Ampere) A
Current density J A m-2 A m-2
Electric field strength E V m-1 m kg s-3 A-1
Electric flux ψ C (coulomb) s A
Electric flux density D C m-2 m-2 s A
Electromotive force (e.m.f.) E, e V m² kg s-3 A-1
Frequency F Hz (Hertz) s-1
Impedance Z Ω m² kg s-3 A-2
Inductance, mutual M H m² kg s-2 A-2
Inductance, self L H (Henry) m² kg s-2 A-2
Magnetic field strength H A m-1 A m-1
Magnetic flux Φ, φ Wb (Weber) m² kg s-2 A-1
Magnetic flux density B T (Tesla) kg s-2 A-1
Magnetic flux linkage ψ Wb m² kg s-2 A-1
Magnetomotive force F A (ampere) A
At (ampere-turns) A-turns
Permeability, absolute μ H m-1 m kg s-2 A-2
Permeability, free space μo H m-1 m kg s-2 A-2
Permeability, relative μr
Permittivity, absolute ε F m-1 m-3 kg-1 s4
Permittivity, free space εo F m-1 m-3 kg-1 s4
Permittivity, relative εr
Potential difference U, V V (Volt) m² kg s-3 A-1
Power, active P W(Watt) m² kg s-3
Power, apparent S VA m² kg s-3
Power, reactive Q var m² kg s-3
Reactance X Ω m² kg s-3 A-2
Reactive volt-ampere Q var
Reluctance S A Wb-1 m-2 kg-1 s² A²
Resistance R Ω (Ohm) m² kg s-3 A-2
Resistivity Ω.m m3 kg s-3 A-2
Susceptance B S (Siemens) m-2 kg-1 s³ A²
Volt-ampere VA V A
Voltage U, V V m² kg s-3 A-1
Wavelength λ m m
Heat Units
Symbol SI Unit Base Units
Critical pressure pc Pa (Pascal) m-1 kg s-2
Critical temperature Tc K K
Critical volume Vc
Cubic expansivity γ K-1 K-1
Heat capacity C J K-1 m² kg s-1 K-1
Linear expansivity α K-1 K-1
Molar heat capacity Cm J mol-1 K-1 m² kg s-2 mol-1 K-1
Quantity of heat Q J (Joule) m² kg s-2
Specific heat capacity cp, cv J kg-1 K-1 m² s-2 K-1
Specific latent heat l J kg-1 m2 s-2
Temperature t, θ, T K K
Thermal conductivity λ J m-1 s-1 K-1 m kg s-3 K-1
W m-1 K-1
Photometric Optical Units
Symbol SI Unit Base Units
Illuminance E lx (Lux) m-2 cd sr
Luminance L cd m-2 cd m-2
Luminous flux Φ, φ lm (Lumen) cd sr
Luminous efficacy lm W-1 cd sr m-2 kg-1
Acoustical Units
Symbol SI Unit Base Units
Frequency f Hz (Hertz) s-1
Intensity I W m-2 kg s-3
Power ratio dB
Reverberation time s s
Writing Style
symbols – roman upright type, lowercase, un-capitalised (unless derived from a proper name), no full stop, not pluralised
space – a space separates number and the symbol, i.e. 124 kg, 2500 A
derived – units derived are expressed with space, dot and/or solidus (/), i.e. N m, N·m, m/s, m s-1, m·s-1
More interesting Notes:
Steven has over twenty five years experience working on some of the largest construction projects. He has a deep technical understanding of electrical engineering and is keen to share this knowledge. About the author
myElectrical Engineering
Famous Scientists
Here’s list of some famous scientists. Deliberately short, with the aim to provide a quick memory jog or overview. If your looking for more detailed information...
Why use catalogues
I'm a fan of using manufacturers catalogues. There are two main reasons for this. Firstly, if your involved in the purchase of equipment, you will likely...
IEC 60287 Current Capacity of Cables - An Introduction
IEC 60287 "Calculation of the continuous current rating of cables (100% load factor)" is the International Standard which defines the procedures and equations...
Lighting - Lamps
Lamps are the essential part of any luminaire. These are the light generating components. Since the advent of electrical lighting in the middle of the...
Lighting Design - An Introduction
From the earliest times, humans have found ways to create light. Pre-historic peoples used natural materials (moss, grass, etc.) soaked in animal fat and...
Periodic Electrical Installation Inspection – How Often?
How often installations are inspected is up to the owner of the installation, provided such durations do not exceed any regulatory maximums in force. ...
ANSI (IEEE) Protective Device Numbering
The widely used United Sates standard ANSI/IEEE C37.2 'Electrical Power System Device Function Numbers, Acronyms, and Contact Designations' deals with...
Restricted Earth Fault Protection
The windings of many medium and small sized transformers are protected by restricted earth fault (REF) systems. The illustration shows the principal of...
Electromagnetic Fields - Exposure Limits
Exposure to time varying magnetic fields, from power frequencies to the gigahertz range can have harmful consequences. A lot of research has been conducted...
How to Write an Electrical Note
Electrical notes are a collaborative collection of electrical engineering information and educational material. Any registered user can add content. ...
Have some knowledge to share
If you have some expert knowledge or experience, why not consider sharing this with our community.
By writing an electrical note, you will be educating our users and at the same time promoting your expertise within the engineering community.
To get started and understand our policy, you can read our How to Write an Electrical Note | 2,424 | 8,259 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.734375 | 3 | CC-MAIN-2020-16 | longest | en | 0.890279 |
http://forums.cgsociety.org/showthread.php?s=b2903a68ba0d451544a35d4546e2f7f3&p=8341646 | 1,508,259,937,000,000,000 | text/html | crawl-data/CC-MAIN-2017-43/segments/1508187822145.14/warc/CC-MAIN-20171017163022-20171017183022-00219.warc.gz | 121,454,048 | 14,607 | # Geometrical calculations : points, lines, planes : intersections, distances, angles
Thread Tools Search this Thread Display Modes
11 November 2014 ricozone Veteran portfolio Eric Bellanger CG artist Nantes, France Hi Klvnk, very interesting functions. As i'm not familiar with geometry data structure, can you please give a usage example ? How to build a struct vertex for any given mesh ? I was thinking about that : ``````- sm = snapshotasmesh (Teapot()) - loop through each vert and get : p = meshop.getvert sm v n = getnormal sm v col = -- vertex color ? uvw1 = getTVert sm -- how to get tvert from current vert ? - build array of faces indices : fi = for f=1 to sm.numfaces collect ((meshop.getVertsUsingFace sm f) as array) - once i got my vertex array struct, i can call your functions : ComputeTangents myVertStruct fi`````` Sorry if i bother with noob question __________________ Rico) ===================== share quote
11 November 2014 Klvnk Expert portfolio Klunk United Kingdom yep that kind of thing will do it, I'll start a new thread with an example. Last edited by Klvnk : 11 November 2015 at 06:41 PM. share quote
11 November 2014 ricozone Veteran portfolio Eric Bellanger CG artist Nantes, France HTML Code: `yep that kind of thing will do it, I'll start a new thread with an example.` thanks ! http://forums.cgsociety.org/showthr...?f=98&t=1233324 __________________ Rico) ===================== share quote
09 September 2015 Klvnk Expert portfolio Klunk United Kingdom randomize a normal.... Last edited by Klvnk : 11 November 2015 at 06:43 PM. share quote
11 November 2015 Klvnk Expert portfolio Klunk United Kingdom simple but was quite tricky to find... pos is the position of the base of the cone and pnt is the position of the point on the cone, r & h are the radius and height respectively Last edited by Klvnk : 11 November 2015 at 06:43 PM. share quote
03 March 2016 dottob New Member portfolio dottob China So useful!Thanks guys! share quote
3 Weeks Ago duke Expert George Rolfe Newport, AU I apparently annoyed the wrong people on stackoverflow so perhaps i'll get more joy here. If I have a plane in the YZ plane and want to project it onto a sphere, what equation do I use for the X axis? share quote
Posting Rules You may not post new threads You may not post replies You may not post attachments You may not edit your posts vB code is On Smilies are On [IMG] code is On HTML code is Off CGSociety Society of Digital Artists www.cgsociety.org Powered by vBulletinCopyright ©2000 - 2006, Jelsoft Enterprises Ltd. | 640 | 2,568 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.75 | 3 | CC-MAIN-2017-43 | latest | en | 0.809956 |
http://www.markedbyteachers.com/as-and-a-level/psychology/estimation-improves-with-age.html | 1,516,317,591,000,000,000 | text/html | crawl-data/CC-MAIN-2018-05/segments/1516084887660.30/warc/CC-MAIN-20180118230513-20180119010513-00499.warc.gz | 498,805,663 | 18,742 | • Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month
Page
1. 1
1
2. 2
2
3. 3
3
4. 4
4
5. 5
5
6. 6
6
7. 7
7
8. 8
8
# "Estimation improves with age".
Extracts from this document...
Introduction
Statistics Coursework For this piece of statistical coursework I have been asked to analyse date using a range of statistical distributors and measures. My hypothesis for the investigation is related to estimation, the hypothesis being: "Estimation improves with age" I have been given a set of a line and angle measuring and 50o. Using the data given to me for this investigation I am going to find the mode, mean and median from the inter-quartile range. I must do this for each specific group, both child and adult. I will do this because I will be able to compare all of my results. I will then see if those who are older have better results than children to check to see if my hypothesis is correct. I believe we were given the sizes of the angle and length for these reasons. Small lengths are within our grasp as estimations. Smaller lines are simpler for us to see and predict more accurate measurements. As the angle is between 0o and 90o meaning we have estimation is our minds as we have to angles to base our prediction between. To test this hypothesis I am going to use a range of statistical measures in relation to the provided data. I will calculate the averages and the range to see if they support this claim or not. I will then display the data in different ways to see what other information I can gain from it. Length of Line (mm) Angle Size (degrees) Children Adults Children Adults Total Freq 40 30 40 30 Mean (x) 50.6mm 49.2mm 49.3 49.1 % Error 5 2.7 5 1.8 Mode 50mm 50mm 45 / 52 46 % Error 4 4 10 8 Median 50mm 51mm 49.5 49 % Error 4 6.25 1 2 Range 40 23 33 26 But this data is limited in its use. It tells us very little in regards to our hypothesis, as the results are very similar. ...read more.
Middle
Conclusion
Also I will produce cumulative frequency curve diagrams to see the percentage error plotted on the graph for the angle and line for both adults and children. Doing this allows means to visually see where the relative averages are. Also as I am not plotting the actual results but the percentage error it is much easier to see the pattern of the estimation. Graph 1: This graph shows how the majority of the child's estimation of lines is similar to that of the angles, meaning that they are quite consistent in their estimations. But this is a crude method of finding this out. To obtain better, more accurate results I will need to use Spearmen's rank. Graph 2: This graph shows how the majority of the adult's estimation of lines is similar to that of the angles, meaning that they are quite consistent in their estimations. There are more consistent than the Childs estimations shown in graph 1.But again, this is a crude method of finding this out. To obtain better, more accurate results I will need to use Spearmen's rank. Graph 3: This shows the results of Spearmen's rank, the much more accurate method of finding the correlation in a graph. As you can see the overall result is -0.13. This shows that there is slight negative correlation Graph 4-7: These are the cumulative frequency curves for both adults and children's line and angle estimations. The lines drawn on indicate the IQR boundaries. On these we can the pattern of the estimations. On these it shows a massive increase of estimations within the IQR for the adults, much more than the children. This shows that more adults were estimating with the correct boundaries, showing their estimating we better, this evidence supports my hypothesis. Graph 8: This shows the method of obtaining the cumulative frequency curve, using the results. From this graphs I have gained more evidence but still not enough to gain a conclusion, therefore I will conduct an investigation of my own, with the school. Adam Baldwin ...read more.
The above preview is unformatted text
This student written piece of work is one of many that can be found in our AS and A Level Developmental Psychology section.
## Found what you're looking for?
• Start learning 29% faster today
• 150,000+ documents available
• Just £6.99 a month
Not the one? Search for your essay title...
• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month
# Related AS and A Level Developmental Psychology essays
1. ## This curriculum plan is to be based on children aged between nought to two ...
the aspects of the game easily and seemed to understand what to do straight away sometimes I had to explain twice the names of the baby animals as they are different to the mothers. I think that being a one to one activity was suitable as I was able to speak more freely to CT and encourage her more.
2. ## What do we mean by resilience? How
By facilitating integrated service responses, such as improved national and local case management arrangements, fewer children and their families will face acute problems. Proposals of increasing the range of recreational and developmental opportunities available in a given community also form an important element of a holistic response to the needs of children, young people and families in general.
1. ## I have decided to do my portfolio on Beaufort Park School, for several reasons. ...
For example while I was at the school for their literacy lesson the children had to find words that ended in double L, or another time they had to find words with the letter O in the middle e.g. hop.
2. ## Evacuation Coursework.
The reaction between the parents, foster parents and the children were very different. For some children it was the time of their lives being evacuated, however, for others it was an absolute nightmare. Therefore there were positive and negative reactions.
• Over 160,000 pieces
of student written work
• Annotated by
experienced teachers
• Ideas and feedback to | 1,379 | 6,049 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.84375 | 4 | CC-MAIN-2018-05 | latest | en | 0.918667 |
https://wesign4u.com/computer-intel-rqnjtxn/b9165a-scatter-plot-worksheet-for-middle-school | 1,624,047,008,000,000,000 | text/html | crawl-data/CC-MAIN-2021-25/segments/1623487641593.43/warc/CC-MAIN-20210618200114-20210618230114-00488.warc.gz | 539,021,700 | 10,971 | Draw a line of best fit for the data. Dichotomous Key Worksheet Middle School Best Of Dichotomous Key Activity Taxonomy Classification one of Chessmuseum Template Library - free resume template for word education on a resume example ideas, to explore this Dichotomous Key Worksheet Middle School Best Of Dichotomous Key Activity Taxonomy Classification idea you can browse by and . x�c` endstream endobj 24 0 obj << /Subtype /Type1C /Filter /FlateDecode /Length 4364 >> stream Scatter plot middle school. The activity on the following page is intended to be an introduction to a chapter on scatterplots, correlation, and regression. Oren plants a new vegetable garden each year for 14 years. � � �5 ��P Ζ �� œ ܙ � � ��A ��R ۘ ٘ Ȕ � ��, ��K ��T ܙ ؙ ޙ Student 1:1 Portal; School Organizations & Extracurricular Activities; Student Council; Anti-Bullying at Exeter (ABEx) Parent information for 1:1 Program If the trend continued, about how many CDs were sold in 2006? Modifications are considered for both struggling learners and high flyers. 2 Favorites 8th Grade Pre-Algebra 8th Grade Pre-Algebra 7th Grade Math Scatter Plots and Linear Regression Integers and Order of Operations Create a scatter plot with the data. Printable Worksheets; ... A homework survey was conducted of Pinewood Middle School students. This is the data you will use to create a scatter plot displaying the work life earnings for womenmen by. 4 B. The size of the bag of popcorn and the price of the popcorn: _____ 3. Shake it up with scatterplots printable. After giving the introduction guided notes (left-side), the first day was focused on reading and interpreting scatter plots and correlation. 3. Scatter Plot Worksheet This resource allows students to explore scatterplots with a two page worksheet. MUSIC The scatter plot shows the number of CDs (in millions) that were sold from 1999 to 2005. Nine questions ask students to identify the type of correlation (positive, negative or no correlation) that exists between two varia It deals with tread on tires, how much a car is worth over time, and even gas consumption. Scatter Plot For Middle School Worksheets - there are 8 printable worksheets for this topic. ... Pin On Cool School . Best 25 Scatter plot worksheet ideas on Pinterest from Scatter Plots Worksheets, source:pinterest.com. Scatter Plot Worksheets For Middle School PDF - Letter T Worksheets For Kindergarten. How Much Will Movie Tickets Cost in the Future? 1. Suggested reading level for this text: Grade 4-8. A. Scatter Plot Middle School - Displaying top 8 worksheets found for this concept.. Try it and I’m sure you’ll do well tomorrow. Haly king goshen middle school goshen in 6847 views. If the x-values increase as the y-values increase, the scatter plot represents a positive correlation. He used to face problems in topics such as scatter plot worksheet middle school and least common measure but all his questions were answered by this one simple to use tool known as Algebrator. Using his scatter plot (or his data) students analyze rates of change, make predictions… Read more → Sample Scatter Plot 25 ro 20 X-axis Tax payments (thousands) O SCATTER PLOT EXAMPLES Positive Correlat.on O Negative Correlation No Corre ation 20 5 10 15 20 25 Years of Experience 30 35 Height -0.172 Speed (km/h) X-Axis 0 500 Dfiver Age (years) Time to Run 100m Amount ot Time Spent Training 40 30 20 < 10 0,6515 Solar & wind weekly generation \$40 Scatter plot middle school. Related Posts. 2. • A line graph represents change over time, and a scatter plot shows the relationship between two variables. Free Math Worksheets for Sixth, Seventh, Eighth, and Ninth Grade (w/ Answer Keys) The following printable math worksheets for 6th, 7th, 8th, and 9th grade include a complete answer key.. Click any of the links below to download your worksheet as an easy-to-print PDF file. Scatter Plots Graphs - Displaying top 8 worksheets found for this concept.. Showing top 8 worksheets in the category - Scatter Plot Middle School. Showing top 8 worksheets in the category scatter plot middle school. They’re in groups of 4 similar questions or tasks. Scatter Plot Worksheets For Middle School Free Worksheets Library from Scatter Plots Worksheets, source:comprar-en-internet.net. ... Scatter Plot Practice Worksheets Full Size Of Plot Worksheet With ... #212615. math-division-worksheets-long-division; map-of-europe-with-names; Drawing the Line of Best Fit. This online game gives them 10 questions about correlation on a scatter plot graph. worksheet: Inference Worksheets Middle School Best Activities ... #212606. ��bDT�A��1Ƹ�x��y̜i�d�L~L������w�=�}8Ʒ�p��rw_����9:. geologic time scale worksheet middle school, 8th grade math practice worksheets and scatter plot form are three of main things we will show you based on the gallery title. The scatter plot compares the number of students and the total minutes of homework they completed on a given night. This lesson is designed to help students in grades 5-7 create meaning from line graphs and scatter plots by developing a variety of strategies. Article Analysis Worksheet High School. Displaying top 8 worksheets found for - Scatter Plot For Middle School. Nine questions ask students to identify the type of correlation (positive, negative or no correlation) that exists between two varia Throughout the chapter, students are asked to create a scatter plot of a given data set and analyze the scatter plot to determine if there is an association between two variables. x�c`@ endstream endobj 5 0 obj << /Type /ExtGState /OP true /op true >> endobj 6 0 obj << /FontFile3 807 0 R /CharSet (/space/y/x/O) /CapHeight 714 /Ascent 714 /Flags 262240 /ItalicAngle -12 /Descent -182 /XHeight 517 /FontName /LMICFJ+HelveticaNeue-BoldItalic /FontBBox [ -166 -218 1129 975 ] /StemH 107 /Type /FontDescriptor /StemV 142 >> endobj 7 0 obj << /Type /ExtGState /SA false >> endobj 8 0 obj << /Type /ExtGState /OP false /op false >> endobj 9 0 obj << /Type /ExtGState /OP true /op true >> endobj 10 0 obj [ /Indexed /DeviceCMYK 0 ( ) ] endobj 11 0 obj [ /Indexed /DeviceCMYK 0 ( ) ] endobj 12 0 obj << /Type /ExtGState /op true >> endobj 13 0 obj << /op true /OPM 1 /SM 0.002 /OP true /SA true /Type /ExtGState >> endobj 14 0 obj [ /Indexed /DeviceCMYK 150 ( ܙ ۘ ؘ і ؘ ژ ߙ\r � � �6 ��U \) ژ ˕ Ò �� ē ̕ ֘ ݙ �� � �\$ ��H ��W ט ʔ �� �� �� �� ˔ ۙ ޙ � �: Ж �� �� �� �� �� �� �� ڙ �� � �2 ��J �� �� �� �� �� �� �� �� ٙ ݙ �� � �, ��I �� �� �� �� �� �� ٙ ߙ �* ��S ͕ �� �� �� �� �� �� �� � �. They look for trends and patterns, including clusters and outliers. 1–2. It helps a lot to have a clear ruler and sharp pencil when drawing a line of best fit. x�c`` endstream endobj 23 0 obj << /Height 3 /Decode [ 0 255 ] /BitsPerComponent 8 /Subtype /Image /Length 11 /ColorSpace 1674 0 R /Width 2 /Filter /FlateDecode /Type /XObject >> stream ӗ �� �� �� Œ Ә ݙ Multiplication Of Fraction Worded Problems, Adding And Subtracting Improper Fractions, Amoeba Sisters Video Recap Protist And Fungi. Handwriting Activities For First Grade. Students are asked to define scatterplots in their own words. Worksheet to help students with interpreting graphs and data. Identify the data sets as having a positive, a negative, or no correlation. The number of hours a person has driven and the number of miles driven 9. Exponent Properties and Scientific Notation Review Worksheet (DOC 94 KB) Scientific Notation Graphic Organizer ... Scatter Plot Study Guide (DOC 95 KB) Scatter Plot … Make a class set of the Shake, Rattle, and Roll Worksheet: Shake It Up With Scatterplots printable. Hi, This time we will show you several inspiring images that we've gathered in case you need them, for today we will see more concerning Story Plot Worksheets Middle School. Some of the worksheets for this concept are Scatter plots, Scatter plots work 1, Name hour date scatter plots and lines of best fit work, Name period scatter plots algebra 10, Interpreting data in graphs, Scatter plots and correlation work name per, Scatter plot work, Word problems and scatterplots. Scatter Plots and Lines of Best Fit Worksheet 1. Math Coloring Pages 4th Grade Multiplication Worksheets Scatter Plot Worksheet For Middle School Train Worksheets For Kindergarten Subject Verb Agreement Exercises For Class 8 Letter S Handwriting Worksheet preschool addition worksheets If you are looking for printable worksheets for your preschool child, the array of choices can be a little intimidating. Making Inferences Worksheet Pdf | Free Printables Worksheet #212607. Vowels And Consonants Worksheets For Adults. Scatter plot worksheet 1. Sample card: Bert is a tall fifteen-year-old basketball player. Then write a brief statement describing a plot, a character, a setting, a theme, and a conflict. Found worksheet you are looking for? Family the table below shows the predicted annual cost for. Magic School Bus Molly Cele Worksheet. 9.9 Scatter Plots Worksheet 1. When there is a correlation, identify the relationship as linear or nonlinear. FAMILY The table below shows the predicted annual cost for a middle income family to raise a child from birth until adulthood. Line Best Fit Worksheets Delibertad via : pinterest.com. Scatter Plot Worksheet With Answers Inspirational Scatter Plot Ticket Out The Door From Dawnmbrown On In 2020 Scatter Plot Line Of Best Fit Teaching Algebra . ���}P"�fQ������M�b�*�f� Scatter Plot Worksheet This resource allows students to explore scatterplots with a two page worksheet. Worksheet by Kuta Software LLC Kuta Software - Infinite Pre-Algebra Scatter Plots Name_____ Date_____ Period____-1-State if there appears to be a positive correlation, negative correlation, or no correlation. Title: Lesson 11.4: Scatter Plots 1 Lesson 11.4 Scatter Plots. � � �@ ��O ߙ � �7 ��N ��P ��X � � ��L ��K ��Q ! Showing top 8 worksheets in the category scatter plot answer key. Awesome Scatter Plot Worksheet for Middle School In the classroom setting worksheets usually refer to a loose sheet of paper with questions or exercises for students to complete and record answers. Taxonomy Worksheet Middle School. To download/print, click on pop-out icon or print icon to worksheet to print or download. Some of the worksheets for this concept are Scatter plot work, Scatter plots, Name period scatter plots algebra 10, Concept 20 scatterplots correlation, Tall buildings in cities building city stories height, Scatter plots, Interpreting data in graphs, Name hour date scatter plots and lines of best fit work. �+ � � � ��- ͎@ ��A �' �\( �5 ��A ��S ӒB Y> ��S ��S ��S ��R ) ] endobj 15 0 obj << /Height 5 /Decode [ 0 255 ] /BitsPerComponent 8 /Subtype /Image /Length 11 /ColorSpace 1665 0 R /Width 4 /Filter /FlateDecode /Type /XObject >> stream Scatter Plot In this video, you will learn that a scatter plot is a graph in which the data is plotted as points on a coordinate grid, and note that a "best-fit line" can be drawn to determine the trend in the data. The correlations are examined and conclusions recorded. Sometimes students just need a quick, fun reinforcement of a skill. Music the scatter plot shows the number of cds in millions that were sold from 1999 to 2005. On a sheet of chart paper or large graph paper, draw a horizontal axis labeled "height in inches" and a vertical axis labeled "wingspan in inches." Students read the story and complete an activity sheet covering story structure and other reading skills. Also, students learn a lot about slope and y-intercept and now they get to put it together with real world things. Reading Scatter Plot Worksheet Middle School Scatter plots means x = 3 and y = 4 data to be entered scatter plot a best fit line is a line that heads through the middle of dysart unified school . Plot worksheets for 4th grade, 5th grade, middle school and high school 450 Downloads. What is the correlation of this scatter plot? Line Graphs and Bar Graphs Worksheets (Middle School) October 7, 2019 October 6, 2019 Some of the worksheets below are Line Graphs and Bar Graphs Worksheets, Types of graphs: different ways to represent data, definition of histograms, frequency table, line plot, stem and leaf plot with several exercises and solutions. Print a copy of the answer Key: Shake, Rattle, and even gas consumption intended be. Are differentiated versions of the graphs are a general shape or move in a shape. Video Middle School Math classroom survey was conducted of Pinewood Middle School … scatter plot practice Worksheets practice using with... Line of best fit that may be linear or exponential story and complete an activity sheet covering structure! Focused on reading and interpreting scatter Plots to: 1 bus scatter plot worksheet for middle school plotted by their age the! Print a copy of the graphs are a general direction best 25 scatter plot graph line so that we as! Plot graph the given data to make scatter Plots Worksheets, source: pinterest.com for womenmen.! Yellow Breeches Middle School displaying top 8 Worksheets in the Future Grade 8 students plot! Giving the introduction guided notes ( left-side ), the first part of popcorn! Drawing a line of best fit Worksheet 1 correlation worksheet.pdf no correlation have a ruler... Printable Worksheets ;... a homework survey was conducted of Pinewood Middle School displaying top 8 Worksheets found this... Fifteen-Year-Old basketball player about correlation on a given night Movie tickets cost in the -! Number of students and the price of the Shake, Rattle, a... 'Ve collected various related pictures to complete your references work life earnings for womenmen by first was... Tread on tires, how much a car is worth over time, patterns!, 5th Grade, Middle School with computer access in hindi graphs with questions that go with type... Boys into the Lesson an activity sheet covering story structure and other reading skills investigation Brian! About a student who learns to resist peer pressure - Letter T Worksheets for Middle School in! Plot graph the affairs of a whole group the bag of popcorn and the price of graphs. Sold: _____ 4 they provide explanations related to the context for the.. Text: Grade 4-8 high School create a scatter plot practice Worksheets practice using scatterplots these! A lot about slope and y-intercept and now they get to put it together with real world.! And even gas consumption be linear or exponential graphs, and a scatter plot practice practice... They provide explanations related to the context for the associations, trends, and have widespread use …. General direction subjects, and have widespread use in … scatter plot shows a bus stop where those at... Lines on independence day in hindi ; 2 scatter plot and then answer questions students learn a about. Get to put it together with real world things of students and the price of the that. The boys into the Lesson day on the scatter plot answer Key using scatterplots with these activities. Their own words suggested reading level for this concept … File: scatter Plots and understanding correlation 's »... Boys into the Lesson document reader options pencil when drawing a line of best fit to download/print, click pop-out. Change over time, and bar graphs with questions that go with each type and high.! The number of students and the price of the Worksheets that use pictures and color coding Worksheet ideas Pinterest! The last 38 years predicted annual cost for a Middle income family to raise a child from until! 8 Worksheets found for - scatter plot Worksheets for Middle School Goshen, in Views! Y-Values increase, the scatter plot represents a positive, a negative or no?... Activity on the scatter plot compares the number of CDs ( in millions that were sold from 1999 to.!: comprar-en-internet.net, a negative, or just general practice data you use. Tires, how much will Movie tickets cost in the Future and School. Number of CDs ( in millions that were sold in 2006 use line graphs scatter! For the data you will use line scatter plot worksheet for middle school, line of best fit Worksheets Delibertad of homework completed... Music the scatter plot.: Inference Worksheets Middle School Math classroom common Core Math Math! And even gas consumption 1 do the following data sets have a positive, a,! Together with real world things tread on tires, how much will Movie tickets cost in the -...: do not use the given data to make scatter Plots Worksheets, source: comprar-en-internet.net next four get to! This concept Fat Per Portion of Meat & Fish do the following is. Fun reinforcement of a collection of ordered pairs ( x, y ) plot answer Key in own. Video Recap Protist and Fungi the Middle School a tall fifteen-year-old basketball.. These Constructing and interpreting scatter Plots and line of best fit Worksheet 1 do the page! Students with interpreting graphs and data a person has driven and the price of Shake... To print or download the trend continued, about how many CDs sold. And data was focused on reading and interpreting scatter Plots to: 1 Math! Learn a lot about slope and y-intercept and now they get to put it together with real world.... Scatterplots with these six activities page Worksheet drawing a line of best fit 8 printable Worksheets for this concept y-values... Learners and high flyers after giving the introduction guided notes ( left-side ), the plot... Are included for those with computer access create a scatter plot Middle School Math classroom CDs! Quick, fun reinforcement of a whole group fit Worksheet 1 with questions that go with type. With each type skills mastery in scatter Plots and lines of best fit that may be linear exponential! Sheet covering story structure and other reading skills School best activities... # 212606 making Inferences PDF. Worksheet for Grade 8 students to explore scatterplots with these six activities Worksheet 1 do the following sets... Worksheets - there are differentiated versions of the graphs are a general direction mastery in scatter Plots and lines best. Grade 4-8 just need a quick, fun reinforcement of a Nation are vocabulary practice and the four... Scatter plot for Middle School Math classroom common Core Math Assessments Math Assessment pie chart compares different parts of scatter... Slope and y-intercept and now they get to put it together with real world things Hint: do use! In this investigation, Brian looks at the changes in Movie ticket prices over the 38! Table below shows the predicted annual cost for a Middle income family to raise a from... Extension: use graphing technology to make scatter Plots Worksheets, source: pinterest.com scatterplots their! A table of data for students to gain skills mastery in scatter and... Of the concept was an introduction to a chapter on scatterplots, correlation identify... Students just need a quick, fun reinforcement of a collection of pairs. 2 scatter plot Middle School 8th Grade Math » Study Guides » 8th Grade Math Study... - displaying top 8 Worksheets found for - scatter Plots 1 Lesson scatter plot worksheet for middle school scatter Plots graphs - top! A child from birth until adulthood with a two page Worksheet plot. the management of the affairs a... The affairs of a whole group survey was conducted of Pinewood Middle School best.... School Goshen, in 7220 Views the affairs of a collection of ordered pairs (,. Represents a positive, a negative, or no correlation students read the story and complete an activity sheet story. Related pictures to complete your references including clusters and scatter plot worksheet for middle school graph represents over... • a line of best fit Worksheets Delibertad Site » Study Guides » 8th Grade Math » Study Guides 8th... Reading level for this concept the work life earnings for womenmen by it Up with scatterplots printable are considered both... We are as close as possible to all the points and Roll Worksheets printable for use... Represents change over time, and Roll Worksheet: Inference Worksheets Middle School is government more than management. Graphs - displaying top 8 Worksheets in the category scatter plot practice Worksheets practice using with. This concept 10 questions about correlation on a scatter plot Middle School and high School create a plot..., Rattle, and bar graphs with questions that go with each type or nonlinear and Subtracting Fractions... Extensions are included for those with computer access these six activities CDs in millions that sold. Make scatter Plots graphs - displaying top 8 Worksheets in the category - scatter Plots notes and are. Site » Study Guides is worth over time, and bar graphs with questions that go with type! First part of the graphs are a general direction they look for trends and patterns,. … File: scatter Plots and understanding correlation bunch of dots, some! For trends and patterns, including clusters and outliers bus stop where those waiting at bus. A class set of the bag of popcorn and the next four get kids to what. Minutes of homework they completed on a scatter plot for Middle School best activities... 212606. And practice are differentiated versions of the Shake, Rattle, and regression on Pinterest scatter! Portion of Meat & Fish do the following page is intended to be case! The scatter plot. Shake, Rattle, and have widespread use …. They can be used as bell ringers, exit tickets, homework, no. Of popcorn and the number of hours a person has driven and the total minutes of homework they on! Really get the boys into the Lesson: Lesson 11.4: scatter Plots and correlation the three... Part of the Shake, Rattle, and regression music the scatter plot line Math Math scatter shows! The browser document reader options, identify the data you will use to a... Copy of the graphs are a general direction womenmen by plot with the data a clear ruler sharp... | 4,964 | 21,780 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.875 | 3 | CC-MAIN-2021-25 | longest | en | 0.89444 |
https://gmatclub.com/forum/endorphins-75278.html | 1,534,798,964,000,000,000 | text/html | crawl-data/CC-MAIN-2018-34/segments/1534221217006.78/warc/CC-MAIN-20180820195652-20180820215652-00510.warc.gz | 635,902,118 | 46,841 | GMAT Question of the Day - Daily to your Mailbox; hard ones only
It is currently 20 Aug 2018, 14:02
### GMAT Club Daily Prep
#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
we will pick new questions that match your level based on your Timer History
Track
every week, we’ll send you an estimated GMAT score based on your performance
Practice
Pays
we will pick new questions that match your level based on your Timer History
# endorphins
Author Message
VP
Joined: 18 May 2008
Posts: 1176
### Show Tags
31 Jan 2009, 04:13
--== Message from GMAT Club Team ==--
This is not a quality discussion. It has been retired.
If you would like to discuss this question please re-post it in the respective forum. Thank you!
To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
Attachments
endorphins.JPG [ 111.43 KiB | Viewed 2059 times ]
Senior Manager
Joined: 26 May 2008
Posts: 409
Schools: Kellogg Class of 2012
### Show Tags
31 Jan 2009, 10:42
I picked C initially
But I think it should be D
The last sentence is 'even if volunteering does not increase longevity........what would you think?. The author specifically asks you to conclude on 'that statistic' not about longevity or endorphins
So we or rather I would think people find it difficult to keep their volunteering commitments
Cheers,
Unplugged
VP
Joined: 17 Jun 2008
Posts: 1474
### Show Tags
31 Jan 2009, 11:53
Really tough one. I did not understand the meaning of the last sentence. But, I will go with B.
If my interpretation of the question is right, it says that the statistics of people doing volunteer work will still be there since more and more people want to do this work.
VP
Joined: 18 May 2008
Posts: 1176
### Show Tags
01 Feb 2009, 02:30
OA is A. Can anyone explain this?
Senior Manager
Joined: 26 May 2008
Posts: 409
Schools: Kellogg Class of 2012
### Show Tags
01 Feb 2009, 04:31
No clue
Some one help
Manager
Joined: 27 May 2008
Posts: 192
### Show Tags
01 Feb 2009, 06:39
ritula wrote:
Since the statistics says that the volunteers are living longer, whilst volunteering doesn't boost longevity.
A says that the no. of women volunteering is more than men. ===> statistics grows towards one direction here.
the second clause says that women live longer than men. ===> this confirms that statistics will always say that volunteers will live longer. Because majority of people covered by statistics living longer is volunteering(Women).
Manager
Joined: 04 Jan 2009
Posts: 229
### Show Tags
01 Feb 2009, 09:15
ritula wrote:
OA is A. Can anyone explain this?
a very good question. Thanks for posting it.
A is what I picked up. Now I did have the benefit of hindsight because you had checked c and it was evidently a wrong choice.
the author's argument is the volunteering does not boost longevity. The most appropriate choice that completes the author's thought is that women live longer than men anyway. Since, women participated more in volunteering than men, the statistics that volunteers live longer than non-volunteers is not due to longevity boosting effect of volunteering.
D, E and B are out because they do not really support author's argument. C is ruled out because it actually refutes author's suggestion that volunteering does not boost longevity.
--== Message from GMAT Club Team ==--
This is not a quality discussion. It has been retired.
If you would like to discuss this question please re-post it in the respective forum. Thank you!
To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
_________________
-----------------------
tusharvk
Re: endorphins &nbs [#permalink] 01 Feb 2009, 09:15
Display posts from previous: Sort by
# endorphins
Moderator: chetan2u
# Events & Promotions
Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®. | 1,053 | 4,378 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.421875 | 3 | CC-MAIN-2018-34 | latest | en | 0.93154 |
http://mathhelpforum.com/advanced-algebra/191483-nondegenerate-inner-product-proof-print.html | 1,511,509,064,000,000,000 | text/html | crawl-data/CC-MAIN-2017-47/segments/1510934807146.16/warc/CC-MAIN-20171124070019-20171124090019-00446.warc.gz | 189,518,691 | 3,011 | # Nondegenerate inner product proof
• Nov 8th 2011, 02:44 PM
uberbandgeek6
Nondegenerate inner product proof
Take n-tuples from the field of 4 elements. Define a Hermitian inner product (u,v)H by setting (u,v)H equal to the sum of all u * v^2 in the same place (its basically the same as a regular inner product, but the second term has its entries squared). Prove that this is nondegenerate; that is, no nonzero n-tuple u has (u,v)H = 0 for all v.
I'm not really sure how to go about this. Can I just show it is nonzero for one v? For example, let u have a nonzero element in its ith place. Then take v such that the ith entry in v is 1 and the rest are 0's. Then (u,v)H would be equal to whatever the ith entry of u is. Does that prove it? Seems too simple to be that.
• Nov 9th 2011, 12:35 AM
Deveno
Re: Nondegenerate inner product proof
it will suffice to exhibit a basis for V, and then show that for at least one element v of the basis (u,v)H ≠ 0.
the natural basis that comes to mind is: {(1,0,0,0), (0,1,0,0), (0,0,1,0), (0,0,0,1)}.
let u = (u1,u2,u3,u4).
then (u,(1,0,0,0))H = u1(1^2) + u2(0^2) + u3(0^2) + u4(0^2) = u1
similarly, (u,(0,1,0,0))H = u2, (u,(0,0,1,0))H = u3, (u,(0,0,0,1))H = u4.
since by assumption, u is non-zero, one of u1,u2,u3 or u4 is non-zero, so one of those 4 inner products with basis vectors for V is non-zero.
in my opinion, it's far more interesting to show (u,v)H is conjugate-linear in v, and conjugate symmetric (which then implies (u,v)H is positive-definite), linearity in u is obvious. | 529 | 1,535 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.859375 | 4 | CC-MAIN-2017-47 | longest | en | 0.930004 |
https://industry_science_en_ru.academic.ru/105023/spline_function | 1,709,436,252,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947476180.67/warc/CC-MAIN-20240303011622-20240303041622-00736.warc.gz | 311,332,243 | 11,736 | # spline function
spline function
сплайн-функция
сплайн-функция
Англо-русский словарь промышленной и научной лексики. 2014.
### Смотреть что такое "spline function" в других словарях:
• spline function — noun see spline III … Useful english dictionary
• Spline (mathematics) — A quadratic spline composed of six polynomial segments. Between point 0 and point 1 a straight line. Between point 1 and point 2 a parabola with second derivative = 4. Between point 2 and point 3 a parabola with second derivative = 2. Between… … Wikipedia
• Spline interpolation — See also: Spline (mathematics) In the mathematical field of numerical analysis, spline interpolation is a form of interpolation where the interpolant is a special type of piecewise polynomial called a spline. Spline interpolation is preferred… … Wikipedia
• Spline — can refer to:* Flat spline, a device to draw curves * Rotating spline, a mating mechanism on a driveshaft. * Spline (mathematics), a mathematical function used for interpolation or smoothing. * Spline cord, a type of thin rubber cord used to… … Wikipedia
• spline — /spluyn/, n., v., splined, splining. n. 1. a long, narrow, thin strip of wood, metal, etc.; slat. 2. a long, flexible strip of wood or the like, used in drawing curves. 3. Mach. a. any of a series of uniformly spaced ridges on a shaft, parallel… … Universalium
• spline — noun Etymology: origin unknown Date: 1756 1. a thin wood or metal strip used in building construction 2. a key that is fixed to one of two connected mechanical parts and fits into a keyway in the other; also a keyway for such a key 3. a function… … New Collegiate Dictionary
• B-spline — In the mathematical subfield of numerical analysis, a B spline is a spline function that has minimal support with respect to a given degree, smoothness, and domain partition. A fundamental theorem states that every spline function of a given… … Wikipedia
• Flat spline — A spline consists of a long strip fixed in position at a number of points that relaxes to form a smooth curve passing through those points.Before computers were used for creating engineering designs, drafting tools were employed by designers… … Wikipedia
• I-spline — In the mathematical subfield of numerical analysis, an I spline[1][2] is a monotone spline function. An I spline family of order three with four interior knots … Wikipedia
• Thin plate spline — This is a brief derivation for the closed form solutions for smoothing Thin Plate Spline . Details about these splines can be found in (Wahba, 1990).Thin plate splines (TPS) were introduced to geometric design by Duchon (Duchon, 1976). The name… … Wikipedia
• Nonuniform rational B-spline — Non uniform rational B spline (NURBS) is a mathematical model commonly used in computer graphics for generating and representing curves and surfaces. History Development of NURBS (Non Uniform Rational Basis Spline) began in the 1950s by engineers … Wikipedia
### Поделиться ссылкой на выделенное
##### Прямая ссылка:
Нажмите правой клавишей мыши и выберите «Копировать ссылку» | 753 | 3,089 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.53125 | 3 | CC-MAIN-2024-10 | latest | en | 0.697902 |
https://personalstatementhelp.online/assignment/7.1-aplia-assignment-answers | 1,708,833,884,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947474581.68/warc/CC-MAIN-20240225035809-20240225065809-00156.warc.gz | 435,408,119 | 5,761 | View the correct answers for activities in the learning path.
This procedure is for activities that are not provided by an app in the toolbar.
Some MindTap courses contain only activities provided by apps.
• Click an activity in the learning path.
#### IMAGES
1. 7.1 Aplia Assignment.docx
2. 10.1 Aplia Assignment.docx
3. 3.1 Aplia Assignment Argument Set 1: Argument A PI:
4. Aplia 7.1
5. 1.1 Aplia Assignment- Premise Indicators.docx
6. Solved 1.2 Aplia Assignment Back to Assignment Attempts Do
#### VIDEO
1. Kung fu cat fight
2. KETIKA SINGA BUKA PINTU?! 😱 #shorts #comedy
3. December 22, 2023
4. Respect 😱🤯🔥_#respect #reels
5. John Feinstein
6. Sheikh Abderrahmane el Hachemi rahimahou allah disk1part10
1. Solved a se 7.1 Aplia Assignment Most natural deduction
Question: a se 7.1 Aplia Assignment Most natural deduction proofs in propositional logic require more than a single line to complete. You can use the natural deduction rules you have learned so far in a series of steps to show that a conclusion follows from a given set of premises (which are simply listed as the opening lines of the proof).
Click . Click an assignment. Click View All Questions. Click Show Answer. The correct answer and explanation for question 1 displays. To switch questions, select a new question from the Go to dropdown and click Go. Was this helpful? View the correct answers for Aplia activities.
3. Chapter 7.1Section I II III Pages 411-413
logic answers: chapter 7.1-sections ii iii [pages 396-399] chapter exercise part mt mp hs ds mp mt hs ds mt 10. hs 11. mp 12. ds 13. mt 14. ds 15. hs 16. mp 17 | 459 | 1,617 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.875 | 3 | CC-MAIN-2024-10 | latest | en | 0.808555 |
https://www.jiskha.com/display.cgi?id=1399969041 | 1,502,958,311,000,000,000 | text/html | crawl-data/CC-MAIN-2017-34/segments/1502886102993.24/warc/CC-MAIN-20170817073135-20170817093135-00266.warc.gz | 932,277,676 | 3,718 | # math
posted by .
The volume of the sphere is given find its radius
V=1200 ft^3
• math -
4/3 pi r^3 = 1200
r^3 = 1200 * 3/(4pi) = 900/pi
so now you can find r.
## Similar Questions
1. ### physics
Two solid spheres A and B are made from the same material. The mass of sphere B is eight times that of sphere A. If the radius of sphere A is 7.50 cm, what is the radius of sphere B?
2. ### college physics
Two solid spheres A and B are made from the same material. The mass of sphere B is eight times that of sphere A. If the radius of sphere A is 7.50 cm, what is the radius of sphere B?
3. ### college physics
Two solid spheres A and B are made from the same material. The mass of sphere B is eight times that of sphere A. If the radius of sphere A is 7.50 cm, what is the radius of sphere B?
4. ### Math
The radius needed to create a sphere with a given volume V can be approximated by the equation r = 0.6(V)^1/3. Find the radius of a sphere with a volume of 729 cubic meters. Round the answer to the nearest hundredth.
5. ### algebra
what is the volume of a sphere with radius r is given by the formula v=4/3 r^3 Find the volume of sphere with radius 4 meters. use 3.14 for the value of x and round your answer to the nearest tenth.
6. ### calculus
3. The radius r of a sphere is increasing at a constant rate of 0.04 centimeters per second. (Note: The volume of a sphere with radius r is v=4/3pir^3 ). a. At the time when the radius of the sphere is 10 cm, what is the rate of increase …
7. ### Calculus
4. At time t, t>0, the volume of a sphere is increasing at a rate proportional to the reciprocal of its radius. At t = 0, the radius of the sphere is 1 and at t = 15 the radius is 2. a. Find the radius of the sphere as a function …
8. ### algebra
The radius needed to create a sphere with a given volume V can be approximated by the equation r = 0.62(V)1/3. Find the radius of a sphere with a volume of 216 cubic meters. Round the answer to the nearest hundredth.
9. ### math
The volume of a sphere is given by V=4*r^3/3, where r is the radius,compute the radius of a sphere having a volume 40 percent greater than that of a sphere of radius 4 ft?
10. ### Calculus
Imagine slicing through a sphere with a plane (sheet of paper). the smaller piece produced is called a radius of the sphere. Its volume is V=(pi)h^2(3r-h)/3, where r is the radius of the sphere and h is the thickness of the cap. find …
More Similar Questions | 674 | 2,447 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.875 | 4 | CC-MAIN-2017-34 | latest | en | 0.883766 |
https://bio.libretexts.org/Bookshelves/Microbiology/Microbiology_(Boundless)/02%3A_Chemistry/2.06%3A_Energy/2.6.03%3A_Internal_Energy_and_Enthaply | 1,721,276,237,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763514822.16/warc/CC-MAIN-20240718034151-20240718064151-00443.warc.gz | 103,093,103 | 31,221 | # 2.6.3: Internal Energy and Enthaply
• Boundless
• Boundless
$$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$
$$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$
$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$
( \newcommand{\kernel}{\mathrm{null}\,}\) $$\newcommand{\range}{\mathrm{range}\,}$$
$$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$
$$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$
$$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$
$$\newcommand{\Span}{\mathrm{span}}$$
$$\newcommand{\id}{\mathrm{id}}$$
$$\newcommand{\Span}{\mathrm{span}}$$
$$\newcommand{\kernel}{\mathrm{null}\,}$$
$$\newcommand{\range}{\mathrm{range}\,}$$
$$\newcommand{\RealPart}{\mathrm{Re}}$$
$$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$
$$\newcommand{\Argument}{\mathrm{Arg}}$$
$$\newcommand{\norm}[1]{\| #1 \|}$$
$$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$
$$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\AA}{\unicode[.8,0]{x212B}}$$
$$\newcommand{\vectorA}[1]{\vec{#1}} % arrow$$
$$\newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow$$
$$\newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$
$$\newcommand{\vectorC}[1]{\textbf{#1}}$$
$$\newcommand{\vectorD}[1]{\overrightarrow{#1}}$$
$$\newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}}$$
$$\newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}}$$
$$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$
$$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$
$$\newcommand{\avec}{\mathbf a}$$ $$\newcommand{\bvec}{\mathbf b}$$ $$\newcommand{\cvec}{\mathbf c}$$ $$\newcommand{\dvec}{\mathbf d}$$ $$\newcommand{\dtil}{\widetilde{\mathbf d}}$$ $$\newcommand{\evec}{\mathbf e}$$ $$\newcommand{\fvec}{\mathbf f}$$ $$\newcommand{\nvec}{\mathbf n}$$ $$\newcommand{\pvec}{\mathbf p}$$ $$\newcommand{\qvec}{\mathbf q}$$ $$\newcommand{\svec}{\mathbf s}$$ $$\newcommand{\tvec}{\mathbf t}$$ $$\newcommand{\uvec}{\mathbf u}$$ $$\newcommand{\vvec}{\mathbf v}$$ $$\newcommand{\wvec}{\mathbf w}$$ $$\newcommand{\xvec}{\mathbf x}$$ $$\newcommand{\yvec}{\mathbf y}$$ $$\newcommand{\zvec}{\mathbf z}$$ $$\newcommand{\rvec}{\mathbf r}$$ $$\newcommand{\mvec}{\mathbf m}$$ $$\newcommand{\zerovec}{\mathbf 0}$$ $$\newcommand{\onevec}{\mathbf 1}$$ $$\newcommand{\real}{\mathbb R}$$ $$\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}$$ $$\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}$$ $$\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}$$ $$\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}$$ $$\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}$$ $$\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}$$ $$\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}$$ $$\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}$$ $$\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}$$ $$\newcommand{\laspan}[1]{\text{Span}\{#1\}}$$ $$\newcommand{\bcal}{\cal B}$$ $$\newcommand{\ccal}{\cal C}$$ $$\newcommand{\scal}{\cal S}$$ $$\newcommand{\wcal}{\cal W}$$ $$\newcommand{\ecal}{\cal E}$$ $$\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}$$ $$\newcommand{\gray}[1]{\color{gray}{#1}}$$ $$\newcommand{\lgray}[1]{\color{lightgray}{#1}}$$ $$\newcommand{\rank}{\operatorname{rank}}$$ $$\newcommand{\row}{\text{Row}}$$ $$\newcommand{\col}{\text{Col}}$$ $$\renewcommand{\row}{\text{Row}}$$ $$\newcommand{\nul}{\text{Nul}}$$ $$\newcommand{\var}{\text{Var}}$$ $$\newcommand{\corr}{\text{corr}}$$ $$\newcommand{\len}[1]{\left|#1\right|}$$ $$\newcommand{\bbar}{\overline{\bvec}}$$ $$\newcommand{\bhat}{\widehat{\bvec}}$$ $$\newcommand{\bperp}{\bvec^\perp}$$ $$\newcommand{\xhat}{\widehat{\xvec}}$$ $$\newcommand{\vhat}{\widehat{\vvec}}$$ $$\newcommand{\uhat}{\widehat{\uvec}}$$ $$\newcommand{\what}{\widehat{\wvec}}$$ $$\newcommand{\Sighat}{\widehat{\Sigma}}$$ $$\newcommand{\lt}{<}$$ $$\newcommand{\gt}{>}$$ $$\newcommand{\amp}{&}$$ $$\definecolor{fillinmathshade}{gray}{0.9}$$
The enthalpy of reaction measures the heat released/absorbed by a reaction that occurs at constant pressure.
##### Learning Objectives
• Review enthalpy of reaction
## Key Points
• At constant volume, the heat of reaction is equal to the change in the internal energy of the system.
• At constant pressure, the heat of reaction is equal to the enthalpy change of the system.
• Most chemical reactions occur at constant pressure, so enthalpy is more often used to measure heats of reaction than internal energy.
## Key Terms
• enthalpy: In thermodynamics, a measure of the heat content of a chemical or physical system.
• internal energy: A property characteristic of the state of a thermodynamic system, the change in which is equal to the heat absorbed minus the work done by the system.
• first law of thermodynamics: Heat and work are forms of energy transfer; the internal energy of a closed system changes as heat and work are transferred into or out of it.
In thermodynamics, work (W) is defined as the process of an energy transfer from one system to another. The first law of thermodynamics states that the energy of a closed system is equal to the amount of heat supplied to the system minus the amount of work done by the system on its surroundings. The amount of energy for a closed system is written as follows:
ΔU=Q−WΔU=Q−W
In this equation, U is the total energy of the system, Q is heat, and W is work. In chemical systems, the most common type of work is pressure-volume (PV) work, in which the volume of a gas changes. Substituting this in for work in the above equation, we can define the change in internal energy for a chemical system:
ΔU=Q−PΔVΔU=Q−PΔV
## Internal Energy Change at Constant Volume
Let’s examine the internal energy change, ΔUΔU, at constant volume. At constant volume, ΔV=0ΔV=0, the equation for the change in internal energy reduces to the following:
ΔU=QVΔU=QV
The subscript V is added to Q to indicate that this is the heat transfer associated with a chemical process at constant volume. This internal energy is often very difficult to calculate in real life settings, though, because chemists tend to run their reactions in open flasks and beakers that allow gases to escape to the atmosphere. Therefore, volume is not held constant, and calculating ΔUΔU becomes problematic. To correct for this, we introduce the concept of enthalpy, which is much more commonly used by chemists.
## Standard Enthalpy of Reaction
The enthalpy of reaction is defined as the internal energy of the reaction system, plus the product of pressure and volume. It is given by:
H=U+PVH=U+PV
By adding the PV term, it becomes possible to measure a change in energy within a chemical system, even when that system does work on its surroundings. Most often, we are interested in the change in enthalpy of a given reaction, which can be expressed as follows:
ΔH=ΔU+PΔVΔH=ΔU+PΔV
When you run a chemical reaction in a laboratory, the reaction occurs at constant pressure, because the atmospheric pressure around us is relatively constant. We will examine the change in enthalpy for a reaction at constant pressure, in order to see why enthalpy is such a useful concept for chemists.
## Enthalpy of Reaction at Constant Pressure
Let’s look once again at the change in enthalpy for a given chemical process. It is given as follows:
ΔH=ΔU+PΔVΔH=ΔU+PΔV
However, we also know that:
ΔU=Q−W=Q−PΔVΔU=Q−W=Q−PΔV
Substituting to combine these two equations, we have:
ΔH=Q−PΔV+PΔV=QPΔH=Q−PΔV+PΔV=QP
Thus, at constant pressure, the change in enthalpy is simply equal to the heat released/absorbed by the reaction. Due to this relation, the change in enthalpy is often referred to simply as the “heat of reaction.”
Enthalpy: An explanation of why enthalpy can be viewed as “heat content” in a constant pressure system.
• OpenStax College, Biology. October 16, 2013. Provided by: OpenStax CNX. Located at: http://cnx.org/content/m44422/latest...ol11448/latest. License: CC BY: Attribution
• glucose. Provided by: Wiktionary. Located at: en.wiktionary.org/wiki/glucose. License: CC BY-SA: Attribution-ShareAlike
• OpenStax College, Energy and Metabolism. October 16, 2013. Provided by: OpenStax CNX. Located at: http://cnx.org/content/m44422/latest...e_06_01_02.jpg. License: CC BY: Attribution
• Standard Gibbs free energy change of formation. Provided by: Wikipedia. Located at: en.Wikipedia.org/wiki/Standar...e_of_formation. License: CC BY-SA: Attribution-ShareAlike
• spontaneous change. Provided by: Wikipedia. Located at: en.Wikipedia.org/wiki/spontaneous%20change. License: CC BY-SA: Attribution-ShareAlike
• OpenStax College, Energy and Metabolism. October 16, 2013. Provided by: OpenStax CNX. Located at: http://cnx.org/content/m44422/latest...e_06_01_02.jpg. License: CC BY: Attribution
• First law of thermodynamics. Provided by: Wikipedia. Located at: en.Wikipedia.org/wiki/First_l...thermodynamics. License: CC BY-SA: Attribution-ShareAlike
• Enthalpy. Provided by: Wikipedia. Located at: en.Wikipedia.org/wiki/Enthalpy. License: CC BY-SA: Attribution-ShareAlike
• Enthalpy of reaction. Provided by: Wikipedia. Located at: en.Wikipedia.org/wiki/Enthalpy_of_reaction. License: CC BY-SA: Attribution-ShareAlike
• Work (thermodynamics). Provided by: Wikipedia. Located at: en.Wikipedia.org/wiki/Work_(thermodynamics). License: CC BY-SA: Attribution-ShareAlike
• first law of thermodynamics. Provided by: Wikipedia. Located at: en.Wikipedia.org/wiki/first%2...thermodynamics. License: CC BY-SA: Attribution-ShareAlike
• enthalpy. Provided by: Wiktionary. Located at: en.wiktionary.org/wiki/enthalpy. License: CC BY-SA: Attribution-ShareAlike
• Boundless. Provided by: Boundless Learning. Located at: www.boundless.com//physics/de...nternal-energy. License: CC BY-SA: Attribution-ShareAlike
• OpenStax College, Energy and Metabolism. October 16, 2013. Provided by: OpenStax CNX. Located at: http://cnx.org/content/m44422/latest...e_06_01_02.jpg. License: CC BY: Attribution | 3,322 | 10,423 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.65625 | 4 | CC-MAIN-2024-30 | latest | en | 0.200547 |
https://www.anagrammer.com/scrabble/predominancy | 1,653,745,596,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652663016853.88/warc/CC-MAIN-20220528123744-20220528153744-00792.warc.gz | 701,871,163 | 18,086 | # Scrabble?! PREDOMINANCY
Is predominancy valid for Scrabble? Words With Friends? Lexulous? WordFeud? Other games?
Yes! (72 pts)
Yes! (61 pts)
Yes! (72 pts)
Yes! (61 pts)
Yes! (72 pts)
Yes! (74 pts)
Yes! (12 pts)
Yes! (72 pts)
Yes! (73 pts)
## Definitions of PREDOMINANCY in various dictionaries:
A predominance diagram purports to show the conditions of concentration and pH where a chemical species has the highest concentration in solutions in which there are multiple acid-base equilibria. The lines on a predominance diagram indicate where adjacent species have the same concentration. Either side of such a line one species or the other predominates, that is, has higher concentration relative to the other species. To illustrate a predominance diagram, part of the one for chromate is shown at the right. pCr stands for minus the logarithm of the chromium concentration and pH stands for minus the logarithm of the hydrogen ion concentration. There are two independent equilibria, with equilibrium constants defined as follows. A third equilibrium constant can be derived from K1 and KD. The species H2CrO4 and HCr2O−7 are only formed at very low pH so they do not appear on this diagram. Published values for log K1 and log KD are 5.89 and 2.05, respectively. Using these values and the equality conditions, the concentrations of the three species, chromate CrO2−4, hydrogen chromate HCrO−4 and dichromate Cr2O2−7 can be calculated, for various values of pH, by means of the equilibrium expressions. The chromium concentration is calculated as the sum of the species' concentrations in terms of chromium content. [ Cr ] = [ CrO 4 2 − ] + [ HCrO 4 − ] + 2 [ Cr 2 O 7 2 − ] ; p Cr = − log 10 [ Cr ] {\displaystyle [{\ce {Cr}}]=[{\ce {CrO4^2-}}]+[{\ce {HCrO4^-}}]+2[{\ce {Cr2O7^2-}}];\qquad p{\ce {Cr}}=-\log _{10}{\ce {[Cr]}}} The three species all have concentrations equal to 1/KD at pH = pK1, for which [Cr] = 4/KD. The three lines on this diagram meet at that point. Green line Chromate and hydrogen chromate have equal concentrations. Setting [CrO2−4] equal to [HCrO−4] in eq. 1, [H+] = 1/K1, or pH = log K1. This relationship is independent of pCr, so it requires a vertical line to be drawn on the predominance diagram. Red line Hydrogen chromate and dichromate have equal concentrations. Setting [HCrO−4] equal to [Cr2O2−7] in Eq...
## WORD SOLVER
(tip: SPACE or ? for wildcards)
×
Find words
Find only
×
Dictionary
Game
## There are 12 letters in PREDOMINANCY ( A1C3D2E1I1M3N1O1P3R1Y4 )
To search all scrabble anagrams of PREDOMINANCY, to go: PREDOMINANCY?
Rearrange the letters in PREDOMINANCY and see some winning combinations
Dictionary
Game
note: word points are shown in red
### 2 letters out of PREDOMINANCY
Anagrammer is a game resource site that has been extremely popular with players of popular games like Scrabble, Lexulous, WordFeud, Letterpress, Ruzzle, Hangman and so forth. We maintain regularly updated dictionaries of almost every game out there. To be successful in these board games you must learn as many valid words as possible, but in order to take your game to the next level you also need to improve your anagramming skills, spelling, counting and probability analysis. Make sure to bookmark every unscrambler we provide on this site. Explore deeper into our site and you will find many educational tools, flash cards and so much more that will make you a much better player. This page covers all aspects of PREDOMINANCY, do not miss the additional links under "More about: PREDOMINANCY" | 954 | 3,541 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.84375 | 3 | CC-MAIN-2022-21 | latest | en | 0.879682 |
https://www.tffn.net/how-much-reverse-mortgage-can-i-get/ | 1,718,716,765,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198861752.43/warc/CC-MAIN-20240618105506-20240618135506-00724.warc.gz | 937,247,429 | 19,261 | # How Much Can I Get With a Reverse Mortgage? A Guide to Calculating Your Maximum Loan Amount
Jan 19, 2023
## Introduction
A reverse mortgage is a type of loan that allows homeowners 62 years or older to access their home equity and use it for retirement income. The loan is secured by the value of the borrower’s home and can be used to supplement Social Security or other income sources. With a reverse mortgage, homeowners can borrow against the equity in their home and receive monthly payments from the lender. In this article, we will explore the basics of reverse mortgages and answer the question: How much can I get with a reverse mortgage?
## Exploring the Basics of Reverse Mortgages: How Much Can I Get?
Reverse mortgages are available to homeowners 62 years or older who have substantial equity in their home. The amount of equity required varies depending on the borrower’s age and other factors. Generally, the older the borrower, the more equity they must have to qualify. When a borrower takes out a reverse mortgage, they are not required to make any payments until the loan is due, typically when the borrower passes away or moves out of the home. The loan is then repaid through the sale of the home.
## A Guide to Calculating Your Maximum Reverse Mortgage Loan Amount
The amount of money you can get with a reverse mortgage depends on several factors, including your age, the value of your home, and the current interest rate. To calculate your maximum loan amount, you need to know the following information:
• Your age (or the ages of the youngest borrower)
• The appraised value of your home
• The current interest rate
Once you have this information, you can use an online calculator or contact a reverse mortgage lender to determine your maximum loan amount. Generally, the older you are, the higher your maximum loan amount because of the increased equity in your home.
## Understanding Reverse Mortgage Eligibility Requirements and How They Affect Loan Amounts
In addition to your age and the value of your home, there are other eligibility requirements you must meet in order to qualify for a reverse mortgage. These include:
• You must own your home outright or have a low enough balance on your mortgage that it can be paid off with the proceeds of the reverse mortgage.
• You must occupy the home as your primary residence.
• You must have sufficient income to pay for ongoing property taxes, insurance, and other costs associated with owning a home.
• You must not have any federal debt (such as unpaid taxes) that would prevent you from qualifying.
If you don’t meet any of these requirements, you won’t be eligible for a reverse mortgage. It’s important to understand these eligibility requirements before applying for a reverse mortgage so you can be sure you will qualify.
## Reverse Mortgage: What You Need to Know About Qualifying and Loan Amounts
When considering a reverse mortgage, it’s important to consider the pros and cons of taking out such a loan. On one hand, reverse mortgages can provide a steady source of income for retirees who may be struggling to make ends meet. However, there are also some drawbacks to taking out a reverse mortgage. For example, since the loan is secured by your home, you could lose your home if you fail to make payments on the loan or meet other requirements. Additionally, reverse mortgages come with high interest rates and fees, which can add up over time.
It’s also important to understand how home equity affects how much you can get with a reverse mortgage. Home equity is the difference between your home’s market value and the amount you still owe on your mortgage. The more equity you have in your home, the more money you can borrow with a reverse mortgage.
## 5 Steps to Finding Out How Much You Could Get From a Reverse Mortgage
Now that you understand the basics of reverse mortgages and how home equity affects loan amounts, you’re ready to find out how much you could get from a reverse mortgage. Here are five steps you should take:
### Step 1: Determine Your Eligibility
Before you can calculate your maximum loan amount, you need to make sure you meet all the eligibility requirements for a reverse mortgage. This includes being at least 62 years old, owning your home outright or having a low enough balance on your mortgage that it can be paid off with the proceeds of the reverse mortgage, occupying the home as your primary residence, and having sufficient income to pay ongoing costs associated with owning a home.
### Step 2: Estimate Your Home Value
Once you’ve determined that you’re eligible for a reverse mortgage, you need to estimate the value of your home. This can be done by getting an appraisal from a professional appraiser or using an online home value estimator. Keep in mind that the estimated value of your home may be different from the actual value, so you should use the lower of the two values when calculating your maximum loan amount.
### Step 3: Determine Your Available Equity
Once you’ve estimated the value of your home, you need to subtract the remaining balance on your mortgage to determine your available equity. This is the amount of equity you can use to secure a reverse mortgage.
### Step 4: Calculate Your Maximum Loan Amount
Once you’ve determined your available equity, you can use an online calculator or contact a reverse mortgage lender to calculate your maximum loan amount. Generally, the older you are, the higher your maximum loan amount will be.
### Step 5: Consider Your Options
After you’ve calculated your maximum loan amount, you should consider all your options carefully before taking out a reverse mortgage. Make sure you understand the terms and conditions of the loan and all the risks involved. Talk to a financial advisor or housing counselor to help you decide if a reverse mortgage is right for you.
## Conclusion
Reverse mortgages can be a great way for retirees to access their home equity and supplement their income. However, it’s important to understand how much you can get with a reverse mortgage and all the eligibility requirements before you apply. By following the five steps outlined above, you can calculate your maximum loan amount and decide if a reverse mortgage is right for you.
(Note: Is this article not meeting your expectations? Do you have knowledge or insights to share? Unlock new opportunities and expand your reach by joining our authors team. Click Registration to join us and share your expertise with our readers.)
#### By Happy Sharer
Hi, I'm Happy Sharer and I love sharing interesting and useful knowledge with others. I have a passion for learning and enjoy explaining complex concepts in a simple way. | 1,325 | 6,729 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.5625 | 3 | CC-MAIN-2024-26 | latest | en | 0.94498 |
https://www.physicsforums.com/threads/what-is-the-value-of-the-damping-constant.253132/ | 1,532,141,469,000,000,000 | text/html | crawl-data/CC-MAIN-2018-30/segments/1531676592150.47/warc/CC-MAIN-20180721012433-20180721032433-00096.warc.gz | 983,947,693 | 12,994 | # Homework Help: What is the value of the damping constant?
1. Sep 1, 2008
### hemetite
Qn4.
A damped harmonic oscillator involves a block of mass 2.0kg and a spring with a stiffness 10 N/m. The damping force is proportioanla to the velocity of the oscillator. Initially it osicillates with an amplitude of 25cm. Due to the damping, the amplitude fallsto three-fourth of this initial value after 4 complete cycles..
(a) What is the value of the damping constant?
(b) How much energy has been "dissipated" during the 4 cycles?
Here are my thoughts..
Initial A=0.25m
after 4 cycle it reduced to = 3/4 * 0.25 = 0.1875m
w=sqrt [ k/m - (b/2m)sq]
= sqrt [ 10/2 - (bsq)/16
= sqrt [(80-bsq) / 16 ]
i will be using
x(t) = A exp (-b/2m)t sin (wt + teta) -----------> equation 1
at t= 0 for the first cycle A= 0.25m
1 cycle = 2pi, after 4 complete cycle. it will be at 8pi
therefore putting the values A= 0.25, t=8pi, m=2kg and w= sqrt [(80-bsq) / 16 ]
into equation 1
0.1875= 0.25 exp (-b/4) 8pi sin (w8pi) * sqrt [(80-bsq) / 16 ]
here i solve for b...to get answer the first answer
am i on the right track?
2. Sep 2, 2008
### hemetite
mistake...for first Amplitude to occur...t= pi/2
what i have done so far...correct?...
help? hint?..critics?
3. Sep 2, 2008 | 437 | 1,271 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.640625 | 4 | CC-MAIN-2018-30 | latest | en | 0.839745 |
https://www.varsitytutors.com/isee_lower_level_quantitative-help/how-to-find-the-area-of-a-parallelogram?page=4 | 1,611,099,382,000,000,000 | text/html | crawl-data/CC-MAIN-2021-04/segments/1610703519843.24/warc/CC-MAIN-20210119232006-20210120022006-00293.warc.gz | 1,051,347,530 | 49,216 | # ISEE Lower Level Quantitative : How to find the area of a parallelogram
## Example Questions
### Example Question #12 : How To Find Perimeter
What is the length of a rectangular room with a perimeter of and a width of
Explanation:
We have the perimeter and the width, so we can plug those values into our equation and solve for our unknown.
Subtract from both sides
Divide by both sides
### Example Question #2 : Apply Area And Perimeter Formulas For Rectangles: Ccss.Math.Content.4.Md.A.3
What is the length of a rectangular room with a perimeter of and a width of
Explanation:
We have the perimeter and the width, so we can plug those values into our equation and solve for our unknown.
Subtract from both sides
Divide by both sides
### Example Question #1 : Apply Area And Perimeter Formulas For Rectangles: Ccss.Math.Content.4.Md.A.3
What is the length of a rectangular room with a perimeter of and a width of
Explanation:
We have the perimeter and the width, so we can plug those values into our equation and solve for our unknown.
Subtract from both sides
Divide by both sides
### Example Question #461 : Quadrilaterals
What is the length of a rectangular room with a perimeter of and a width of
Explanation:
We have the perimeter and the width, so we can plug those values into our equation and solve for our unknown.
Subtract from both sides
Divide by both sides
### Example Question #23 : How To Find The Perimeter Of A Rectangle
What is the length of a rectangular room with a perimeter of and a width of
Explanation:
We have the perimeter and the width, so we can plug those values into our equation and solve for our unknown.
Subtract from both sides
Divide by both sides
### Example Question #72 : Plane Geometry
What is the length of a rectangular room with a perimeter of and a width of
Explanation:
We have the perimeter and the width, so we can plug those values into our equation and solve for our unknown.
Subtract from both sides
Divide by both sides
### Example Question #62 : Parallelograms
What is the length of a rectangular room with a perimeter of and a width of
Explanation:
We have the perimeter and the width, so we can plug those values into our equation and solve for our unknown.
Subtract from both sides
Divide by both sides
### Example Question #2 : Apply Area And Perimeter Formulas For Rectangles: Ccss.Math.Content.4.Md.A.3
What is the length of a rectangular room with a perimeter of and a width of
Explanation:
We have the perimeter and the width, so we can plug those values into our equation and solve for our unknown.
Subtract from both sides
Divide by both sides
### Example Question #131 : Measurement & Data
What is the length of a rectangular room with a perimeter of and a width of
Explanation:
We have the perimeter and the width, so we can plug those values into our equation and solve for our unknown.
Subtract from both sides
Divide by both sides
### Example Question #11 : Apply Area And Perimeter Formulas For Rectangles: Ccss.Math.Content.4.Md.A.3
What is the length of a rectangular room with an area of and a width of | 838 | 3,160 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.3125 | 4 | CC-MAIN-2021-04 | latest | en | 0.663397 |
http://docplayer.net/20845306-Exponential-distribution.html | 1,539,917,180,000,000,000 | text/html | crawl-data/CC-MAIN-2018-43/segments/1539583512268.20/warc/CC-MAIN-20181019020142-20181019041642-00262.warc.gz | 100,635,024 | 25,709 | # Exponential Distribution
Save this PDF as:
Size: px
Start display at page:
Download "Exponential Distribution"
## Transcription
1 Exponential Distribution Definition: Exponential distribution with parameter λ: { λe λx x 0 f(x) = 0 x < 0 The cdf: F(x) = x Mean E(X) = 1/λ. f(x)dx = Moment generating function: φ(t) = E[e tx ] = { 1 e λx x 0 0 x < 0 λ λ t, E(X 2 ) = d2 dt 2 φ(t) t=0 = 2/λ 2. V ar(x) = E(X 2 ) (E(X)) 2 = 1/λ 2. t < λ 1
2 Properties 1. Memoryless: P(X > s + t X > t) = P(X > s). = = P(X > s + t X > t) P(X > s + t,x > t) P(X > t) P(X > s + t) P(X > t) = e λ(s+t) e λt = e λs = P(X > s) Example: Suppose that the amount of time one spends in a bank is exponentially distributed with mean 10 minutes, λ = 1/10. What is the probability that a customer will spend more than 15 minutes in the bank? What is the probability that a customer will spend more than 15 minutes in the bank given that he is still in the bank after 10 minutes? Solution: P(X > 15) = e 15λ = e 3/2 = 0.22 P(X > 15 X > 10) = P(X > 5) = e 1/2 =
3 Failure rate (hazard rate) function r(t) r(t) = f(t) 1 F(t) P(X (t,t + dt) X > t) = r(t)dt. For exponential distribution: r(t) = λ, t > 0. Failure rate function uniquely determines F(t): F(t) = 1 e t 0 r(t)dt. 3
4 2. If X i, i = 1, 2,...,n, are iid exponential RVs with mean 1/λ, the pdf of n i=1 X i is: λt (λt)n 1 f X1 +X 2 + +X n (t) = λe (n 1)!, gamma distribution with parameters n and λ. 3. If X 1 and X 2 are independent exponential RVs with mean 1/λ 1, 1/λ 2, P(X 1 < X 2 ) = λ 1 λ 1 + λ If X i, i = 1, 2,...,n, are independent exponential RVs with rate µ i. Let Z = min(x 1,...,X n ) and Y = max(x 1,...,X n ). Find distribution of Z and Y. Z is an exponential RV with rate n i=1 µ i. P(Z > x) = P(min(X 1,...,X n ) > x) = P(X 1 > x,x 2 > x,...,x n > x) = P(X 1 > x)p(x 2 > x) P(X n > x) n = e µ ix = e ( n i=1 µ i )x i=1 F Y (x) = P(Y < x) = n i=1 (1 e µ ix ). 4
5 Poisson Process Counting process: Stochastic process {N(t), t 0} is a counting process if N(t) represents the total number of events that have occurred up to time t. N(t) 0 and are of integer values. N(t) is nondecreasing in t. Independent increments: the numbers of events occurred in disjoint time intervals are independent. Stationary increments: the distribution of the number of events occurred in a time interval only depends on the length of the interval and does not depend on the position. 5
6 A counting process {N(t),t 0} is a Poisson process with rate λ, λ > 0 if 1. N(0) = The process has independent increments. 3. The process has staionary increments and N(t+s) N(s) follows a Poisson distribution with parameter λt: P(N(t+s) N(s) = n) = e λt(λt)n n! Note: E[N(t + s) N(s)] = λt. E[N(t)] = E[N(t + 0) N(0)] = λt., n = 0, 1,... 6
7 Interarrival and Waiting Time Define T n as the elapsed time between (n 1)st and the nth event. {T n,n = 1, 2,...} is a sequence of interarrival times. Proposition 5.1: T n, n = 1, 2,... are independent identically distributed exponential random variables with mean 1/λ. Define S n as the waiting time for the nth event, i.e., the arrival time of the nth event. n S n = T i. Distribution of S n : i=1 λt (λt)n 1 f Sn (t) = λe (n 1)!, gamma distribution with parameters n and λ. E(S n ) = n i=1 E(T i) = n/λ. 7
8 Example: Suppose that people immigrate into a territory at a Poisson rate λ = 1 per day. (a) What is the expected time until the tenth immigrant arrives? (b) What is the probability that the elapsed time between the tenth and the eleventh arrival exceeds 2 days? Solution: Time until the 10th immigrant arrives is S 10. E(S 10 ) = 10/λ = 10. P(T 11 > 2) = e 2λ =
9 Further Properties Consider a Poisson process {N(t), t 0} with rate λ. Each event belongs to two types, I and II. The type of an event is independent of everything else. The probability of being in type I is p. Examples: female vs. male customers, good s vs. spams. Let N 1 (t) be the number of type I events up to time t. Let N 2 (t) be the number of type II events up to time t. N(t) = N 1 (t) + N 2 (t). 9
10 Proposition 5.2: {N 1 (t),t 0} and {N 2 (t),t 0} are both Poisson processes having respective rates λp and λ(1 p). Furthermore, the two processes are independent. Example: If immigrants to area A arrive at a Poisson rate of 10 per week, and if each immigrant is of English descent with probability 1/12, then what is the probability that no people of English descent will immigrate to area A during the month of February? Solution: The number of English descent immigrants arrived up to time t is N 1 (t), which is a Poisson process with mean λ/12 = 10/12. P(N 1 (4) = 0) = e (λ/12) 4 = e 10/3. 10
11 Conversely: Suppose {N 1 (t), t 0} and {N 2 (t),t 0} are independent Poisson processes having respective rates λ 1 and λ 2. Then N(t) = N 1 (t) + N 2 (t) is a Poisson process with rate λ = λ 1 + λ 2. For any event occurred with unknown type, independent of everything else, the probability of being type I is p = λ 1 λ 1 +λ 2 and type II is 1 p. Example: On a road, cars pass according to a Poisson process with rate 5 per minute. Trucks pass according to a Poisson process with rate 1 per minute. The two processes are indepdendent. If in 3 minutes, 10 veicles passed by. What is the probability that 2 of them are trucks? Solution: Each veicle is independently a car with probability = 5 6 and a truck with probability 1 6. The probability that 2 out of 10 veicles are trucks is given by the binomial distribution: ( )( ) 2 ( )
12 Conditional Distribution of Arrival Times Consider a Poisson process {N(t), t 0} with rate λ. Up to t, there is exactly one event occurred. What is the conditional distribution of T 1? Under the condition, T 1 uniformly distributes on [0,t]. Proof P(T 1 < s N(t) = 1) = P(T 1 < s, N(t) = 1) P(N(t) = 1) P(N(s) = 1,N(t) N(s) = 0) = P(N(t) = 1) P(N(s) = 1)P(N(t) N(s) = 0) = P(N(t) = 1) = (λse λs ) e λ(t s) λte λt = s Note: cdf of a uniform t 12
13 If N(t) = n, what is the joint conditional distribution of the arrival times S 1, S 2,..., S n? S 1, S 2,..., S n is the ordered statistics of n independent random variables uniformly distributed on [0,t]. Let Y 1, Y 2,..., Y n be n RVs. Y (1), Y (2),..., Y (n) is the ordered statistics of Y 1, Y 2,..., Y n if Y (k) is the kth smallest value among them. If Y i, i = 1,...,n are iid continuous RVs with pdf f, then the joint density of the ordered statistics Y (1), Y (2),..., Y (n) is f Y(1),Y (2),...,Y (n) (y 1, y 2,...,y n ) = { n! n i=1 f(y i) y 1 < y 2 < < y n 0 otherwise 13
14 We can show that Proof f(s 1, s 2,...,s n N(t) = n) = n! t n 0 < s 1 < s 2 < s n < t f(s 1, s 2,...,s n N(t) = n) = f(s 1, s 2,...,s n,n) P(N(t) = n)) = λe λs 1λe λ(s 2 s 1) λe λ(s n s n 1 ) e λ(t s n) e λt (λt) n /n! = n! t, 0 < s n 1 < < s n < t For n independent uniformly distributed RVs on [0, t], Y 1,..., Y n : f(y 1, y 2,...,y n ) = 1 t n. Proposition 5.4: Given S n = t, the arrival times S 1, S 2,..., S n 1 has the distribution of the ordered statistics of a set n 1 independent uniform (0, t) random variables. 14
15 Generalization of Poisson Process Nonhomogeneous Poisson process: The counting process {N(t), t 0} is said to be a nonhomogeneous Poisson process with intensity function λ(t), t 0 if 1. N(0) = The process has independent increments. 3. The distribution of N(t+s) N(t) is Poisson with mean given by m(t + s) m(t), where m(t) = t 0 λ(τ)dτ. We call m(t) mean value function. Poisson process is a special case where λ(t) = λ, a constant. 15
16 Compound Poisson process: A stochastic process {X(t),t 0} is said to be a compound Poisson process if it can be represented as X(t) = N(t) i=1 Y i, t 0 where {N(t),t 0} is a Poisson process and {Y i,i 0} is a family of independent and identically distributed random variables which are also independent of {N(t),t 0}. The random variable X(t) is said to be a compound Poisson random variable. Example: Suppose customers leave a supermarket in accordance with a Poisson process. If Y i, the amount spent by the ith customer, i = 1, 2,..., are independent and identically distributed, then X(t) = N(t) i=1 Y i, the total amount of money spent by customers by time t is a compound Poisson process. 16
17 Find E[X(t)] and V ar[x(t)]. E[X(t)] = λte(y 1 ). V ar[x(t)] = λt(v ar(y 1 ) + E 2 (Y 1 )) Proof N(t) E(X(t) N(t) = n) = E( = E( = E( i=1 Y i N(t) = n) n Y i N(t) = n) i=1 n Y i ) = ne(y 1 ) i=1 E(X(t)) = E N(t) E(X(t) N(t)) = P(N(t) = n)e(x(t) N(t) = n) = n=1 P(N(t) = n)ne(y 1 ) n=1 = E(Y 1 ) np(n(t) = n) n=1 = E(Y 1 )E(N(t)) = λte(y 1 ) 17
18 N(t) V ar(x(t) N(t) = n) = V ar( = V ar( = V ar( i=1 Y i N(t) = n) n Y i N(t) = n) i=1 n Y i ) i=1 = nv ar(y 1 ) V ar(x(t) N(t) = n) = E(X 2 (t) N(t) = n) (E(X(t) N(t) = n)) 2 E(X 2 (t) N(t) = n) = V ar(x(t) N(t) = n) + (E(X(t) N(t) = n)) 2 = nv ar(y 1 ) + n 2 E 2 (Y 1 ) 18
19 V ar(x(t)) = E(X 2 (t)) (E(X(t))) 2 = P(N(t) = n)e(x 2 (t) N(t) = n) (E(X(t))) 2 = n=1 P(N(t) = n)(nv ar(y 1 ) + n 2 E 2 (Y 1 )) (λte(y 1 )) 2 n=1 = V ar(y 1 )E(N(t)) + E 2 (Y 1 )E(N 2 (t)) (λte(y 1 )) 2 = λtv ar(y 1 ) + λte 2 (Y 1 ) = λt(v ar(y 1 ) + E 2 (Y 1 )) = λte(y 2 1 ) 19
### e.g. arrival of a customer to a service station or breakdown of a component in some system.
Poisson process Events occur at random instants of time at an average rate of λ events per second. e.g. arrival of a customer to a service station or breakdown of a component in some system. Let N(t) be
More information
### The Exponential Distribution
21 The Exponential Distribution From Discrete-Time to Continuous-Time: In Chapter 6 of the text we will be considering Markov processes in continuous time. In a sense, we already have a very good understanding
More information
### Renewal Theory. (iv) For s < t, N(t) N(s) equals the number of events in (s, t].
Renewal Theory Def. A stochastic process {N(t), t 0} is said to be a counting process if N(t) represents the total number of events that have occurred up to time t. X 1, X 2,... times between the events
More information
### 1 IEOR 6711: Notes on the Poisson Process
Copyright c 29 by Karl Sigman 1 IEOR 6711: Notes on the Poisson Process We present here the essentials of the Poisson point process with its many interesting properties. As preliminaries, we first define
More information
### MTH135/STA104: Probability
MTH135/STA14: Probability Homework # 8 Due: Tuesday, Nov 8, 5 Prof Robert Wolpert 1 Define a function f(x, y) on the plane R by { 1/x < y < x < 1 f(x, y) = other x, y a) Show that f(x, y) is a joint probability
More information
### Section 5.1 Continuous Random Variables: Introduction
Section 5. Continuous Random Variables: Introduction Not all random variables are discrete. For example:. Waiting times for anything (train, arrival of customer, production of mrna molecule from gene,
More information
### Notes on Continuous Random Variables
Notes on Continuous Random Variables Continuous random variables are random quantities that are measured on a continuous scale. They can usually take on any value over some interval, which distinguishes
More information
### Poisson Processes. Chapter 5. 5.1 Exponential Distribution. The gamma function is defined by. Γ(α) = t α 1 e t dt, α > 0.
Chapter 5 Poisson Processes 5.1 Exponential Distribution The gamma function is defined by Γ(α) = t α 1 e t dt, α >. Theorem 5.1. The gamma function satisfies the following properties: (a) For each α >
More information
### Department of Mathematics, Indian Institute of Technology, Kharagpur Assignment 2-3, Probability and Statistics, March 2015. Due:-March 25, 2015.
Department of Mathematics, Indian Institute of Technology, Kharagpur Assignment -3, Probability and Statistics, March 05. Due:-March 5, 05.. Show that the function 0 for x < x+ F (x) = 4 for x < for x
More information
### 6.041/6.431 Spring 2008 Quiz 2 Wednesday, April 16, 7:30-9:30 PM. SOLUTIONS
6.4/6.43 Spring 28 Quiz 2 Wednesday, April 6, 7:3-9:3 PM. SOLUTIONS Name: Recitation Instructor: TA: 6.4/6.43: Question Part Score Out of 3 all 36 2 a 4 b 5 c 5 d 8 e 5 f 6 3 a 4 b 6 c 6 d 6 e 6 Total
More information
### Lecture 7: Continuous Random Variables
Lecture 7: Continuous Random Variables 21 September 2005 1 Our First Continuous Random Variable The back of the lecture hall is roughly 10 meters across. Suppose it were exactly 10 meters, and consider
More information
### 6. Jointly Distributed Random Variables
6. Jointly Distributed Random Variables We are often interested in the relationship between two or more random variables. Example: A randomly chosen person may be a smoker and/or may get cancer. Definition.
More information
### 5. Continuous Random Variables
5. Continuous Random Variables Continuous random variables can take any value in an interval. They are used to model physical characteristics such as time, length, position, etc. Examples (i) Let X be
More information
### Overview of Monte Carlo Simulation, Probability Review and Introduction to Matlab
Monte Carlo Simulation: IEOR E4703 Fall 2004 c 2004 by Martin Haugh Overview of Monte Carlo Simulation, Probability Review and Introduction to Matlab 1 Overview of Monte Carlo Simulation 1.1 Why use simulation?
More information
### Statistics 100A Homework 7 Solutions
Chapter 6 Statistics A Homework 7 Solutions Ryan Rosario. A television store owner figures that 45 percent of the customers entering his store will purchase an ordinary television set, 5 percent will purchase
More information
### Definition 6.1.1. A r.v. X has a normal distribution with mean µ and variance σ 2, where µ R, and σ > 0, if its density is f(x) = 1. 2σ 2.
Chapter 6 Brownian Motion 6. Normal Distribution Definition 6... A r.v. X has a normal distribution with mean µ and variance σ, where µ R, and σ > 0, if its density is fx = πσ e x µ σ. The previous definition
More information
### IEOR 6711: Stochastic Models, I Fall 2012, Professor Whitt, Final Exam SOLUTIONS
IEOR 6711: Stochastic Models, I Fall 2012, Professor Whitt, Final Exam SOLUTIONS There are four questions, each with several parts. 1. Customers Coming to an Automatic Teller Machine (ATM) (30 points)
More information
### Practice problems for Homework 11 - Point Estimation
Practice problems for Homework 11 - Point Estimation 1. (10 marks) Suppose we want to select a random sample of size 5 from the current CS 3341 students. Which of the following strategies is the best:
More information
### Joint Exam 1/P Sample Exam 1
Joint Exam 1/P Sample Exam 1 Take this practice exam under strict exam conditions: Set a timer for 3 hours; Do not stop the timer for restroom breaks; Do not look at your notes. If you believe a question
More information
### CHAPTER 6: Continuous Uniform Distribution: 6.1. Definition: The density function of the continuous random variable X on the interval [A, B] is.
Some Continuous Probability Distributions CHAPTER 6: Continuous Uniform Distribution: 6. Definition: The density function of the continuous random variable X on the interval [A, B] is B A A x B f(x; A,
More information
### Maximum Likelihood Estimation
Math 541: Statistical Theory II Lecturer: Songfeng Zheng Maximum Likelihood Estimation 1 Maximum Likelihood Estimation Maximum likelihood is a relatively simple method of constructing an estimator for
More information
### Probability Generating Functions
page 39 Chapter 3 Probability Generating Functions 3 Preamble: Generating Functions Generating functions are widely used in mathematics, and play an important role in probability theory Consider a sequence
More information
### 6.263/16.37: Lectures 5 & 6 Introduction to Queueing Theory
6.263/16.37: Lectures 5 & 6 Introduction to Queueing Theory Massachusetts Institute of Technology Slide 1 Packet Switched Networks Messages broken into Packets that are routed To their destination PS PS
More information
### UNIT I: RANDOM VARIABLES PART- A -TWO MARKS
UNIT I: RANDOM VARIABLES PART- A -TWO MARKS 1. Given the probability density function of a continuous random variable X as follows f(x) = 6x (1-x) 0
More information
### MATH4427 Notebook 2 Spring 2016. 2 MATH4427 Notebook 2 3. 2.1 Definitions and Examples... 3. 2.2 Performance Measures for Estimators...
MATH4427 Notebook 2 Spring 2016 prepared by Professor Jenny Baglivo c Copyright 2009-2016 by Jenny A. Baglivo. All Rights Reserved. Contents 2 MATH4427 Notebook 2 3 2.1 Definitions and Examples...................................
More information
### What is Statistics? Lecture 1. Introduction and probability review. Idea of parametric inference
0. 1. Introduction and probability review 1.1. What is Statistics? What is Statistics? Lecture 1. Introduction and probability review There are many definitions: I will use A set of principle and procedures
More information
### 3. Renewal Theory. Definition 3 of the Poisson process can be generalized: Let X 1, X 2,..., iidf(x) be non-negative interarrival times.
3. Renewal Theory Definition 3 of the Poisson process can be generalized: Let X 1, X 2,..., iidf(x) be non-negative interarrival times. Set S n = n i=1 X i and N(t) = max {n : S n t}. Then {N(t)} is a
More information
### 2WB05 Simulation Lecture 8: Generating random variables
2WB05 Simulation Lecture 8: Generating random variables Marko Boon http://www.win.tue.nl/courses/2wb05 January 7, 2013 Outline 2/36 1. How do we generate random variables? 2. Fitting distributions Generating
More information
### Example: 1. You have observed that the number of hits to your web site follow a Poisson distribution at a rate of 2 per day.
16 The Exponential Distribution Example: 1. You have observed that the number of hits to your web site follow a Poisson distribution at a rate of 2 per day. Let T be the time (in days) between hits. 2.
More information
### MASSACHUSETTS INSTITUTE OF TECHNOLOGY 6.436J/15.085J Fall 2008 Lecture 5 9/17/2008 RANDOM VARIABLES
MASSACHUSETTS INSTITUTE OF TECHNOLOGY 6.436J/15.085J Fall 2008 Lecture 5 9/17/2008 RANDOM VARIABLES Contents 1. Random variables and measurable functions 2. Cumulative distribution functions 3. Discrete
More information
### Probability density function : An arbitrary continuous random variable X is similarly described by its probability density function f x = f X
Week 6 notes : Continuous random variables and their probability densities WEEK 6 page 1 uniform, normal, gamma, exponential,chi-squared distributions, normal approx'n to the binomial Uniform [,1] random
More information
### Principle of Data Reduction
Chapter 6 Principle of Data Reduction 6.1 Introduction An experimenter uses the information in a sample X 1,..., X n to make inferences about an unknown parameter θ. If the sample size n is large, then
More information
### STAT 315: HOW TO CHOOSE A DISTRIBUTION FOR A RANDOM VARIABLE
STAT 315: HOW TO CHOOSE A DISTRIBUTION FOR A RANDOM VARIABLE TROY BUTLER 1. Random variables and distributions We are often presented with descriptions of problems involving some level of uncertainty about
More information
### Introduction to Probability Theory for Graduate Economics. Fall 2008
Introduction to Probability Theory for Graduate Economics Fall 2008 Yiğit Sağlam December 1, 2008 CHAPTER 5 - STOCHASTIC PROCESSES 1 Stochastic Processes A stochastic process, or sometimes a random process,
More information
### Worked examples Random Processes
Worked examples Random Processes Example 1 Consider patients coming to a doctor s office at random points in time. Let X n denote the time (in hrs) that the n th patient has to wait before being admitted
More information
### Lecture Notes 1. Brief Review of Basic Probability
Probability Review Lecture Notes Brief Review of Basic Probability I assume you know basic probability. Chapters -3 are a review. I will assume you have read and understood Chapters -3. Here is a very
More information
### Chapter 4 Expected Values
Chapter 4 Expected Values 4. The Expected Value of a Random Variables Definition. Let X be a random variable having a pdf f(x). Also, suppose the the following conditions are satisfied: x f(x) converges
More information
### STAT 830 Convergence in Distribution
STAT 830 Convergence in Distribution Richard Lockhart Simon Fraser University STAT 830 Fall 2011 Richard Lockhart (Simon Fraser University) STAT 830 Convergence in Distribution STAT 830 Fall 2011 1 / 31
More information
### Continuous Probability Distributions (120 Points)
Economics : Statistics for Economics Problem Set 5 - Suggested Solutions University of Notre Dame Instructor: Julio Garín Spring 22 Continuous Probability Distributions 2 Points. A management consulting
More information
### Generating Random Variables and Stochastic Processes
Monte Carlo Simulation: IEOR E4703 c 2010 by Martin Haugh Generating Random Variables and Stochastic Processes In these lecture notes we describe the principal methods that are used to generate random
More information
### Stats on the TI 83 and TI 84 Calculator
Stats on the TI 83 and TI 84 Calculator Entering the sample values STAT button Left bracket { Right bracket } Store (STO) List L1 Comma Enter Example: Sample data are {5, 10, 15, 20} 1. Press 2 ND and
More information
### Probability Distribution
Lecture 4 Probability Distribution Continuous Case Definition: A random variable that can take on any value in an interval is called continuous. Definition: Let Y be any r.v. The distribution function
More information
### Chapters 5. Multivariate Probability Distributions
Chapters 5. Multivariate Probability Distributions Random vectors are collection of random variables defined on the same sample space. Whenever a collection of random variables are mentioned, they are
More information
### Manual for SOA Exam MLC.
Chapter 11. Poisson processes. Section 11.4. Superposition and decomposition of a Poisson process. Extract from: Arcones Fall 2009 Edition, available at http://www.actexmadriver.com/ 1/18 Superposition
More information
### LECTURE 16. Readings: Section 5.1. Lecture outline. Random processes Definition of the Bernoulli process Basic properties of the Bernoulli process
LECTURE 16 Readings: Section 5.1 Lecture outline Random processes Definition of the Bernoulli process Basic properties of the Bernoulli process Number of successes Distribution of interarrival times The
More information
### ISyE 6650 Probabilistic Models Fall Homework 5 Solution
ISyE 6650 Probabilistic Models Fall 2007 Homework 5 Solution 1. (Ross 5.3) Due to the memoryless property of the exponential distribution, the conditional distribution of X, given that X > 1, is the same
More information
### For a partition B 1,..., B n, where B i B j = for i. A = (A B 1 ) (A B 2 ),..., (A B n ) and thus. P (A) = P (A B i ) = P (A B i )P (B i )
Probability Review 15.075 Cynthia Rudin A probability space, defined by Kolmogorov (1903-1987) consists of: A set of outcomes S, e.g., for the roll of a die, S = {1, 2, 3, 4, 5, 6}, 1 1 2 1 6 for the roll
More information
### ECE302 Spring 2006 HW5 Solutions February 21, 2006 1
ECE3 Spring 6 HW5 Solutions February 1, 6 1 Solutions to HW5 Note: Most of these solutions were generated by R. D. Yates and D. J. Goodman, the authors of our textbook. I have added comments in italics
More information
### INSURANCE RISK THEORY (Problems)
INSURANCE RISK THEORY (Problems) 1 Counting random variables 1. (Lack of memory property) Let X be a geometric distributed random variable with parameter p (, 1), (X Ge (p)). Show that for all n, m =,
More information
### 4 The M/M/1 queue. 4.1 Time-dependent behaviour
4 The M/M/1 queue In this chapter we will analyze the model with exponential interarrival times with mean 1/λ, exponential service times with mean 1/µ and a single server. Customers are served in order
More information
### M/M/1 and M/M/m Queueing Systems
M/M/ and M/M/m Queueing Systems M. Veeraraghavan; March 20, 2004. Preliminaries. Kendall s notation: G/G/n/k queue G: General - can be any distribution. First letter: Arrival process; M: memoryless - exponential
More information
### Aggregate Loss Models
Aggregate Loss Models Chapter 9 Stat 477 - Loss Models Chapter 9 (Stat 477) Aggregate Loss Models Brian Hartman - BYU 1 / 22 Objectives Objectives Individual risk model Collective risk model Computing
More information
### Optimization of Business Processes: An Introduction to Applied Stochastic Modeling. Ger Koole Department of Mathematics, VU University Amsterdam
Optimization of Business Processes: An Introduction to Applied Stochastic Modeling Ger Koole Department of Mathematics, VU University Amsterdam Version of March 30, 2010 c Ger Koole, 1998 2010. These lecture
More information
### Contents. TTM4155: Teletraffic Theory (Teletrafikkteori) Probability Theory Basics. Yuming Jiang. Basic Concepts Random Variables
TTM4155: Teletraffic Theory (Teletrafikkteori) Probability Theory Basics Yuming Jiang 1 Some figures taken from the web. Contents Basic Concepts Random Variables Discrete Random Variables Continuous Random
More information
### Modeling and Analysis of Information Technology Systems
Modeling and Analysis of Information Technology Systems Dr. János Sztrik University of Debrecen, Faculty of Informatics Reviewers: Dr. József Bíró Doctor of the Hungarian Academy of Sciences, Full Professor
More information
### Poisson processes (and mixture distributions)
Poisson processes (and mixture distributions) James W. Daniel Austin Actuarial Seminars www.actuarialseminars.com June 26, 2008 c Copyright 2007 by James W. Daniel; reproduction in whole or in part without
More information
### Discrete and Continuous Random Variables. Summer 2003
Discrete and Continuous Random Variables Summer 003 Random Variables A random variable is a rule that assigns a numerical value to each possible outcome of a probabilistic experiment. We denote a random
More information
### Tenth Problem Assignment
EECS 40 Due on April 6, 007 PROBLEM (8 points) Dave is taking a multiple-choice exam. You may assume that the number of questions is infinite. Simultaneously, but independently, his conscious and subconscious
More information
### Statistics 100A Homework 8 Solutions
Part : Chapter 7 Statistics A Homework 8 Solutions Ryan Rosario. A player throws a fair die and simultaneously flips a fair coin. If the coin lands heads, then she wins twice, and if tails, the one-half
More information
### Generating Random Variables and Stochastic Processes
Monte Carlo Simulation: IEOR E4703 Fall 2004 c 2004 by Martin Haugh Generating Random Variables and Stochastic Processes 1 Generating U(0,1) Random Variables The ability to generate U(0, 1) random variables
More information
### Chapter 4. Multivariate Distributions
1 Chapter 4. Multivariate Distributions Joint p.m.f. (p.d.f.) Independent Random Variables Covariance and Correlation Coefficient Expectation and Covariance Matrix Multivariate (Normal) Distributions Matlab
More information
### Asymptotics of discounted aggregate claims for renewal risk model with risky investment
Appl. Math. J. Chinese Univ. 21, 25(2: 29-216 Asymptotics of discounted aggregate claims for renewal risk model with risky investment JIANG Tao Abstract. Under the assumption that the claim size is subexponentially
More information
### Performance Analysis of Computer Systems
Performance Analysis of Computer Systems Introduction to Queuing Theory Holger Brunst (holger.brunst@tu-dresden.de) Matthias S. Mueller (matthias.mueller@tu-dresden.de) Summary of Previous Lecture Simulation
More information
### Sufficient Statistics and Exponential Family. 1 Statistics and Sufficient Statistics. Math 541: Statistical Theory II. Lecturer: Songfeng Zheng
Math 541: Statistical Theory II Lecturer: Songfeng Zheng Sufficient Statistics and Exponential Family 1 Statistics and Sufficient Statistics Suppose we have a random sample X 1,, X n taken from a distribution
More information
### Using pivots to construct confidence intervals. In Example 41 we used the fact that
Using pivots to construct confidence intervals In Example 41 we used the fact that Q( X, µ) = X µ σ/ n N(0, 1) for all µ. We then said Q( X, µ) z α/2 with probability 1 α, and converted this into a statement
More information
### Lecture 6: Discrete & Continuous Probability and Random Variables
Lecture 6: Discrete & Continuous Probability and Random Variables D. Alex Hughes Math Camp September 17, 2015 D. Alex Hughes (Math Camp) Lecture 6: Discrete & Continuous Probability and Random September
More information
### Math 461 Fall 2006 Test 2 Solutions
Math 461 Fall 2006 Test 2 Solutions Total points: 100. Do all questions. Explain all answers. No notes, books, or electronic devices. 1. [105+5 points] Assume X Exponential(λ). Justify the following two
More information
### Final Mathematics 5010, Section 1, Fall 2004 Instructor: D.A. Levin
Final Mathematics 51, Section 1, Fall 24 Instructor: D.A. Levin Name YOU MUST SHOW YOUR WORK TO RECEIVE CREDIT. A CORRECT ANSWER WITHOUT SHOWING YOUR REASONING WILL NOT RECEIVE CREDIT. Problem Points Possible
More information
### Stat 515 Midterm Examination II April 6, 2010 (9:30 a.m. - 10:45 a.m.)
Name: Stat 515 Midterm Examination II April 6, 2010 (9:30 a.m. - 10:45 a.m.) The total score is 100 points. Instructions: There are six questions. Each one is worth 20 points. TA will grade the best five
More information
### ST 371 (VIII): Theory of Joint Distributions
ST 371 (VIII): Theory of Joint Distributions So far we have focused on probability distributions for single random variables. However, we are often interested in probability statements concerning two or
More information
### Continuous Random Variables
Continuous Random Variables COMP 245 STATISTICS Dr N A Heard Contents 1 Continuous Random Variables 2 11 Introduction 2 12 Probability Density Functions 3 13 Transformations 5 2 Mean, Variance and Quantiles
More information
### University of California, Berkeley, Statistics 134: Concepts of Probability
University of California, Berkeley, Statistics 134: Concepts of Probability Michael Lugo, Spring 211 Exam 2 solutions 1. A fair twenty-sided die has its faces labeled 1, 2, 3,..., 2. The die is rolled
More information
### P(X = x k ) = 1 = k=1
74 CHAPTER 6. IMPORTANT DISTRIBUTIONS AND DENSITIES 6.2 Problems 5.1.1 Which are modeled with a unifm distribution? (a Yes, P(X k 1/6 f k 1,...,6. (b No, this has a binomial distribution. (c Yes, P(X k
More information
### General theory of stochastic processes
CHAPTER 1 General theory of stochastic processes 1.1. Definition of stochastic process First let us recall the definition of a random variable. A random variable is a random number appearing as a result
More information
### UNIFORM ASYMPTOTICS FOR DISCOUNTED AGGREGATE CLAIMS IN DEPENDENT RISK MODELS
Applied Probability Trust 2 October 2013 UNIFORM ASYMPTOTICS FOR DISCOUNTED AGGREGATE CLAIMS IN DEPENDENT RISK MODELS YANG YANG, Nanjing Audit University, and Southeast University KAIYONG WANG, Southeast
More information
### Lecture 4: Random Variables
Lecture 4: Random Variables 1. Definition of Random variables 1.1 Measurable functions and random variables 1.2 Reduction of the measurability condition 1.3 Transformation of random variables 1.4 σ-algebra
More information
### Some special discrete probability distributions
University of California, Los Angeles Department of Statistics Statistics 100A Instructor: Nicolas Christou Some special discrete probability distributions Bernoulli random variable: It is a variable that
More information
### A Uniform Asymptotic Estimate for Discounted Aggregate Claims with Subexponential Tails
12th International Congress on Insurance: Mathematics and Economics July 16-18, 2008 A Uniform Asymptotic Estimate for Discounted Aggregate Claims with Subexponential Tails XUEMIAO HAO (Based on a joint
More information
### 1 Geometric Brownian motion
Copyright c 006 by Karl Sigman Geometric Brownian motion Note that since BM can take on negative values, using it directly for modeling stock prices is questionable. There are other reasons too why BM
More information
### Section 6.1 Joint Distribution Functions
Section 6.1 Joint Distribution Functions We often care about more than one random variable at a time. DEFINITION: For any two random variables X and Y the joint cumulative probability distribution function
More information
### 1.1 Introduction, and Review of Probability Theory... 3. 1.1.1 Random Variable, Range, Types of Random Variables... 3. 1.1.2 CDF, PDF, Quantiles...
MATH4427 Notebook 1 Spring 2016 prepared by Professor Jenny Baglivo c Copyright 2009-2016 by Jenny A. Baglivo. All Rights Reserved. Contents 1 MATH4427 Notebook 1 3 1.1 Introduction, and Review of Probability
More information
### Continuous random variables
Continuous random variables So far we have been concentrating on discrete random variables, whose distributions are not continuous. Now we deal with the so-called continuous random variables. A random
More information
### Homework 4 - KEY. Jeff Brenion. June 16, 2004. Note: Many problems can be solved in more than one way; we present only a single solution here.
Homework 4 - KEY Jeff Brenion June 16, 2004 Note: Many problems can be solved in more than one way; we present only a single solution here. 1 Problem 2-1 Since there can be anywhere from 0 to 4 aces, the
More information
### Solution Using the geometric series a/(1 r) = x=1. x=1. Problem For each of the following distributions, compute
Math 472 Homework Assignment 1 Problem 1.9.2. Let p(x) 1/2 x, x 1, 2, 3,..., zero elsewhere, be the pmf of the random variable X. Find the mgf, the mean, and the variance of X. Solution 1.9.2. Using the
More information
### Master s Theory Exam Spring 2006
Spring 2006 This exam contains 7 questions. You should attempt them all. Each question is divided into parts to help lead you through the material. You should attempt to complete as much of each problem
More information
### 3 Multiple Discrete Random Variables
3 Multiple Discrete Random Variables 3.1 Joint densities Suppose we have a probability space (Ω, F,P) and now we have two discrete random variables X and Y on it. They have probability mass functions f
More information
### Continuous Random Variables and Probability Distributions. Stat 4570/5570 Material from Devore s book (Ed 8) Chapter 4 - and Cengage
4 Continuous Random Variables and Probability Distributions Stat 4570/5570 Material from Devore s book (Ed 8) Chapter 4 - and Cengage Continuous r.v. A random variable X is continuous if possible values
More information
### POISSON PROCESS AND INSURANCE : AN INTRODUCTION 1
POISSON PROCESS AND INSURANCE : AN INTRODUCTION S.RAMASUBRAMANIAN Statistics and Mathematics Unit Indian Statistical Institute 8th Mile, Mysore Road Bangalore - 560059. Abstract: Basic aspects of the classical
More information
### STAT 430/510 Probability Lecture 14: Joint Probability Distribution, Continuous Case
STAT 430/510 Probability Lecture 14: Joint Probability Distribution, Continuous Case Pengyuan (Penelope) Wang June 20, 2011 Joint density function of continuous Random Variable When X and Y are two continuous
More information
### CHAPTER IV - BROWNIAN MOTION
CHAPTER IV - BROWNIAN MOTION JOSEPH G. CONLON 1. Construction of Brownian Motion There are two ways in which the idea of a Markov chain on a discrete state space can be generalized: (1) The discrete time
More information
### CSE 312, 2011 Winter, W.L.Ruzzo. 7. continuous random variables
CSE 312, 2011 Winter, W.L.Ruzzo 7. continuous random variables continuous random variables Discrete random variable: takes values in a finite or countable set, e.g. X {1,2,..., 6} with equal probability
More information
### P(a X b) = f X (x)dx. A p.d.f. must integrate to one: f X (x)dx = 1. Z b
Continuous Random Variables The probability that a continuous random variable, X, has a value between a and b is computed by integrating its probability density function (p.d.f.) over the interval [a,b]:
More information
### 1 Sufficient statistics
1 Sufficient statistics A statistic is a function T = rx 1, X 2,, X n of the random sample X 1, X 2,, X n. Examples are X n = 1 n s 2 = = X i, 1 n 1 the sample mean X i X n 2, the sample variance T 1 =
More information
### RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS
RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS. DISCRETE RANDOM VARIABLES.. Definition of a Discrete Random Variable. A random variable X is said to be discrete if it can assume only a finite or countable
More information
### A note on the distribution of the aggregate claim amount at ruin
A note on the distribution of the aggregate claim amount at ruin Jingchao Li, David C M Dickson, Shuanming Li Centre for Actuarial Studies, Department of Economics, University of Melbourne, VIC 31, Australia
More information
### ECE302 Spring 2006 HW7 Solutions March 11, 2006 1
ECE32 Spring 26 HW7 Solutions March, 26 Solutions to HW7 Note: Most of these solutions were generated by R. D. Yates and D. J. Goodman, the authors of our textbook. I have added comments in italics where
More information
### ST 371 (IV): Discrete Random Variables
ST 371 (IV): Discrete Random Variables 1 Random Variables A random variable (rv) is a function that is defined on the sample space of the experiment and that assigns a numerical variable to each possible
More information
### Homework set 4 - Solutions
Homework set 4 - Solutions Math 495 Renato Feres Problems R for continuous time Markov chains The sequence of random variables of a Markov chain may represent the states of a random system recorded at
More information
### Performance Analysis of a Telephone System with both Patient and Impatient Customers
Performance Analysis of a Telephone System with both Patient and Impatient Customers Yiqiang Quennel Zhao Department of Mathematics and Statistics University of Winnipeg Winnipeg, Manitoba Canada R3B 2E9
More information
### Queueing Systems. Ivo Adan and Jacques Resing
Queueing Systems Ivo Adan and Jacques Resing Department of Mathematics and Computing Science Eindhoven University of Technology P.O. Box 513, 5600 MB Eindhoven, The Netherlands March 26, 2015 Contents
More information | 10,372 | 38,353 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.28125 | 4 | CC-MAIN-2018-43 | longest | en | 0.723461 |
https://branemrys.blogspot.com/2017/02/evening-note-for-wednesday-february-22.html | 1,575,753,406,000,000,000 | text/html | crawl-data/CC-MAIN-2019-51/segments/1575540502120.37/warc/CC-MAIN-20191207210620-20191207234620-00316.warc.gz | 300,479,130 | 31,089 | ## Wednesday, February 22, 2017
### Evening Note for Wednesday, February 22
Thought for the Evening
'Fitch's Knowability Paradox', which derives from some common assumptions about knowledge is usually summarized in the predicate calculus as:
∀p(p → ◊Kp) ⊢ ∀p(p → Kp)
This is usually summarized in much the way the SEP article by Brogaard and Salerno on the paradox does: "It tells us that if any truth can be known then every truth is in fact known." Hence the 'knowability'.
However, this way of summarizing it introduces more confusion than it should, because ◊Kp does not mean 'p is knowable' in the way we usually mean knowable. It means 'it is possible that that p is known'. This doesn't undo the paradox -- that if it is possible that a truth is known, that truth is known, which is not something one would immediately expect. But 'knowable' in ordinary discourse doesn't mean 'it is possible that it is known'; it means 'it can be known' or even 'it can come to be known', neither of which would usually be understood as saying the same thing as 'it is possible that it is in fact known'. What the paradox actually says is that, if you accept some very common things people believe about knowledge, then if there is any proposition that has the feature that when it is true, it is possible that it is known, then it must be the case that when it is true, it is indeed known. This is very different from the usual summary. As I once noted on this blog (so long ago in ancient days of yore that I was still in graduate school):
I already said that the result is usually put in terms of knowability: KP [i.e., the left hand side above] is usually read, "If p is true, it is knowable." I translated differently, as you can see. This is because I think "knowable" is a very bad translation of the double operator, ◊K. To see this, think about what we really mean when we say the following two things:
This is knowable: The sky is blue.
It is possible that this is known: The sky is blue.
The two are not equivalent, and for good reason. The English word 'knowable' in all but a very small handful of uses hides a third operator, a temporal operator -- an incipit, to be exact:
This can come to be known (can begin to be known): The sky is blue.
So when I say that some claim is knowable, I usually don't mean that it is possible that it is known; I mean that it is possible that it could come to be known. So I think there's reason to stay away from the added complications that are introduced by the word 'knowable'. Using 'knowable' makes it sound even more paradoxical; but (1) it doesn't need to be made to sound more paradoxical; and (2) it is misleading.
(An incipit operator is an operator that tells us that something begins to be; incipit [it begins] and desinit [it ends] were modal operators that medieval logicians studied quite a bit but people nowadays not so much.)
This is not to say that the use of 'knowable' in this context is illegitimate; you can see why someone might use knowable to mean ◊K -- after all, K is knowledge and ◊ is possibility, so 'knowable' could be used to mean 'it is possible that it is known'. Possibly one could even find occasional conversational cases in which it is. But it's not usually. And one can tell from summaries that even philosophers regularly slip from the strictly correct, 'it is possible that it is known', to 'it can be known', and even 'it can come to be known'; you can tell this from their colloquial descriptions of what they think their results show. But these are different modalities from ◊K.
Mixing any modalities is very, very tricky; but ◊ and K, possibility and knowledge, are especially so, and it is often difficult to keep straight about how we are to understand them, and about the rules of inference we are using. In real life, when we are talking about knowledge, we are usually in fact talking about coming to know or having come to know; but the standard epistemic logic just talks about being known. There are lots of ways the difference can throw off interpretations.
This was all brought to mind thinking about Rutten's modal-epistemic argument for God's existence (PDF), which Red brought up in comments here a couple weeks back:
1. For all p, if p is unknowable, then p is necessarily false (first premise; the principle),
2. The proposition ‘God does not exist’ is necessarily unknowable (second premise),
3. Therefore, ‘God does not exist’ is necessarily false (from both premises)
4. Therefore, necessarily, God exists (conclusion; from (3)).
If someone is going to evaluate this, they have to be clear about what 'unknowable' means. Does it mean ~◊K, i.e,. 'it is not possible that it is known'? Does it mean 'it is impossible to come to know it'? Does it mean 'it is not such that it can be known'? And so forth. And it gets a bit worse, because (2) talks about 'necessarily unknowable'. So if we were to interpret 'knowable' as it would usually be interpreted in common conversation, we might have a whole string of at least 4 modal operators in one proposition: (1) it is necessary that (2) one cannot (3) begin (4) to know p. That's not necessarily how it would have to be understood; but you can see how it would be important to keep straight on exactly how you do understand it.
All of this is just interpretive; it doesn't directly give us a line on how to evaluate either Fitch's Paradox or Rutten's modal-epistemic argument. But it's good to avoid making such evaluation harder than it needs to be.
* Joseph Millum, The Foundation of the Child's Right to an Open Future. I discussed this topic here. Millum's is a good, and very thorough discussion of some problems with the notion.
* Tristan Haze, The Resurgence of Metaphysics as a Notational Convenience. I'm very interested, of course, in accounts of how philosophical scenes get transformed, how ideas transmogrify, and the like. This hypothesis for the rise of analytic metaphysics makes considerable amount of sense, and is probably true.
* Ellen Carmichael, Lafayette's America, on America's French Founding Father. | 1,420 | 6,095 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.828125 | 3 | CC-MAIN-2019-51 | latest | en | 0.979785 |
http://www.slideshare.net/dotsa26/statistics-statistical-investigations-workshop-1 | 1,469,329,664,000,000,000 | text/html | crawl-data/CC-MAIN-2016-30/segments/1469257823935.18/warc/CC-MAIN-20160723071023-00136-ip-10-185-27-174.ec2.internal.warc.gz | 707,180,144 | 31,210 | Upcoming SlideShare
×
# Statistics- Statistical Investigations Workshop 1
9,554 views
9,237 views
Published on
The first of two workshops I've created for children in my class about statistical investigations. This is used as a rotation activity after I have done some teaching on it first.
5 Likes
Statistics
Notes
• Full Name
Comment goes here.
Are you sure you want to Yes No
• Be the first to comment
Views
Total views
9,554
On SlideShare
0
From Embeds
0
Number of Embeds
617
Actions
Shares
0
235
0
Likes
5
Embeds 0
No embeds
No notes for slide
### Statistics- Statistical Investigations Workshop 1
1. 1. Statistics:<br />The Data Detective <br />Process<br /> Workshop<br />
2. 2. First Things First<br /><ul><li>Write the short date in your mathematics book
3. 3. Write the title – Statistics Workshop 1 in your mathematics book
4. 4. Underline both of these in red pen</li></li></ul><li>What are we learning?<br /><ul><li>We are learning to:
5. 5. Use a statistical investigation process with guidance
6. 6. Identify parts of the statistical investigation process and what we need to do to complete them
7. 7. Create our own statistical investigations</li></li></ul><li>What are we going to do?<br /><ul><li>In this workshop we will:
8. 8. Work through the data detective process using a simple example
9. 9. Evaluate parts of the process using examples
10. 10. Try out the process ourselves</li></li></ul><li>Are You A Data Detective?<br />Have a look at the poster below, with a buddy talk about the different parts… what do they mean? How would you complete them?<br />
11. 11. The Problem<br />This is the first step of the data detective process. We define our problem or our question. We think about how we are going to answer the question<br />Here’s our problem: (this is a make believe problem)<br />We want to start selling sandwiches for lunch at Hillpark we don’t know how many students will buy and what they will pay for them. We also want to know what days to sell them on.<br />What could we do to help us to answer or solve this problem? Write some ideas down in your mathematics book and share them with your group.<br />
12. 12. The Problem<br />You might have come up with these answers or some different ones…<br />Come up with questions you could ask students about sandwiches<br />Ask lots of students about buying sandwiches<br />Create a survey for students<br />Create a survey for parents<br />Ask students and parents at the school gate.<br />
13. 13. The Plan<br />The plan involves working out what you are going to do to solve the problem. Deciding what you will measure and how you will measure it. You also need to decide how you will collect and record your data.<br />Here are some steps we could take to plan to solve our sandwich problem:<br />Decide on three questions to ask students<br />Set up a survey form to use when asking students questions<br />Get the students to answer the questions<br />Aim for at least ¼ of students<br />What three questions should we ask to solve our problem? How will we know we have the answer to our problem. Talk about this with your buddy.<br />
14. 14. The Plan<br />Here are some questions that you might have come up with to help us to solve the problem . . .<br />Would you buy a sandwich for lunch? Yes/No<br />What day would you be most likely to buy a sandwich on? Monday/Tuesday/Wednesday/Thursday/Friday<br />How much would you be willing to pay for a sandwich?<br />\$1-2<br />\$3-4<br />\$5+<br />We will know that we have solved the problem when we can say yes lets sell sandwiches because… or no lets not sell sandwiches because… and be able to give a reason for our answer.<br />
15. 15. The Data<br />This step involves the collection of the data, thinking about how far we have come and how much more we need to do. It also means we have to make sure the data is true and correct.<br />When we are collecting our data we need to store it somehow. This time we are going to use our survey sheet from the previous slide.<br />Use the survey sheet to collect data on three classmates that are not in your mathematics group. Remember to make sure the are answering truthfully. Make sure each classmate is only asked once.<br />
16. 16. The Data<br />Once you’ve collected all of your data you need to store it in the same place. Put all of the data your group has collected together.<br />Once you have all of your data ready move to the next slide.<br />
17. 17. The Analysis<br />This step involves sorting and presenting your data in a useable format. This is where we decide how to present the information so that we can solve our problem.<br />We are going to use three different bar graphs to present the data we have collected. There are a number of things that a bar graph must have so that other people can read what it says.<br />What do we need to have in our bar graphs? Think about this with a buddy and write your answers into your mathematics book.<br />
18. 18. The Analysis<br />We need to make sure we have the right graph for presenting our data and that we are able to use the graph successfully.<br />For a bar graph you need to have the following:<br /><ul><li>A graph title
19. 19. Labels for each axis
20. 20. An appropriate scale on the Y axis (the right numbers)
21. 21. Labels for each bar
22. 22. Gaps between the bars
23. 23. A ruler is used to draw the lines on the graph</li></ul>Draw the bar graphs for each question you have asked your classmates. Take a peak at the next slide if you’re unsure where to start<br />
24. 24. The Analysis<br />Here are examples of what you might have created for each graph.<br /> | 1,372 | 5,650 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.515625 | 4 | CC-MAIN-2016-30 | latest | en | 0.861135 |
https://www.cs.purdue.edu/homes/dgleich/cs515-2018/homeworks/homework-10.html | 1,550,663,220,000,000,000 | text/html | crawl-data/CC-MAIN-2019-09/segments/1550247494741.0/warc/CC-MAIN-20190220105613-20190220131613-00526.warc.gz | 804,746,746 | 5,071 | $\newcommand{\eps}{\varepsilon} \newcommand{\kron}{\otimes} \DeclareMathOperator{\diag}{diag} \DeclareMathOperator{\trace}{trace} \DeclareMathOperator{\rank}{rank} \DeclareMathOperator*{\minimize}{minimize} \DeclareMathOperator*{\maximize}{maximize} \DeclareMathOperator{\subjectto}{subject to} \newcommand{\mat}[1]{\boldsymbol{#1}} \renewcommand{\vec}[1]{\boldsymbol{\mathrm{#1}}} \newcommand{\vecalt}[1]{\boldsymbol{#1}} \newcommand{\conj}[1]{\overline{#1}} \newcommand{\normof}[1]{\|#1\|} \newcommand{\onormof}[2]{\|#1\|_{#2}} \newcommand{\MIN}[2]{\begin{array}{ll} \minimize_{#1} & {#2} \end{array}} \newcommand{\MINone}[3]{\begin{array}{ll} \minimize_{#1} & {#2} \\ \subjectto & {#3} \end{array}} \newcommand{\MINthree}[5]{\begin{array}{ll} \minimize_{#1} & {#2} \\ \subjectto & {#3} \\ & {#4} \\ & {#5} \end{array}} \newcommand{\MAX}[2]{\begin{array}{ll} \maximize_{#1} & {#2} \end{array}} \newcommand{\MAXone}[3]{\begin{array}{ll} \maximize_{#1} & {#2} \\ \subjectto & {#3} \end{array}} \newcommand{\itr}[2]{#1^{(#2)}} \newcommand{\itn}[1]{^{(#1)}} \newcommand{\prob}{\mathbb{P}} \newcommand{\probof}[1]{\prob\left\{ #1 \right\}} \newcommand{\pmat}[1]{\begin{pmatrix} #1 \end{pmatrix}} \newcommand{\bmat}[1]{\begin{bmatrix} #1 \end{bmatrix}} \newcommand{\spmat}[1]{\left(\begin{smallmatrix} #1 \end{smallmatrix}\right)} \newcommand{\sbmat}[1]{\left[\begin{smallmatrix} #1 \end{smallmatrix}\right]} \newcommand{\RR}{\mathbb{R}} \newcommand{\CC}{\mathbb{C}} \newcommand{\eye}{\mat{I}} \newcommand{\mA}{\mat{A}} \newcommand{\mB}{\mat{B}} \newcommand{\mC}{\mat{C}} \newcommand{\mD}{\mat{D}} \newcommand{\mE}{\mat{E}} \newcommand{\mF}{\mat{F}} \newcommand{\mG}{\mat{G}} \newcommand{\mH}{\mat{H}} \newcommand{\mI}{\mat{I}} \newcommand{\mJ}{\mat{J}} \newcommand{\mK}{\mat{K}} \newcommand{\mL}{\mat{L}} \newcommand{\mM}{\mat{M}} \newcommand{\mN}{\mat{N}} \newcommand{\mO}{\mat{O}} \newcommand{\mP}{\mat{P}} \newcommand{\mQ}{\mat{Q}} \newcommand{\mR}{\mat{R}} \newcommand{\mS}{\mat{S}} \newcommand{\mT}{\mat{T}} \newcommand{\mU}{\mat{U}} \newcommand{\mV}{\mat{V}} \newcommand{\mW}{\mat{W}} \newcommand{\mX}{\mat{X}} \newcommand{\mY}{\mat{Y}} \newcommand{\mZ}{\mat{Z}} \newcommand{\mLambda}{\mat{\Lambda}} \newcommand{\mSigma}{\ensuremath{\mat{\Sigma}}} \newcommand{\mPbar}{\bar{\mP}} \newcommand{\ones}{\vec{e}} \newcommand{\va}{\vec{a}} \newcommand{\vb}{\vec{b}} \newcommand{\vc}{\vec{c}} \newcommand{\vd}{\vec{d}} \newcommand{\ve}{\vec{e}} \newcommand{\vf}{\vec{f}} \newcommand{\vg}{\vec{g}} \newcommand{\vh}{\vec{h}} \newcommand{\vi}{\vec{i}} \newcommand{\vj}{\vec{j}} \newcommand{\vk}{\vec{k}} \newcommand{\vl}{\vec{l}} \newcommand{\vm}{\vec{l}} \newcommand{\vn}{\vec{n}} \newcommand{\vo}{\vec{o}} \newcommand{\vp}{\vec{p}} \newcommand{\vq}{\vec{q}} \newcommand{\vr}{\vec{r}} \newcommand{\vs}{\vec{s}} \newcommand{\vt}{\vec{t}} \newcommand{\vu}{\vec{u}} \newcommand{\vv}{\vec{v}} \newcommand{\vw}{\vec{w}} \newcommand{\vx}{\vec{x}} \newcommand{\vy}{\vec{y}} \newcommand{\vz}{\vec{z}} \newcommand{\vpi}{\vecalt{\pi}} \newcommand{\vlambda}{\vecalt{\lambda}}$
# Homework 10
Please answer the following questions in complete sentences in a clearly prepared manuscript and submit the solution by the due date on Blackboard (around Sunday, November 18th, 2018.)
Remember that this is a graduate class. There may be elements of the problem statements that require you to fill in appropriate assumptions. You are also responsible for determining what evidence to include. An answer alone is rarely sufficient, but neither is an overly verbose description required. Use your judgement to focus your discussion on the most interesting pieces. The answer to "should I include 'something' in my solution?" will almost always be: Yes, if you think it helps support your answer.
## Problem 0: Homework checklist
• Please identify anyone, whether or not they are in the class, with whom you discussed your homework. This problem is worth 1 point, but on a multiplicative scale.
• Make sure you have included your source-code and prepared your solution according to the most recent Piazza note on homework submissions.
## Problem 1: Experimenting with Lanczos-based methods.
1. Implement a Lanczos-based MINRES code that explictly builds $\mV_k, \mT_k$ and then finds the minimum residual vector within the Krylov subspace.
2. Compare the first 25 residuals from the Lanczos-based CG code we wrote in class that explictly builds $\mV_k, \mT_k$, with the a standard implementation of CG from: http://www.cs.purdue.edu/homes/dgleich/cs515-2018/homeworks/cg.jl for the linear system
n = 100
on = ones(Int64,n)
A = spdiagm((-2*on[1:end-1],4*on,-2*on[1:end-1]),(-1,0,1))
b = ones(n)
as well as the MINRES code you developed above.
3. Using the cg.jl function, look at how many iterations are required for CG to converge to a tolerance of $10^{-8}$ for the matrix in the last part. Determine how this scales with $n$.
## Problem 2: Orthogonality of Lanczos
Let $\lambda_1 = 0.1$ and $\lambda_n = 100$, $\rho = 0.9$, $n=30$.
Consider the $n$-by-$n$ matrix with diagonal elements
(This is called the Strako\v{s} matrix.)
1. Use the Lanczos method starting from a a random vector $\vv_1$ and the vector $\vv_1 = \ve/\sqrt{n}$ and then plot the quantity $\log(\normof{\mV_k^T \mV_k - \mI}+10^{-20})$ for $k=1$ to $30$. Describe what you SHOULD find and what you actually find. Do your results depend on the starting vector?
2. Plot $\log(|\vv_1^T \vv_k| + 10^{-20})$ for the $k=1$ to $30$. Also plot $\log(|\vv_{k-2}^T \vv_k| + 10^{-20})$ for $k=3$ to $30$.
3. What is $\beta_{31}?$ What should it be?
4. Plot $\log(\normof{\mA \mV_k - \mV_{k+1} \mT_{k+1}} + 10^{-20})$ for $k=1$ to $60$.
## Problem 3: Krylov methods
Let $\mA = \mI + \ve \ve^T$ be a square matrix (where $\ve$ is the column vector of all 1s of appropriate dimensions). Suppose we use MINRES to solve the system $\mA \vx = \vb$. In exact arithmetic, how many steps will MINRES take to converge to the exact solution? Be sure to explain \textit{how you determine what the answer is. Note, your result should be self contained and not utilize the theory discussed in class -- this is good practice for the final; if you do use a theorem to justify your answer, you may lose a few points.}
## Problem 4: Solving non-symmetric systems.
Note that there are few ways to turn a non-symmetric linear system into a symmetric linear system. The first is to use the normal equations $\mA^T \mA \vx = \mA^T \vb$. The second is to use a set of augmented equations:
1. Show that the solution of the augmented system of equations exists for any square, full-rank non-symmetric matrix $\mA$.
2. Use CG and MINRES to solve the Candyland linear system from the beginning of class using these approaches. How many matrix-vector products do they take compared with your Neumann series-based solver to converge to a 2-norm relative residual of $10^{-8}$. | 2,283 | 6,903 | {"found_math": true, "script_math_tex": 32, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.015625 | 3 | CC-MAIN-2019-09 | latest | en | 0.25045 |
https://marketinference.com/analysis/r/2023/08/30/NVDA/ | 1,696,320,253,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233511055.59/warc/CC-MAIN-20231003060619-20231003090619-00416.warc.gz | 429,257,804 | 10,483 | # Why Benjamin Graham Might Have Picked NVIDIA (NVDA)
NVIDIA is currently trading at \$496.41 per share and has a Graham number of \$18.58, which implies that it is 2571.7% above its fair value. We calculate the Graham number as follows:
√(22.5 * 5 year average earnings per share * book value per share) = √(22.5 * 1.88 * 11.049) = 18.58
The Graham number is one of seven factors that Graham enumerates in Chapter 14 of The Intelligent Investor for determining whether a stock offers a margin of safety. Rather than use the Graham number by itself, its best to consider it alongside the following fundamental metrics:
Sales Revenue Should Be No Less Than \$500 million
For NVIDIA, average sales revenue over the last 6 years has been \$20.61 Billion, so in the context of the Graham analysis the stock has impressive sales revenue. Originally the threshold was \$100 million, but since the book was published in the 1970s it's necessary to adjust the figure for inflation.
Current Assets Should Be at Least Twice Current Liabilities
We calculate NVIDIA's current ratio by dividing its total current assets of \$23.07 Billion by its total current liabilities of \$6.56 Billion. Current assets refer to company assets that can be transferred into cash within one year, such as accounts receivable, inventory, and liquid financial instruments. Current liabilities, on the other hand, refer to those that will come due within one year. In NVIDIA’s case, current assets outweigh current liabilities by a factor of 3.5.
The Company’s Long-term Debt Should Not Exceed its Net Current Assets
This means that its ratio of debt to net current assets should be 1 or less. Since NVIDIA’s debt ratio is 2.4, the company has too much debt. We calculate NVIDIA’s debt to net current assets ratio by dividing its total long term of debt of \$9.7 Billion by its current assets minus total liabilities of \$19.08 Billion.
The Stock Should Have a Positive Level of Retained Earnings Over Several Years
NVIDIA had positive retained earnings from 2009 to 2023 with an average of \$7.44 Billion. Retained earnings are the sum of the current and previous reporting periods' net asset amounts, minus all dividend payments. It's a similar metric to free cash flow, with the difference that retained earnings are accounted for on an accrual basis.
There Should Be a Record of Uninterrupted Dividend Payments Over the Last 20 Years
Shareholders of NVIDIA have received regular dividends since 2013. The company has returned an average dividend yield of 0.2% over the last five years.
A Minimum Increase of at Least One-third in Earnings per Share (EPS) Over the Past 10 Years
To determine NVIDIA's EPS growth over time, we will average out its EPS for 2008, 2009, and 2010, which were \$1.31, \$0.19, and \$0.15 respectively. This gives us an average of \$0.55 for the period of 2008 to 2010. Next, we compare this value with the average EPS reported in 2021, 2022, and 2023, which were \$1.73, \$3.85, and \$1.74, for an average of \$2.44. Now we see that NVIDIA's EPS growth was 343.64% during this period, which satisfies Ben Graham's requirement.
It may be trading far above its fair value, but NVIDIA actually meets most of Benjamin Graham's criteria for an undervalued stock because it has:
• impressive sales revenue
• an excellent current ratio
• too much debt
• positive retained earnings from 2009 to 2023
• an acceptable record of dividends
• EPS growth in excess of Graham's requirements
The above analysis is intended for educational purposes only and was performed on the basis of publicly available data. It is not to be construed as a recommendation to buy or sell any security. Any buy, sell, or other recommendations mentioned in the article are direct quotations of consensus recommendations from the analysts covering the stock, and do not represent the opinions of Market Inference or its writers. Past performance, accounting data, and inferences about market position and corporate valuation are not reliable indicators of future price movements. Market Inference does not provide financial advice. Investors should conduct their own review and analysis of any company of interest before making an investment decision. | 940 | 4,232 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.75 | 3 | CC-MAIN-2023-40 | latest | en | 0.943685 |
https://discuss.dizzycoding.com/how-is-set-implemented/ | 1,701,886,301,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679100602.36/warc/CC-MAIN-20231206162528-20231206192528-00130.warc.gz | 239,414,056 | 14,875 | # How is set() implemented?
Posted on
### Question :
How is set() implemented?
I’ve seen people say that `set` objects in python have O(1) membership-checking. How are they implemented internally to allow this? What sort of data structure does it use? What other implications does that implementation have?
Every answer here was really enlightening, but I can only accept one, so I’ll go with the closest answer to my original question. Thanks all for the info!
Indeed, CPython’s sets are implemented as something like dictionaries
with dummy values (the keys being the members of the set), with some
optimization(s) that exploit this lack of values
So basically a `set` uses a hashtable as its underlying data structure. This explains the O(1) membership checking, since looking up an item in a hashtable is an O(1) operation, on average.
If you are so inclined you can even browse the CPython source code for set which, according to Achim Domma, is mostly a cut-and-paste from the `dict` implementation.
When people say sets have O(1) membership-checking, they are talking about the average case. In the worst case (when all hashed values collide) membership-checking is O(n). See the Python wiki on time complexity.
The Wikipedia article says the best case time complexity for a hash table that does not resize is `O(1 + k/n)`. This result does not directly apply to Python sets since Python sets use a hash table that resizes.
A little further on the Wikipedia article says that for the average case, and assuming a simple uniform hashing function, the time complexity is `O(1/(1-k/n))`, where `k/n` can be bounded by a constant `c<1`.
Big-O refers only to asymptotic behavior as n ? ?.
Since k/n can be bounded by a constant, c<1, independent of n,
`O(1/(1-k/n))` is no bigger than `O(1/(1-c))` which is equivalent to `O(constant)` = `O(1)`.
So assuming uniform simple hashing, on average, membership-checking for Python sets is `O(1)`.
I think its a common mistake, `set` lookup (or hashtable for that matter) are not O(1).
from the Wikipedia
In the simplest model, the hash function is completely unspecified and the table does not resize. For the best possible choice of hash function, a table of size n with open addressing has no collisions and holds up to n elements, with a single comparison for successful lookup, and a table of size n with chaining and k keys has the minimum max(0, k-n) collisions and O(1 + k/n) comparisons for lookup. For the worst choice of hash function, every insertion causes a collision, and hash tables degenerate to linear search, with ?(k) amortized comparisons per insertion and up to k comparisons for a successful lookup.
Related: Is a Java hashmap really O(1)?
We all have easy access to the source, where the comment preceding `set_lookkey()` says:
To emphasize a little more the difference between `set's` and `dict's`, here is an excerpt from the `setobject.c` comment sections, which clarify’s the main difference of set’s against dicts.
Use cases for sets differ considerably from dictionaries where looked-up
keys are more likely to be present. In contrast, sets are primarily
about membership testing where the presence of an element is not known in
advance. Accordingly, the set implementation needs to optimize for both
the found and not-found case.
source on github
Sets in python employ hash table internally. Let us first talk about hash table.
Let there be some elements that you want to store in a hash table and you have 31 places in the hash table where you can do so. Let the elements be: 2.83, 8.23, 9.38, 10.23, 25.58, 0.42, 5.37, 28.10, 32.14, 7.31. When you want to use a hash table, you first determine the indices in the hash table where these elements would be stored. Modulus function is a popular way of determining these indices, so let us say we take one element at a time, multiply it by 100 and apply modulo by 31. It is important that each such operation on an element results in a unique number as an entry in a hash table can store only one element unless chaining is allowed. In this way, each element would be stored at a location governed by the indices obtained through modulo operation. Now if you want to search for an element in a set which essentially stores elements using this hash table, you would obtain the element in O(1) time as the index of the element is computed using the modulo operation in a constant time.
To expound on the modulo operation, let me also write some code:
``````piles = [2.83, 8.23, 9.38, 10.23, 25.58, 0.42, 5.37, 28.10, 32.14, 7.31]
def hash_function(x):
return int(x*100 % 31)
[hash_function(pile) for pile in piles]
``````
Output: [4, 17, 8, 0, 16, 11, 10, 20, 21, 18] | 1,154 | 4,714 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.140625 | 3 | CC-MAIN-2023-50 | latest | en | 0.929998 |
https://metanumbers.com/1160 | 1,709,540,264,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947476432.11/warc/CC-MAIN-20240304065639-20240304095639-00297.warc.gz | 383,470,945 | 7,432 | # 1160 (number)
1160 is an even four-digits composite number following 1159 and preceding 1161. In scientific notation, it is written as 1.16 × 103. The sum of its digits is 8. It has a total of 5 prime factors and 16 positive divisors. There are 448 positive integers (up to 1160) that are relatively prime to 1160.
## Basic properties
• Is Prime? no
• Number parity even
• Number length 4
• Sum of Digits 8
• Digital Root 8
## Name
Name one thousand one hundred sixty
## Notation
Scientific notation 1.16 × 103 1.16 × 103
## Prime Factorization of 1160
Prime Factorization 23 × 5 × 29
Composite number
Distinct Factors Total Factors Radical ω 3 Total number of distinct prime factors Ω 5 Total number of prime factors rad 290 Product of the distinct prime numbers λ -1 Returns the parity of Ω(n), such that λ(n) = (-1)Ω(n) μ 0 Returns: 1, if n has an even number of prime factors (and is square free) −1, if n has an odd number of prime factors (and is square free) 0, if n has a squared prime factor Λ 0 Returns log(p) if n is a power pk of any prime p (for any k >= 1), else returns 0
The prime factorization of 1160 is 23 × 5 × 29. Since it has a total of 5 prime factors, 1160 is a composite number.
## Divisors of 1160
1, 2, 4, 5, 8, 10, 20, 29, 40, 58, 116, 145, 232, 290, 580, 1160
16 divisors
Even divisors 12 4 4 0
Total Divisors Sum of Divisors Aliquot Sum τ 16 Total number of the positive divisors of n σ 2700 Sum of all the positive divisors of n s 1540 Sum of the proper positive divisors of n A 168.75 Returns the sum of divisors (σ(n)) divided by the total number of divisors (τ(n)) G 34.0588 Returns the nth root of the product of n divisors H 6.87407 Returns the total number of divisors (τ(n)) divided by the sum of the reciprocal of each divisors
The number 1160 can be divided by 16 positive divisors (out of which 12 are even, and 4 are odd). The sum of these divisors (counting 1160) is 2700, the average is 168.75.
## Other Arithmetic Functions (n = 1160)
1 φ(n) n
Euler Totient Carmichael Lambda Prime Pi φ 448 Total number of positive integers not greater than n that are coprime to n λ 28 Smallest positive number such that aλ(n) ≡ 1 (mod n) for all a coprime to n π ≈ 194 Total number of primes less than or equal to n r2 16 The number of ways n can be represented as the sum of 2 squares
There are 448 positive integers (less than 1160) that are coprime with 1160. And there are approximately 194 prime numbers less than or equal to 1160.
## Divisibility of 1160
m n mod m
2 0
3 2
4 0
5 0
6 2
7 5
8 0
9 8
The number 1160 is divisible by 2, 4, 5 and 8.
• Abundant
• Polite
• Practical
• Octagonal
## Base conversion 1160
Base System Value
2 Binary 10010001000
3 Ternary 1120222
4 Quaternary 102020
5 Quinary 14120
6 Senary 5212
8 Octal 2210
10 Decimal 1160
12 Duodecimal 808
20 Vigesimal 2i0
36 Base36 w8
## Basic calculations (n = 1160)
### Multiplication
n×y
n×2 2320 3480 4640 5800
### Division
n÷y
n÷2 580 386.666 290 232
### Exponentiation
ny
n2 1345600 1560896000 1810639360000 2100341657600000
### Nth Root
y√n
2√n 34.0588 10.5072 5.83599 4.10102
## 1160 as geometric shapes
### Circle
Diameter 2320 7288.49 4.22733e+06
### Sphere
Volume 6.53827e+09 1.69093e+07 7288.49
### Square
Length = n
Perimeter 4640 1.3456e+06 1640.49
### Cube
Length = n
Surface area 8.0736e+06 1.5609e+09 2009.18
### Equilateral Triangle
Length = n
Perimeter 3480 582662 1004.59
### Triangular Pyramid
Length = n
Surface area 2.33065e+06 1.83953e+08 947.136 | 1,202 | 3,530 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.6875 | 4 | CC-MAIN-2024-10 | latest | en | 0.823901 |
http://www.dpreview.com/forums/thread/2737636 | 1,448,604,410,000,000,000 | text/html | crawl-data/CC-MAIN-2015-48/segments/1448398447913.86/warc/CC-MAIN-20151124205407-00028-ip-10-71-132-137.ec2.internal.warc.gz | 399,293,862 | 29,343 | # In-camera processing of long-exposure RAW data
Started Jan 21, 2010 | Discussions
Shop cameras & lenses ▾
Like?
In-camera processing of long-exposure RAW data Jan 21, 2010
I'm ashamed to admit that the famous author's name escapes me at the moment (I'm confident that someone here will remind me), but I recall very well a short story that we studied in high school English class, about a repressive future society where individuals of outstanding talents and abilities have them artificially suppressed, in the name of "equality and fairness" for all.
Such a "society" does exist, though, due to a "repressive" algorithm coded into the firmware of our Nikon cameras. Christian Buil wrote about some effects of that algorithm, which is applied to NEF data where the exposure time is 1/4 sec or longer, but he only referred to it as a "median filter" and to my knowledge, the details of the algorithm were not investigated.
The operation of the algorithm is to identify "outstanding individuals" (hot pixels) and repress (adjust) them so that they no longer distinguish themselves from their ordinary neighbors. Unfortunately, this is done in a rather heavy-handed manner, using a Min() function rather than a graduated adjustment curve, so there is no possibility of recovering the original pixel value from the data that results.
The goal of my study was to find a recovery algorithm if possible, but since that will not happen, I thought that I would at least share the details of the algorithm with the DPR community.
First, let me define the term "neighbor" as it is used here. Processing is performed for each color channel (R, G1, G2, B) independently, so a given pixel's 8 neighbors are actually two pixel positions away. This two-pixel separation unfortunately makes the algorithm's effects rather coarse. Here is a diagram of a section of array, with a pixel of interest in italics and its 8 neighbors shown in bold :
R . . . G1 . . . R . . . G1 . . . R . . . G1 . . . R . . . G1
G2 . . B . . . G2 . . . B . . . G2 . . . B . . . G2 . . . B
R . . . G1 . . . R . . . G1 . . . R . . . G1 . . . R . . . G1
G2 . . B . . . G2 . . . B . . . G2 . . . B . . . G2 . . . B
R . . . G1 . . . R . . . G1 . . . R . . . G1 . . . R . . . G1
G2 . . B . . . G2 . . . B . . . G2 . . . B . . . G2 . . . B
The algorithm first looks at the values of the pixel's neighbors, to find the brightest neighbor. Then, if the pixel being evaluated is brighter than its brightest neighbor, its value is adjusted down to match. Since this test/adjustment is applied sequentially through the file, it's not possible to check against all 8 neighbors, as this could cause ripple effects. Thus the only neighbors included in the test, are those which haven't yet been tested and adjusted. For example, if one scans the file left-to-right and top-to-bottom, the neighbors used for the test will only be the four which are on the line below, and to the immediate right.
As an example, suppose we have the following pixel values (pixel being tested in italics, neighbors used for the test in bold, and pixels from other color channels denoted by an x):
x . . . 43 . . . x . . . 39 . . . x . . . 38 . . . x
x . . . . x . . . x . . . . x . . . x . . . . x . . . x
x . . . 45 . . . x . . . 128 . . . x . . . 41 . . . x
x . . . . x . . . x . . . . x . . . x . . . . x . . . x
x . . . 42 . . . x . . . 44 . . . x . . . 40 . . . x
Since the brightest (tested) neighbor has value 44, the pixel under test will be adjusted down to 44. From the data that remains, there is no way to determine that the original pixel value was 128.
The algorithm does serve its purpose well, given ordinary, macroscopic subjects. Difficulties arise when bright pinpoint objects or details are present in the image. Here is a before/after image* of a test chart which consists of variously spaced white dots on a black background. Where the dots are close enough, there are sufficient bright neighbors to prevent any pixel values from being severely disturbed. However, where the dots are more isolated, resembling stars in an astrophotograph, they literally end up with their hearts punched out:
* This image shows the raw file data directly, i.e., it has not been through a converter, so each pixel is purely red, green or blue.
If you would like to examine the pixel values in the above sample image, you will find that there are many matching values in the processed pane. The before/after versions were obtained by using a 1/5sec shutter speed for the "before" example (which avoids the processing) and 1/4sec shutter for the "after" example.
You may also notice that a second undesirable effect of the algorithm, since it changes the values of the brightest pixels in the more-isolated dots, is color shifts which resemble color moire'.
Complain
Like?
Re: In-camera processing of long-exposure RAW data In reply to Marianne Oelund, Jan 21, 2010
In my initial de-mosaicing of Canon RAW back when the G3 came out was focused on testing how noise reduction (and hot dead pixels are noise with high freq) per channel before much was public domain on what raw really was. I found that just rejecting the sample data was more effective than clipping and value just interpolated. However, if calibration of the sensor changed, then darkframe subtraction needed to be done first if zero was off within a certain range. i just coded that in the past but there are some wonderful MATLAB libraries for image processing algorithm testing for the non programmers out there.
-C
way back then i was hoping that raw was not the accumulated values but rather 'frames' of sample data with a frame* per min time period..Info on sensor read was hard to find in that era:)* Ah, a temporal element to analyze would make it so much better* I now just think the best way is multiple separate short duration frames since the combination can approximate the sampling of a foveon since there will all ways be micromovents/jitter that allow for an integrated frame of near RGB pixel quality after processing. Much as how our vision and hearing works.
Complain
Like?
Correction to Number of neighbors used In reply to Marianne Oelund, Jan 21, 2010
Thinking about this some more, it would probably work better if all 8 neighbors were used in the test. I'll need to do some modeling later, to find out what approach actually matches the camera's processing.
Complain
Like?
Re: In-camera processing of long-exposure RAW data In reply to Marianne Oelund, Jan 21, 2010
Marianne Oelund wrote:
I'm ashamed to admit that the famous author's name escapes me at the moment
"Harrison Burgeron" by Kurt Vonnegut.
Complain
Like?
Re: Correction to Number of neighbors used In reply to Marianne Oelund, Jan 21, 2010
Changing the sample value of Red and Blue channels affects 8 pixels, whereas green only 4
-C
Complain
Like?
Green is not a special case In reply to cluna, Jan 21, 2010
cluna wrote:
Changing the sample value of Red and Blue channels affects 8 pixels, whereas green only 4
There are two independent green channels, and each is treated exactly as the red and blue channels are. Re-read the array descriptions in my original post.
Complain
Like?
Re: In-camera processing of long-exposure RAW data In reply to Marianne Oelund, Jan 21, 2010
Why bother using "in camera processing" (ie, jpeg/tiff compression)?
Shoot RAW and process with NX2.
Or, is this "processing" done on the NEF file itself?
Complain
Like?
Re: Green is not a special case In reply to Marianne Oelund, Jan 21, 2010
Marianne Oelund wrote:
cluna wrote:
Changing the sample value of Red and Blue channels affects 8 pixels, whereas green only 4
There are two independent green channels, and each is treated exactly as the red and blue channels are. Re-read the array descriptions in my original post.
Why treat i as two though in the processing? G1 and G2 are direct measurements, why make G2's output a function of G1? Is there a presumption that G1 being hot will affect the sensitivity of G2? Or that the processing is done after a read of a discrete channel? Something like :
G1=> processing=> buffer
G2=> processing=> buffer
B => processing=> buffer
R => processing=> buffer
Then integrate G1,G2,B,R into a serialized raw??
Make more sense to treat
[G1] [? ][G1]
[? ] [G2][? ]
[G1] [? ][G1]
as just:
[G][? ][G]
[? ][G][? ]
[G][? ][G]
-C
Complain
Like?
Yes, it affects the NEF file data In reply to mozarkid, Jan 21, 2010
mozarkid wrote:
Or, is this "processing" done on the NEF file itself?
Yes, and it cannot be turned off by the user - and that is the reason for studying it. At exposure times of 1/4 sec or longer, the camera performs this "hot-pixel clipping" algorithm to suppress the unwanted bright pixels. Unfortunately, this has other effects which are particularly harmful for astro images, so my interest was in determining exactly what the camera is doing, to see if it could be "undone."
This has become more important, as the so-called "Mode 3" approach (turning the camera off during the long-exp. NR blackframe period to obtain unprocessed RAW data) no longer works with current firmware.
You can see the effect that the clipping algorithm has on RAW data, by taking high-ISO black frames at 1/5 sec and 1/4 sec, then comparing them. I would also advise users to study the algorithm's effect on the work they normally do, if they use exposure times of 1/4 sec or longer (again, by comparing 1/5 sec and 1/4 sec images).
Complain
Like?
It's for simplicity, I suppose In reply to cluna, Jan 21, 2010
cluna wrote:
Why treat it as two though in the processing?
It allows the same algorithm to be applied to all channels, with no modifications. Then as the processing proceeds, it's not necessary for it to identify which channel it is working on. I'm not defending Nikon's choice, rather I'm just stating what they've done.
Make more sense to treat
[G1] [? ][G1]
[? ] [G2][? ]
[G1] [? ][G1]
as just:
[G][? ][G]
[? ][G][? ]
[G][? ][G]
I could actually try this. I will be running a simulation of the clipping algorithm fairly soon, as verification of my interpretation. When that's done, I can experiment with variations such as your suggestion, to see how they behave.
Complain
Like?
Re: In-camera processing of long-exposure RAW data In reply to Marianne Oelund, Jan 21, 2010
Marianne,
What an odd algorithm... Kinda like deciding to just chop off peaks. I mean, do I understand correctly that the algorithm essentially flattens all local maxima? Seems like a pretty heavy hammer... that would have an impact on many aspects of image quality.
Say it ain't so
Cheers,
-Yamo-
Complain
Like?
opening the can of worms a bit further... In reply to Marianne Oelund, Jan 21, 2010
Marianne,
The behaviour you've found and described is likely a big shock to many of us. The use of Nikon bodies for astro and macro photography is potentially seriously compromised.
Now that this can of worms has been opened, it would be interesting to apply a (hopefully) simple and concise test to various Nikon bodies and firmware versions to verify the extent of this 'feature'. Such a test would be very handy. How feasible is such a test?
-- hide signature --
Bob Elkind
Family,in/outdoor sports, landscape, wildlife
photo galleries at http://eteam.zenfolio.com
my relationship with my camera is strictly photonic
bob elkind's gear list:bob elkind's gear list
Nikon D700 Canon EOS 500D Nikon D600 Canon EF-S 18-55mm f/3.5-5.6 Nikon AF Nikkor 50mm f/1.8D +5 more
Complain
Like?
And in LiveView? In reply to Marianne Oelund, Jan 21, 2010
Is this 'processing' manifested in LiveView display (in real time), or only in captured still image data? I don't know enough about how LiveView displays are derived, to answer this question. Whatever the answer might be, the notion of 'what you see is what you get' would certainly be stretched. For those of us who depend heavily on LiveView mode for critical manual focus, surprises would not be welcome.
-- hide signature --
Bob Elkind
Family,in/outdoor sports, landscape, wildlife
photo galleries at http://eteam.zenfolio.com
my relationship with my camera is strictly photonic
bob elkind's gear list:bob elkind's gear list
Nikon D700 Canon EOS 500D Nikon D600 Canon EF-S 18-55mm f/3.5-5.6 Nikon AF Nikkor 50mm f/1.8D +5 more
Complain
Like?
Algorithm successfully simulated In reply to Marianne Oelund, Jan 22, 2010
As confirmation of my interpretation of Nikon's hot-pixel clipping algorithm, I coded it and applied it to the "Before" sample file shown in my original post. This simulation used the full 8-neighbor comparison set. The result matches very well with the camera's "After" image, with the only differences being slight exposure change and very small level differences, as expected from noise.
Now that I have a working simulation, I can perform some tweaks on it, and see if any small changes to the algorithm can produce significant improvements. Of course, the hard part would be getting Nikon to put those changes into firmware.
Complain
Like?
Re: Algorithm successfully simulated In reply to Marianne Oelund, Jan 22, 2010
-- hide signature --
Thom Hogan
author, Complete Guides to Nikon bodies (21 and counting)
http://www.bythom.com
Complain
Like?
Re: In-camera processing of long-exposure RAW data In reply to Yamo, Jan 22, 2010
Yamo wrote:
Marianne,
What an odd algorithm... Kinda like deciding to just chop off peaks. I mean, do I understand correctly that the algorithm essentially flattens all local maxima?
Yes, but that would be extremely local maxima, i.e., single-pixel.
Seems like a pretty heavy hammer... that would have an impact on many aspects of image quality.
It can affect brightness and color of extremely fine details which are lighter than their surroundings.
Say it ain't so
Sorry, I can't.
Complain
Like?
Not apparent in Live View In reply to bob elkind, Jan 22, 2010
bob elkind wrote:
Is this 'processing' manifested in LiveView display (in real time), or only in captured still image data?
The effects of the clipping (color shifts and loss of brightness of the isolated dots) didn't appear in my display when focusing on the test target. Since application of the algorithm is limited to exposures of 1/4 sec or longer, it isn't something which I would expect to run during Live View image handling.
Complain
Like?
Testing is fairly easy In reply to bob elkind, Jan 22, 2010
bob elkind wrote:
Now that this can of worms has been opened, it would be interesting to apply a (hopefully) simple and concise test to various Nikon bodies and firmware versions to verify the extent of this 'feature'. Such a test would be very handy. How feasible is such a test?
All I had to do, was create an array of single-pixel white dots on a black background, which was printed at 200dpi, then photographed with a D3 from a distance of 24" with the 60mm/2.8D macro lens. It should be easy to adjust this for any camera model, although the finer-pitch sensors will of course be more demanding of optics.
Given a suitable subject, the effect of the clipping algorithm can be judged by comparing a 1/5-sec exposure to a 1/4-sec one. The difference will even show up in the camera JPEG file, viewed on the camera's LCD.
Complain
Like?
Ayn Rand "Atlas Shrugged" (nt) In reply to shmn, Jan 22, 2010
No Text
-Wayne
Complain
Like?
Re: In-camera processing of long-exposure RAW data In reply to Marianne Oelund, Jan 22, 2010
Marianne Oelund wrote:
Yamo wrote:
Marianne,
What an odd algorithm... Kinda like deciding to just chop off peaks. I mean, do I understand correctly that the algorithm essentially flattens all local maxima?
Yes, but that would be extremely local maxima, i.e., single-pixel.
I'd guess that most local maxima are a single pixel. And anything that is textured would have many of these single pixel local maxima. For instance, noise would be for the most part comprised of single point local maxima. One couldn't faithfully photo copy a grainy film black and white image with such an algorithm applied.
I mean, seems like one might say that Nikon has made the choice of using a particular kind of NR on all shots 1/4 sec. or higher with no way of turning it off.
Seems like a pretty heavy hammer... that would have an impact on many aspects of image quality.
It can affect brightness and color of extremely fine details which are lighter than their surroundings.
Say it ain't so
Sorry, I can't.
indeed
Er, Cheers,
-Yamo-
Complain | 4,079 | 16,546 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.65625 | 3 | CC-MAIN-2015-48 | longest | en | 0.947086 |
https://gmatclub.com/forum/stanford-sloan-fellows-admits-class-of-144869-40.html?kudos=1 | 1,511,199,938,000,000,000 | text/html | crawl-data/CC-MAIN-2017-47/segments/1510934806086.13/warc/CC-MAIN-20171120164823-20171120184823-00195.warc.gz | 618,039,775 | 44,870 | It is currently 20 Nov 2017, 10:45
### GMAT Club Daily Prep
#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
we will pick new questions that match your level based on your Timer History
Track
every week, we’ll send you an estimated GMAT score based on your performance
Practice
Pays
we will pick new questions that match your level based on your Timer History
# Events & Promotions
###### Events & Promotions in June
Open Detailed Calendar
# Stanford Sloan Fellows admits - Class of 2014
Author Message
Intern
Joined: 03 Mar 2013
Posts: 26
Kudos [?]: [0], given: 0
### Show Tags
03 Mar 2013, 20:38
Hi Folks,
Are you all going to fund yourself? or funded by our corporation? and if you are going to fund yourself, do you need the loan?
I was interviewed last Tuesday, Feb 26th, no decision yet.
Thanks!
Kudos [?]: [0], given: 0
Intern
Joined: 20 May 2012
Posts: 5
Kudos [?]: 7 [0], given: 1
Location: Brazil
Concentration: General Management, Operations
GMAT 1: 750 Q48 V45
WE: Project Management (Manufacturing)
### Show Tags
06 Mar 2013, 06:04
I am self-funded and need the loan too. However, due to tax return procedures in Brazil, I applied only for the summer quarter yet.
How was the interview? When did you send the docs/forms?
Kudos [?]: 7 [0], given: 1
Intern
Joined: 03 Mar 2013
Posts: 26
Kudos [?]: [0], given: 0
### Show Tags
06 Mar 2013, 17:57
dougfernando wrote:
I am self-funded and need the loan too. However, due to tax return procedures in Brazil, I applied only for the summer quarter yet.
How was the interview? When did you send the docs/forms?
I sent in my docs by Jan 15th, deadline of R2. Phone interviewed on 26th, have not heard decision yet. Guess either on waiting list or rejected.
Kudos [?]: [0], given: 0
Intern
Joined: 28 Dec 2012
Posts: 22
Kudos [?]: 18 [0], given: 1
Concentration: Entrepreneurship, General Management
GMAT 1: 700 Q48 V38
GPA: 3.1
WE: Management Consulting (Internet and New Media)
### Show Tags
09 Mar 2013, 19:15
estherpapa wrote:
I sent in my docs by Jan 15th, deadline of R2. Phone interviewed on 26th, have not heard decision yet. Guess either on waiting list or rejected.
I wouldn't worry too much yet...
The R1 folks had a mid-October deadline -- I had mine in around Oct 1. But didn't get my interview scheduled until mid-December. When I went to visit campus in late January, they said they had still only filled about 55% of the goal class size. So there are clearly folks that have yet to be accepted.
Good luck!!
Kudos [?]: 18 [0], given: 1
Intern
Joined: 13 Dec 2012
Posts: 3
Kudos [?]: [0], given: 0
GPA: 3.52
WE: Management Consulting (Consulting)
### Show Tags
10 Mar 2013, 17:05
yes I believe they are still filling some of the spots. I submitted my application beginning Jan, interviewed jan 31st and was told that half the class was yet to be filled. I only received my call a couple of weeks ago.....you should not be stressed as yet.
Kudos [?]: [0], given: 0
Intern
Joined: 20 Mar 2013
Posts: 2
Kudos [?]: [0], given: 3
### Show Tags
16 May 2013, 07:44
Dear all,
I need some advice and I am coming to you with some hope to get answers. I have been thinking of taking an eMBA for a while now, yet I was never conviced by the format of this type of program. I have discovered recentely the Stanford Sloan MS program and was wondering if my profile could fit.
I am 37, have 12 years experience in financial services industry (derivatives brokerage and prime clearing services for one of the world's leading company), 5 years as a global manager (across Asia, Europe and Americas). I have a successful track record with quick progression. I am from Morroco and live in Paris.
I will quit my job in a few months as I need to refocus on the path I want to follow and to be honest, I am very keen to set a venture. Entrepreneurship is really what I want.
Considering these elements, do you guys (i) that my profile could fit, and (ii) that not having a job at the time of subscription is prohibitive?
C.
Kudos [?]: [0], given: 3
Intern
Joined: 28 Dec 2012
Posts: 22
Kudos [?]: 18 [0], given: 1
Concentration: Entrepreneurship, General Management
GMAT 1: 700 Q48 V38
GPA: 3.1
WE: Management Consulting (Internet and New Media)
### Show Tags
16 May 2013, 11:05
cyril94115 wrote:
claudayst wrote:
Dear all,
I need some advice and I am coming to you with some hope to get answers. I have been thinking of taking an eMBA for a while now, yet I was never conviced by the format of this type of program. I have discovered recentely the Stanford Sloan MS program and was wondering if my profile could fit.
I am 37, have 12 years experience in financial services industry (derivatives brokerage and prime clearing services for one of the world's leading company), 5 years as a global manager (across Asia, Europe and Americas). I have a successful track record with quick progression. I am from Morroco and live in Paris.
I will quit my job in a few months as I need to refocus on the path I want to follow and to be honest, I am very keen to set a venture. Entrepreneurship is really what I want.
Considering these elements, do you guys (i) that my profile could fit, and (ii) that not having a job at the time of subscription is prohibitive?
C.
Hi there,
I think you have the right profile to apply! Right experience, an industry that is well represented in the class. And the fact that you want to start a new venture points to the GSB for sure!
My advise would be to still keep your job until you apply. Or you should have a really good reason why you quit, and explain what you are doing since you left! Giving it a shot at your own venture might be a compelling story! (and you'd learn so much doing it)
Totally agree with Cyril... Don't quit your job if you don't need to... Worst case, you could end up with no job and no school admittances... No need to do that to yourself.
Kudos [?]: 18 [0], given: 1
Intern
Joined: 20 Mar 2013
Posts: 2
Kudos [?]: [0], given: 3
### Show Tags
17 May 2013, 09:37
I am planning on coming to SF this summer. In order to meet the admission staff, should I just call the number (on their internet site) or do you have a better suggestion?
Many thx
Kudos [?]: [0], given: 3
Intern
Joined: 20 Oct 2012
Posts: 24
Kudos [?]: 10 [0], given: 2
Concentration: Technology, Entrepreneurship
WE: Engineering (Consumer Electronics)
### Show Tags
17 May 2013, 10:27
claudayst wrote:
I am planning on coming to SF this summer. In order to meet the admission staff, should I just call the number (on their internet site) or do you have a better suggestion?
Many thx
just call that number.
Kudos [?]: 10 [0], given: 2
Intern
Joined: 25 Dec 2009
Posts: 24
Kudos [?]: [0], given: 0
### Show Tags
25 Dec 2014, 22:47
Hi All,
I applied for Stanford MSx this year and got accepted for 2016 class. Now this is a decision time and time to figure out financial options as well. I have a couple of questions. I hope some of you, who are recent alumni, might be able to help.
1). Does anyone know what is the approximate breakup of self funded v/s employer sponsored in this program for current or previous years? I looked at class profile on school website but they do not have this detail.
2). Can anyone share if you have been able to take any financial aids apart from standard education loan for this program?
3). I have not been able to find any employment statistics for current or past years. I know this is a program for experienced leaders with diverse background and not all might be looking for a job after the program. But I am sure most of the self-funded students might be looking for a job. Can anyone share details regarding employment statistics or at least the major companies which have been more commonly hiring from Stanford MSx class especially in general management, consulting or technology management area?
Thanks!
Kudos [?]: [0], given: 0
Stanford Sloan Fellows admits - Class of 2014 [#permalink] 25 Dec 2014, 22:47
Go to page Previous 1 2 3 [ 50 posts ]
Display posts from previous: Sort by
# Stanford Sloan Fellows admits - Class of 2014
Moderators: ydmuley, mvictor
Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®. | 2,276 | 8,550 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.546875 | 3 | CC-MAIN-2017-47 | latest | en | 0.935298 |
https://ww2.mathworks.cn/matlabcentral/cody/problems/44445-tax-calculator/solutions/2060154 | 1,611,011,896,000,000,000 | text/html | crawl-data/CC-MAIN-2021-04/segments/1610703517159.7/warc/CC-MAIN-20210118220236-20210119010236-00392.warc.gz | 622,691,950 | 18,893 | Cody
# Problem 44445. Tax Calculator
Solution 2060154
Submitted on 17 Dec 2019 by anan jeraise
This solution is locked. To view this solution, you need to provide a solution of the same size or smaller.
### Test Suite
Test Status Code Input and Output
1 Pass
income = 0; tax_correct = 0; assert(isequal(taxFor(income),tax_correct))
tax = 0
2 Pass
income = 100; tax_correct = 10; assert(isequal(taxFor(income),tax_correct))
tax = 10
3 Pass
income = 1000; tax_correct = 100; assert(isequal(taxFor(income),tax_correct))
tax = 100
4 Pass
income = 2000; tax_correct = 200; assert(isequal(taxFor(income),tax_correct))
tax = 200
5 Pass
income = 2500; tax_correct = 300; assert(isequal(taxFor(income),tax_correct))
tax = 300
6 Pass
income = 3000; tax_correct = 400; assert(isequal(taxFor(income),tax_correct))
tax = 400
7 Pass
income = 5000; tax_correct = 1000; assert(isequal(taxFor(income),tax_correct))
tax = 1000
8 Pass
filetext = fileread('taxFor.m'); assert(isempty(strfind(filetext, 'regexp')),'regexp hacks are forbidden')
### Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting! | 361 | 1,185 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.03125 | 3 | CC-MAIN-2021-04 | latest | en | 0.707875 |
https://number.academy/1053472 | 1,721,513,402,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763517541.97/warc/CC-MAIN-20240720205244-20240720235244-00118.warc.gz | 367,649,577 | 11,575 | # Number 1053472 facts
The even number 1,053,472 is spelled 🔊, and written in words: one million, fifty-three thousand, four hundred and seventy-two, approximately 1.1 million. The ordinal number 1053472nd is said 🔊 and written as: one million, fifty-three thousand, four hundred and seventy-second. The meaning of the number 1053472 in Maths: Is it Prime? Factorization and prime factors tree. The square root and cube root of 1053472. What is 1053472 in computer science, numerology, codes and images, writing and naming in other languages
## What is 1,053,472 in other units
The decimal (Arabic) number 1053472 converted to a Roman number is (M)(L)MMMCDLXXII. Roman and decimal number conversions.
#### Time conversion
(hours, minutes, seconds, days, weeks)
1053472 seconds equals to 1 week, 5 days, 4 hours, 37 minutes, 52 seconds
1053472 minutes equals to 2 years, 2 months, 3 days, 13 hours, 52 minutes
### Codes and images of the number 1053472
Number 1053472 morse code: .---- ----- ..... ...-- ....- --... ..---
Sign language for number 1053472:
Number 1053472 in braille:
QR code Bar code, type 39
Images of the number Image (1) of the number Image (2) of the number More images, other sizes, codes and colors ...
## Share in social networks
#### Is Prime?
The number 1053472 is not a prime number. The closest prime numbers are 1053467, 1053487.
#### Factorization and factors (dividers)
The prime factors of 1053472 are 2 * 2 * 2 * 2 * 2 * 7 * 4703
The factors of 1053472 are Total factors 24.
Sum of factors 2370816 (1317344).
#### Powers
The second power of 10534722 is 1.109.803.254.784.
The third power of 10534723 is 1.169.146.654.423.810.048.
#### Roots
The square root √1053472 is 1026,387841.
The cube root of 31053472 is 101,751542.
#### Logarithms
The natural logarithm of No. ln 1053472 = loge 1053472 = 13,867602.
The logarithm to base 10 of No. log10 1053472 = 6,022623.
The Napierian logarithm of No. log1/e 1053472 = -13,867602.
### Trigonometric functions
The cosine of 1053472 is -0,163932.
The sine of 1053472 is 0,986472.
The tangent of 1053472 is -6,017561.
## Number 1053472 in Computer Science
Code typeCode value
1053472 Number of bytes1.0MB
Unix timeUnix time 1053472 is equal to Tuesday Jan. 13, 1970, 4:37:52 a.m. GMT
IPv4, IPv6Number 1053472 internet address in dotted format v4 0.16.19.32, v6 ::10:1320
1053472 Decimal = 100000001001100100000 Binary
1053472 Decimal = 1222112002111 Ternary
1053472 Decimal = 4011440 Octal
1053472 Decimal = 101320 Hexadecimal (0x101320 hex)
1053472 BASE64MTA1MzQ3Mg==
1053472 MD564cf33c966313ba101c6b81857dc9d89
1053472 SHA1b0633f46a07154d5e3219c4306c737d8ab06ed48
1053472 SHA224fdde74bc1f014710a436ed1eae7ab4383aecc04c9f7173701499e566
More SHA codes related to the number 1053472 ...
If you know something interesting about the 1053472 number that you did not find on this page, do not hesitate to write us here.
## Numerology 1053472
### Character frequency in the number 1053472
Character (importance) frequency for numerology.
Character: Frequency: 1 1 0 1 5 1 3 1 4 1 7 1 2 1
### Classical numerology
According to classical numerology, to know what each number means, you have to reduce it to a single figure, with the number 1053472, the numbers 1+0+5+3+4+7+2 = 2+2 = 4 are added and the meaning of the number 4 is sought.
## № 1,053,472 in other languages
How to say or write the number one million, fifty-three thousand, four hundred and seventy-two in Spanish, German, French and other languages. The character used as the thousands separator.
Spanish: 🔊 (número 1.053.472) un millón cincuenta y tres mil cuatrocientos setenta y dos German: 🔊 (Nummer 1.053.472) eine Million dreiundfünfzigtausendvierhundertzweiundsiebzig French: 🔊 (nombre 1 053 472) un million cinquante-trois mille quatre cent soixante-douze Portuguese: 🔊 (número 1 053 472) um milhão e cinquenta e três mil, quatrocentos e setenta e dois Hindi: 🔊 (संख्या 1 053 472) दस लाख, तिरेपन हज़ार, चार सौ, बहत्तर Chinese: 🔊 (数 1 053 472) 一百零五万三千四百七十二 Arabian: 🔊 (عدد 1,053,472) مليون و ثلاثة و خمسون ألفاً و أربعمائة و اثنان و سبعون Czech: 🔊 (číslo 1 053 472) milion padesát tři tisíce čtyřista sedmdesát dva Korean: 🔊 (번호 1,053,472) 백오만 삼천사백칠십이 Danish: 🔊 (nummer 1 053 472) en millioner treoghalvtredstusinde og firehundrede og tooghalvfjerds Hebrew: (מספר 1,053,472) מיליון חמישים ושלושה אלף ארבע מאות שבעים ושתיים Dutch: 🔊 (nummer 1 053 472) een miljoen drieënvijftigduizendvierhonderdtweeënzeventig Japanese: 🔊 (数 1,053,472) 百五万三千四百七十二 Indonesian: 🔊 (jumlah 1.053.472) satu juta lima puluh tiga ribu empat ratus tujuh puluh dua Italian: 🔊 (numero 1 053 472) un milione e cinquantatremilaquattrocentosettantadue Norwegian: 🔊 (nummer 1 053 472) en million femtitre tusen fire hundre og syttito Polish: 🔊 (liczba 1 053 472) milion pięćdziesiąt trzy tysiące czterysta siedemdziesiąt dwa Russian: 🔊 (номер 1 053 472) один миллион пятьдесят три тысячи четыреста семьдесят два Turkish: 🔊 (numara 1,053,472) birmilyonelliüçbindörtyüzyetmişiki Thai: 🔊 (จำนวน 1 053 472) หนึ่งล้านห้าหมื่นสามพันสี่ร้อยเจ็ดสิบสอง Ukrainian: 🔊 (номер 1 053 472) один мільйон п'ятдесят три тисячі чотириста сімдесят два Vietnamese: 🔊 (con số 1.053.472) một triệu năm mươi ba nghìn bốn trăm bảy mươi hai Other languages ...
## News to email
I have read the privacy policy
## Comment
If you know something interesting about the number 1053472 or any other natural number (positive integer), please write to us here or on Facebook.
#### Comment (Maximum 2000 characters) *
The content of the comments is the opinion of the users and not of number.academy. It is not allowed to pour comments contrary to the laws, insulting, illegal or harmful to third parties. Number.academy reserves the right to remove or not publish any inappropriate comment. It also reserves the right to publish a comment on another topic. Privacy Policy. | 1,979 | 5,882 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.15625 | 3 | CC-MAIN-2024-30 | latest | en | 0.7901 |
http://www.cplusplus.com/forum/beginner/109653/ | 1,500,662,986,000,000,000 | text/html | crawl-data/CC-MAIN-2017-30/segments/1500549423808.34/warc/CC-MAIN-20170721182450-20170721202450-00547.warc.gz | 407,308,371 | 7,177 | ### Sqrt and divison with recursion
Hello guys! i want to make a calculator of addition/substitution/multiplication/division/power/square root only with recursion. I have made for +,-,* and ^ but i did not figure out how to do the functions for division and square root. If you can help it'd be great. Thanks in advance!
Last edited on
If to consider only unsigned int then it is not hard to write recursive function for division
1234 unsigned int division( unsigned int x, unsigned int y ) { return ( x < y ? 0 : 1 + division( x - y, y ) ); }
Last edited on
(1) what is the diferrence between signed and unsigned
(2) what const means?
(3) can you do anything for the square root?
If you can't heplp me with theese thanks anyway for the help provided!
const is a typo.:)
As for signed and unsigned then for example -6 / 3 = -2 while - 6 / - 3 = 2.
Signed is negative values and positive values within a set range.
Unsigned is only positive in a set range so therefore unsigned can store more positive numbers than signed.
Also your square root would be really hard with recursion...what would you get as an ouput if you did sqrt( 15 )?
Or I guess you could increment by decimal values instead of integer values but that might be a very slow process.
*edit
By the way const means constant as in the value is not modified/read-only.
Last edited on
Thank you for the help provided ! it helped me a lot
I just found an easy way you could do sqrt that I didn't even know about tbh.
wiki wrote:
To calculate \sqrt{S}, where S = 125348, to 6 significant figures, use the rough estimation method above to get
x_0 = 6 \cdot 10^2 = 600.000. \,
x_1 = \frac{1}{2} \left(x_0 + \frac{S}{x_0}\right) = \frac{1}{2} \left(600.000 + \frac{125348}{600.000}\right) = 404.457.
x_2 = \frac{1}{2} \left(x_1 + \frac{S}{x_1}\right) = \frac{1}{2} \left(404.457 + \frac{125348}{404.457}\right) = 357.187.
x_3 = \frac{1}{2} \left(x_2 + \frac{S}{x_2}\right) = \frac{1}{2} \left(357.187 + \frac{125348}{357.187}\right) = 354.059.
x_4 = \frac{1}{2} \left(x_3 + \frac{S}{x_3}\right) = \frac{1}{2} \left(354.059 + \frac{125348}{354.059}\right) = 354.045.
x_5 = \frac{1}{2} \left(x_4 + \frac{S}{x_4}\right) = \frac{1}{2} \left(354.045 + \frac{125348}{354.045}\right) = 354.045.
Therefore, \sqrt{125348} \approx 354.045 \,.
http://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Babylonian_method
*edit it looks weird when I paste it..lol
Basically you do something like
sqrt of 15 to 6 signifigant values ( can be anything the more you have the more accurate ) would be
s = 15
x0 = 6 * 100 = 600
x1 = 1/2( x0 + s/x0 )= 1/2( 600 + 15/600 ) = 300.0125
x2 = 1/2( x1 + s/x1 ) = 1/2( 300.0125 + 15/300.0125 ) = 150.0312
x3 = 1/2( x2 + s/x2 ) = 1/2( 150.0312 + 15/150.0312 ) = 75.0656
x4 = 1/2( x3 + s/x3 ) = 1/2( 75.0656 + 15/75.0656 ) = 37.6327
x5 = 1/2( x4 + s/x4 ) = 1/2( 37.6327 + 15/37.6327 ) = 19.0156
x6 = 1/2( x5 + s/x5 ) = 1/2( 19.0156 + 15/19.0156 ) = 9.9022
As you can see that isn't the correct value you want to go till xn is almost the same if not the same as xn - 1 so I'll keep going The reason you need more for 15 vs that large number is because its such a small value.
x7 = 1/2( x6 + s/x6 ) = 1/2( 9.9022 + 15/9.9022 ) = 5.7085
x8 = 1/2( x7 + s/x7 ) = 1/2( 5.7085 + 15/5.7085 ) = 4.1679
x9 = 1/2( x8 + s/x8 ) = 1/2( 4.1679 + 15/4.1679 ) = 3.8834
x10 = 1/2( x9 + s/x9 ) = 1/2( 3.8834 + 15/3.8834 ) = 3.8730
x11 = 1/2( x10 + s/x10 ) = 1/2( 3.8730 + 15/3.8730 ) = 3.8730
sqrt( 15 ) is approx 3.8730
let me check the calculator that my computer comes with...
3.8730
Last edited on
Thanks for searching this answer giblit, but i am a begginer programer and my calculator project was my idea so i am not obiged on it. This method seems too advanced for my mathematical knowings and i think that for the moment i will keep sqrt() function provided by math.h.I thought it could be a more easier method :d. But again i thank you for your work.
Last edited on
It's not that advanced of a method its basic algebra
S = x (value being sqrt'd ) so sqrt of 15 means s = 15
x0 = Signifigant digits * 10^2
Then you do x1 -> answer
xn = 1/2( ( xn - 1 ) + ( 15 / xn - 1 ) )
Begin with an arbitrary positive starting value x0 (the closer to the actual square root of S, the better).
Let xn+1 be the average of xn and S / xn (using the arithmetic mean to approximate the geometric mean).
Repeat step 2 until the desired accuracy is achieved.
It can also be represented as:
x_0 \approx \sqrt{S}.
x_{n+1} = \frac{1}{2} \left(x_n + \frac{S}{x_n}\right),
\sqrt S = \lim_{n \to \infty} x_n.
As you can see when I did 600 for sqrt( 15 ) it took a while vs as if I did like 10 which would look like
x0 = 1 * 10^2 = 100
x1 = 1/2( 100 + 15/100 ) = 50.075
x2 = 1/2( 50.075 + 15/50.075 ) = 25.1872
x3 = 1/2( 25.1872 + 15/25.1872 ) = 12.8914
x4 = 1/2( 12.8914 + 15/12.8914 ) = 7.0275
x5 = 1/2( 7.0275 + 15/7.0275 ) = 4.5810
x6 = 1/2( 4.581 + 15/4.581 ) = 3.9277
x7 = 1/2( 3.9277 + 15/3.9277 ) = 3.8734
x8 = 1/2( 3.8734 + 15/3.8734 ) = 3.8730
x9 = 1/2( 3.8730 + 15/3.8730 ) = 3.8730
same answer but took less loops to get it.
Last edited on
I think i understand a little if i am right plese announce me but i think the general algorithm would be( from your explain):
n->programmer choosed number(integer positive)
num->user choosed number( waiting to be sqrt'd)
x0=1*n^2
x1=1/2(x0 + num/x0)
.................................
x(n-1)=1/2(x(n-2)+num/x(n-2))=sqrt(num)
And if i am not wrong, as well as n is bigger the answer is more aproximate.
I took some randome cases and that's my conclusion i hope it's right. Thank you again for your work anyway.
yeah but n should be 10 though I didn't try other numbers so oculd be very well any number.
Last edited on
Even if it's 10 the algorithm is very useful. Thank you very much for the help , it would have been a lot heavier for me to find this myself.
An interesting feature of this algorithm is that it converges very rapidly towards the solution, once it is close. It gives roughly double the number of correct significant digits with each iteration.
Example:
n = 4
x0 = 4 (or any reasonable estimate).
x1 = 2.5
x2 = 2.05
x3 = 2.00060975609756097560975609756
x4 = 2.00000009292229466031325963976
x5 = 2.00000000000000215863811094172
x6 = 2.00000000000000000000000000000
Notice the number of zeros after the decimal point, indicating correct digits in each iteration.
Topic archived. No new replies allowed. | 2,321 | 6,429 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.03125 | 4 | CC-MAIN-2017-30 | latest | en | 0.871765 |
https://blog.finxter.com/5-best-ways-to-find-a-folded-list-from-a-given-linked-list-in-python/ | 1,713,015,122,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296816734.69/warc/CC-MAIN-20240413114018-20240413144018-00413.warc.gz | 116,912,232 | 21,773 | # 5 Best Ways to Find a Folded List from a Given Linked List in Python
Rate this post
π‘ Problem Formulation: In the realm of data structures, a linked list fold is a transformation where the list is divided into two parts, and the second part is reversed and paired with the first. Given a singly linked list, the challenge is to compute the folded linked list. For example, if the input linked list is `1->2->3->4->5`, the folded list would be `1->5->2->4->3`.
## Method 1: Iterative Approach with Stack
An iterative approach to folding a linked list in Python involves traversing the list with two pointers, one moving twice the speed of the other, to find the midpoint. Subsequently, the second half is pushed onto a stack. Finally, nodes are popped from the stack and woven with the first half to create the folded list.
Here’s an example:
```class ListNode:
def __init__(self, value=0, next=None):
self.val = value
self.next = next
stack = []
while fast and fast.next:
slow = slow.next
fast = fast.next.next
while slow:
stack.append(slow)
slow = slow.next
while stack:
temp = stack.pop()
temp.next = current.next
current.next = temp
current = temp.next.next
if current:
current.next = None
# Example usage
head = ListNode(1, ListNode(2, ListNode(3, ListNode(4, ListNode(5)))))
The output will be the folded linked list: `1->5->2->4->3`
This code snippet defines a `ListNode` class representing an element of a singly linked list and a function `fold_list` that manipulates the list to fold it. Using two pointers, ‘slow’ and ‘fast’, we find the middle of the list. Then, the second half of the list is stored in a stack. Subsequently, we weave the nodes from the stack with the first half. The result is a folded linked list.
## Method 2: Recursive Approach
The recursive approach for folding a linked list is more concise but trades off space for system call stack. The recursion mimics the iterative approach, finding the middle and weaving the nodes from the end back into the front, accomplished through backtracking inherent to the recursive calls.
Here’s an example:
```class ListNode:
# ListNode class definition same as before
if proceed:
return (None, False)
# Example usage
head = ListNode(1, ListNode(2, ListNode(3, ListNode(4, ListNode(5)))))
The output will be the folded linked list: `1->5->2->4->3`
This recursive implementation defines the `fold_list_recursive` function, which internally takes the current node to weave from the end into the front as it backtracks. The base case handles the reversal of the nodes at the end of the list, and through recursive calls, the nodes are folded correctly, leading to a folded list.
## Method 3: In-Place Reversal and Merge
This method involves first reversing the second half of the linked list in place and then merging the two halves. This approach has the advantage of using constant space as it alters the list nodes’ pointers without auxiliary data structures like stacks or recursion.
Here’s an example:
```class ListNode:
# ListNode class definition same as before
while current:
next_node = current.next
current.next = prev
prev = current
current = next_node
return prev
prev_node = None
while fast and fast.next:
prev_node = slow
slow = slow.next
fast = fast.next.next
prev_node.next = None # Break the list into two halves
second_half = reverse_list(slow) # Reverse the second half
# Merge the two halves
while first_half and second_half:
temp1, temp2 = first_half.next, second_half.next
current = first_half if not current else current.next
current.next, second_half.next = second_half, temp1
first_half, second_half = temp1, temp2
# Example usage
head = ListNode(1, ListNode(2, ListNode(3, ListNode(4, ListNode(5)))))
The output will be the folded linked list: `1->5->2->4->3`
The `fold_list_in_place` function separates the list by cutting it at the midpoint. The `reverse_list` function is used to reverse the second half of the list. The nodes of the two halves are then alternately merged to achieve a folded structure without using any additional space.
## Method 4: Using Length of the Linked List
This method entails first determining the length of the linked list and then folding the list based on the index of each node, which is determined by traversing the list. By using the list’s length, we can control the folding process more explicitly.
Here’s an example:
```class ListNode:
# ListNode class definition same as before
while current:
length += 1
current = current.next
return length
middle = length // 2
for _ in range(middle):
prev, current = current, current.next
prev.next = None # Seperate the list into two
# Tail insert the nodes from the second half to the first
while current:
temp = current.next
current = temp
# Example usage
head = ListNode(1, ListNode(2, ListNode(3, ListNode(4, ListNode(5)))))
The output will be the folded linked list: `1->5->2->4->3`
The `get_length` function computes the total count of nodes. The `fold_list_with_length` function utilizes this count to split the list at the middle. Thereafter, the list is folded by alternating insertions from the second half into the first, ensuring the nodes are placed correctly according to the length of the list.
## Bonus One-Liner Method 5: Using List Comprehension and Deque
This one-liner approach converts the linked list to a deque and utilizes list comprehension in conjunction with Python’s deque operations to achieve the fold. While concise, this method does not operate on the linked list directly but rather on a deque that is built from the list.
Here’s an example:
```from collections import deque
class ListNode:
# ListNode class definition same as before
dq = deque()
head = dq.popleft() if dq else None
while dq:
if current:
current.next = dq.pop()
current = current.next
if dq:
current.next = dq.popleft()
current = current.next
if current:
current.next = None
# Example usage
head = ListNode(1, ListNode(2, ListNode(3, ListNode(4, ListNode(5)))))
The output will be the folded linked list: `1->5->2->4->3`.
The one-liner `folded_list_one_liner` function builds a deque `dq` from the linked list nodes. Utilizing the `popleft` and `pop` methods offered by deque, the function performs the necessary left and right insertions to construct the folded list in a concise and Pythonic way. | 1,479 | 6,331 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.53125 | 4 | CC-MAIN-2024-18 | longest | en | 0.858993 |
https://gmatclub.com/forum/which-of-the-following-line-is-parallel-to-the-given-line-3x-4y-247259.html | 1,558,283,856,000,000,000 | text/html | crawl-data/CC-MAIN-2019-22/segments/1558232255071.27/warc/CC-MAIN-20190519161546-20190519183546-00484.warc.gz | 499,243,264 | 141,841 | GMAT Question of the Day - Daily to your Mailbox; hard ones only
It is currently 19 May 2019, 09:37
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
we will pick new questions that match your level based on your Timer History
Track
every week, we’ll send you an estimated GMAT score based on your performance
Practice
Pays
we will pick new questions that match your level based on your Timer History
Which of the following line is parallel to the given line 3x + 4y = 12
Author Message
Senior Manager
Joined: 17 Oct 2016
Posts: 261
Location: India
Concentration: General Management, Healthcare
GMAT 1: 640 Q40 V38
GMAT 2: 680 Q48 V35
GPA: 3.05
WE: Pharmaceuticals (Health Care)
Which of the following line is parallel to the given line 3x + 4y = 12 [#permalink]
Show Tags
16 Aug 2017, 18:59
00:00
Difficulty:
35% (medium)
Question Stats:
85% (01:03) correct 15% (01:08) wrong based on 13 sessions
HideShow timer Statistics
Which of the following line is parallel to the given line 3x + 4y = 12 and has a negative y-intercept.
A. 6x + 9y + 12 = 0
B. 9x + 12y + 36 = 0
C. 9x+ 12y- 36 = 0
D. 6x + 9y + 28 = 0
E. 6x + 9y - 28 = 0
--== Message from the GMAT Club Team ==--
THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.
If you would like to discuss this question please re-post it in the respective forum. Thank you!
To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
_________________
_____________________
Chasing the dragon
Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3386
Location: India
GPA: 3.12
Which of the following line is parallel to the given line 3x + 4y = 12 [#permalink]
Show Tags
16 Aug 2017, 20:03
Two lines are parallel if they have the same slope
The side parallel with ax + by = c1 will be ax + by = c2
Since we are given the equation of the first line 3x + 4y = 12, the second line should also have the equation 3x + 4y = c2
Of the answer options, Only Option B(9x + 12y + 36 = 0) and Option C(9x+ 12y- 36 = 0) have equations such that parallel lines can be formed.
Since we need a line which has a negative y-intercept
Consider Option B
9x + 12y = -36 => 3x + 4y = -9 (when dividing by 3)
The y intercept of an equation is when x=0
Let x = 0, we get y = -9/4 (which is a negative y-intercept)
Hence, Option B is our answer
_________________
You've got what it takes, but it will take everything you've got
Manager
Status: Math Tutor
Joined: 12 Aug 2017
Posts: 73
GMAT 1: 750 Q50 V42
WE: Education (Education)
Re: Which of the following line is parallel to the given line 3x + 4y = 12 [#permalink]
Show Tags
16 Aug 2017, 22:51
Two lines are parallel if one of the equation is multiple of the other
Option A: 6x is 2*3x but 2*4y is not equal to 9y so wrong.
Thus Option D and E are also wrong
Option B is going to give -36 when transferred to right hand side. (General equation of line is y=mx+c)
Option C is going to give +36.
Since question is asking for negative slope, thus option B is correct
_________________
Abhishek Parikh
Math Tutor
Whatsapp- +919983944321
Mobile- +971568653827
Website: http://www.holamaven.com
Math Expert
Joined: 02 Aug 2009
Posts: 7671
Re: Which of the following line is parallel to the given line 3x + 4y = 12 [#permalink]
Show Tags
16 Aug 2017, 23:31
fitzpratik wrote:
Which of the following line is parallel to the given line 3x + 4y = 12 and has a negative y-intercept.
A. 6x + 9y + 12 = 0
B. 9x + 12y + 36 = 0
C. 9x+ 12y- 36 = 0
D. 6x + 9y + 28 = 0
E. 6x + 9y - 28 = 0
Hi...
Get the equation in slope form y=mx+C where m is slope and C is y intercept..
$$3x+4y=12.....Y=3-\frac{3}{4}x$$..
Let's check for slope as -3/4..
Only B and C have slope -9/12=-3/4..
Let's check both B and C..
B. 9x+12y+36=0...
So 12y=-36-9x......Y=-(3/4)x-3..
Here c or y intercept is -3 and slope -3/4.. ANS
C. 9x+12y-36=0..
y=-(3/4)+3..
So slope is same but c is positive..NO
B
--== Message from the GMAT Club Team ==--
THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.
If you would like to discuss this question please re-post it in the respective forum. Thank you!
To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
_________________
Re: Which of the following line is parallel to the given line 3x + 4y = 12 [#permalink] 16 Aug 2017, 23:31
Display posts from previous: Sort by | 1,529 | 4,898 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.90625 | 4 | CC-MAIN-2019-22 | latest | en | 0.88502 |
https://www.saving.org/compare-loans/612000 | 1,591,020,058,000,000,000 | text/html | crawl-data/CC-MAIN-2020-24/segments/1590347417746.33/warc/CC-MAIN-20200601113849-20200601143849-00101.warc.gz | 888,449,331 | 7,233 | #### Compare a \$612,000 Mortgage Loan
Loan 1
\$
%
years
Loan 2
\$
%
years
Summary Loan #1 Payment Loan #2 Payment
Use this calculator to compare the payments of several loans.
Loan Amount: Amount of loan taken.
Interest Rate: Interest rate of the loan.
Years: Time period of loan, in years.
#### Compare a 612k mortgage loan based on interest rates.
What is the cost of a loan based on loan length and interest rate? Monthly payments shown.
Compare a 612000 dollar loan for 15 years versus 10 years.
A \$612k loan for 3 years versus 5 years.
Compare interest rates for a loan. How much does the payment change based on interest rates? Looking for rates?
Rate 30 Year Loan 15 Year Loan 10 Year Loan 5 Year Loan 3 Year Loan 0.05% \$1,713 \$3,413 \$5,113 \$10,213 \$17,013 0.10% \$1,726 \$3,426 \$5,126 \$10,226 \$17,026 0.15% \$1,739 \$3,439 \$5,139 \$10,239 \$17,039 0.20% \$1,752 \$3,452 \$5,152 \$10,252 \$17,052 0.25% \$1,765 \$3,465 \$5,165 \$10,265 \$17,066 0.30% \$1,778 \$3,478 \$5,178 \$10,278 \$17,079 0.35% \$1,791 \$3,491 \$5,191 \$10,291 \$17,092 0.40% \$1,804 \$3,504 \$5,204 \$10,304 \$17,105 0.45% \$1,818 \$3,517 \$5,217 \$10,317 \$17,118 0.50% \$1,831 \$3,530 \$5,230 \$10,330 \$17,131 0.55% \$1,844 \$3,543 \$5,243 \$10,343 \$17,145 0.60% \$1,858 \$3,556 \$5,256 \$10,356 \$17,158 0.65% \$1,872 \$3,569 \$5,269 \$10,369 \$17,171 0.70% \$1,885 \$3,583 \$5,282 \$10,383 \$17,184 0.75% \$1,899 \$3,596 \$5,295 \$10,396 \$17,197 0.80% \$1,913 \$3,609 \$5,308 \$10,409 \$17,210 0.85% \$1,927 \$3,623 \$5,322 \$10,422 \$17,224 0.90% \$1,940 \$3,636 \$5,335 \$10,435 \$17,237 0.95% \$1,954 \$3,649 \$5,348 \$10,448 \$17,250 1.00% \$1,968 \$3,663 \$5,361 \$10,461 \$17,263 1.05% \$1,983 \$3,676 \$5,375 \$10,475 \$17,277 1.10% \$1,997 \$3,690 \$5,388 \$10,488 \$17,290 1.15% \$2,011 \$3,703 \$5,401 \$10,501 \$17,303 1.20% \$2,025 \$3,717 \$5,415 \$10,514 \$17,316 1.25% \$2,040 \$3,730 \$5,428 \$10,527 \$17,330 1.30% \$2,054 \$3,744 \$5,441 \$10,541 \$17,343 1.35% \$2,068 \$3,758 \$5,455 \$10,554 \$17,356 1.40% \$2,083 \$3,771 \$5,468 \$10,567 \$17,369 1.45% \$2,097 \$3,785 \$5,482 \$10,580 \$17,383 1.50% \$2,112 \$3,799 \$5,495 \$10,594 \$17,396 1.55% \$2,127 \$3,813 \$5,509 \$10,607 \$17,409 1.60% \$2,142 \$3,827 \$5,522 \$10,620 \$17,423 1.65% \$2,156 \$3,840 \$5,536 \$10,634 \$17,436 1.70% \$2,171 \$3,854 \$5,549 \$10,647 \$17,449 1.75% \$2,186 \$3,868 \$5,563 \$10,660 \$17,463 1.80% \$2,201 \$3,882 \$5,577 \$10,674 \$17,476 1.85% \$2,216 \$3,896 \$5,590 \$10,687 \$17,489 1.90% \$2,232 \$3,910 \$5,604 \$10,700 \$17,503 1.95% \$2,247 \$3,924 \$5,618 \$10,714 \$17,516 2.00% \$2,262 \$3,938 \$5,631 \$10,727 \$17,529 2.05% \$2,277 \$3,952 \$5,645 \$10,740 \$17,543 2.10% \$2,293 \$3,967 \$5,659 \$10,754 \$17,556 2.15% \$2,308 \$3,981 \$5,672 \$10,767 \$17,569 2.20% \$2,324 \$3,995 \$5,686 \$10,781 \$17,583 2.25% \$2,339 \$4,009 \$5,700 \$10,794 \$17,596 2.30% \$2,355 \$4,023 \$5,714 \$10,808 \$17,610 2.35% \$2,371 \$4,038 \$5,728 \$10,821 \$17,623 2.40% \$2,386 \$4,052 \$5,742 \$10,834 \$17,636 2.45% \$2,402 \$4,066 \$5,755 \$10,848 \$17,650 2.50% \$2,418 \$4,081 \$5,769 \$10,861 \$17,663 2.55% \$2,434 \$4,095 \$5,783 \$10,875 \$17,677 2.60% \$2,450 \$4,110 \$5,797 \$10,888 \$17,690 2.65% \$2,466 \$4,124 \$5,811 \$10,902 \$17,703 2.70% \$2,482 \$4,139 \$5,825 \$10,915 \$17,717 2.75% \$2,498 \$4,153 \$5,839 \$10,929 \$17,730 2.80% \$2,515 \$4,168 \$5,853 \$10,943 \$17,744 2.85% \$2,531 \$4,182 \$5,867 \$10,956 \$17,757 2.90% \$2,547 \$4,197 \$5,881 \$10,970 \$17,771 2.95% \$2,564 \$4,212 \$5,895 \$10,983 \$17,784 3.00% \$2,580 \$4,226 \$5,910 \$10,997 \$17,798 3.05% \$2,597 \$4,241 \$5,924 \$11,010 \$17,811 3.10% \$2,613 \$4,256 \$5,938 \$11,024 \$17,825 3.15% \$2,630 \$4,271 \$5,952 \$11,038 \$17,838 3.20% \$2,647 \$4,285 \$5,966 \$11,051 \$17,852 3.25% \$2,663 \$4,300 \$5,980 \$11,065 \$17,865 3.30% \$2,680 \$4,315 \$5,995 \$11,079 \$17,879 3.35% \$2,697 \$4,330 \$6,009 \$11,092 \$17,892 3.40% \$2,714 \$4,345 \$6,023 \$11,106 \$17,906 3.45% \$2,731 \$4,360 \$6,037 \$11,120 \$17,919 3.50% \$2,748 \$4,375 \$6,052 \$11,133 \$17,933 3.55% \$2,765 \$4,390 \$6,066 \$11,147 \$17,946 3.60% \$2,782 \$4,405 \$6,081 \$11,161 \$17,960 3.65% \$2,800 \$4,420 \$6,095 \$11,175 \$17,974 3.70% \$2,817 \$4,435 \$6,109 \$11,188 \$17,987 3.75% \$2,834 \$4,451 \$6,124 \$11,202 \$18,001 3.80% \$2,852 \$4,466 \$6,138 \$11,216 \$18,014 3.85% \$2,869 \$4,481 \$6,153 \$11,230 \$18,028 3.90% \$2,887 \$4,496 \$6,167 \$11,243 \$18,041 3.95% \$2,904 \$4,512 \$6,182 \$11,257 \$18,055 4.00% \$2,922 \$4,527 \$6,196 \$11,271 \$18,069 4.05% \$2,939 \$4,542 \$6,211 \$11,285 \$18,082 4.10% \$2,957 \$4,558 \$6,225 \$11,299 \$18,096 4.15% \$2,975 \$4,573 \$6,240 \$11,312 \$18,110 4.20% \$2,993 \$4,588 \$6,255 \$11,326 \$18,123 4.25% \$3,011 \$4,604 \$6,269 \$11,340 \$18,137 4.30% \$3,029 \$4,619 \$6,284 \$11,354 \$18,150 4.35% \$3,047 \$4,635 \$6,299 \$11,368 \$18,164 4.40% \$3,065 \$4,651 \$6,313 \$11,382 \$18,178 4.45% \$3,083 \$4,666 \$6,328 \$11,396 \$18,191 4.50% \$3,101 \$4,682 \$6,343 \$11,410 \$18,205 4.55% \$3,119 \$4,697 \$6,357 \$11,423 \$18,219 4.60% \$3,137 \$4,713 \$6,372 \$11,437 \$18,232 4.65% \$3,156 \$4,729 \$6,387 \$11,451 \$18,246 4.70% \$3,174 \$4,745 \$6,402 \$11,465 \$18,260 4.75% \$3,192 \$4,760 \$6,417 \$11,479 \$18,274 4.80% \$3,211 \$4,776 \$6,432 \$11,493 \$18,287 4.85% \$3,229 \$4,792 \$6,446 \$11,507 \$18,301 4.90% \$3,248 \$4,808 \$6,461 \$11,521 \$18,315 4.95% \$3,267 \$4,824 \$6,476 \$11,535 \$18,328 5.00% \$3,285 \$4,840 \$6,491 \$11,549 \$18,342
Rate 30 Year Loan 15 Year Loan 10 Year Loan 5 Year Loan 3 Year Loan 5.05% \$3,304 \$4,856 \$6,506 \$11,563 \$18,356 5.10% \$3,323 \$4,872 \$6,521 \$11,577 \$18,370 5.15% \$3,342 \$4,888 \$6,536 \$11,591 \$18,383 5.20% \$3,361 \$4,904 \$6,551 \$11,605 \$18,397 5.25% \$3,379 \$4,920 \$6,566 \$11,619 \$18,411 5.30% \$3,398 \$4,936 \$6,581 \$11,634 \$18,425 5.35% \$3,417 \$4,952 \$6,596 \$11,648 \$18,439 5.40% \$3,437 \$4,968 \$6,612 \$11,662 \$18,452 5.45% \$3,456 \$4,984 \$6,627 \$11,676 \$18,466 5.50% \$3,475 \$5,001 \$6,642 \$11,690 \$18,480 5.55% \$3,494 \$5,017 \$6,657 \$11,704 \$18,494 5.60% \$3,513 \$5,033 \$6,672 \$11,718 \$18,508 5.65% \$3,533 \$5,049 \$6,687 \$11,732 \$18,521 5.70% \$3,552 \$5,066 \$6,703 \$11,746 \$18,535 5.75% \$3,571 \$5,082 \$6,718 \$11,761 \$18,549 5.80% \$3,591 \$5,099 \$6,733 \$11,775 \$18,563 5.85% \$3,610 \$5,115 \$6,748 \$11,789 \$18,577 5.90% \$3,630 \$5,131 \$6,764 \$11,803 \$18,591 5.95% \$3,650 \$5,148 \$6,779 \$11,817 \$18,604 6.00% \$3,669 \$5,164 \$6,794 \$11,832 \$18,618 6.05% \$3,689 \$5,181 \$6,810 \$11,846 \$18,632 6.10% \$3,709 \$5,198 \$6,825 \$11,860 \$18,646 6.15% \$3,728 \$5,214 \$6,841 \$11,874 \$18,660 6.20% \$3,748 \$5,231 \$6,856 \$11,889 \$18,674 6.25% \$3,768 \$5,247 \$6,872 \$11,903 \$18,688 6.30% \$3,788 \$5,264 \$6,887 \$11,917 \$18,702 6.35% \$3,808 \$5,281 \$6,903 \$11,932 \$18,715 6.40% \$3,828 \$5,298 \$6,918 \$11,946 \$18,729 6.45% \$3,848 \$5,314 \$6,934 \$11,960 \$18,743 6.50% \$3,868 \$5,331 \$6,949 \$11,974 \$18,757 6.55% \$3,888 \$5,348 \$6,965 \$11,989 \$18,771 6.60% \$3,909 \$5,365 \$6,980 \$12,003 \$18,785 6.65% \$3,929 \$5,382 \$6,996 \$12,018 \$18,799 6.70% \$3,949 \$5,399 \$7,012 \$12,032 \$18,813 6.75% \$3,969 \$5,416 \$7,027 \$12,046 \$18,827 6.80% \$3,990 \$5,433 \$7,043 \$12,061 \$18,841 6.85% \$4,010 \$5,450 \$7,059 \$12,075 \$18,855 6.90% \$4,031 \$5,467 \$7,074 \$12,089 \$18,869 6.95% \$4,051 \$5,484 \$7,090 \$12,104 \$18,883 7.00% \$4,072 \$5,501 \$7,106 \$12,118 \$18,897 7.05% \$4,092 \$5,518 \$7,122 \$12,133 \$18,911 7.10% \$4,113 \$5,535 \$7,137 \$12,147 \$18,925 7.15% \$4,133 \$5,552 \$7,153 \$12,162 \$18,939 7.20% \$4,154 \$5,569 \$7,169 \$12,176 \$18,953 7.25% \$4,175 \$5,587 \$7,185 \$12,191 \$18,967 7.30% \$4,196 \$5,604 \$7,201 \$12,205 \$18,981 7.35% \$4,217 \$5,621 \$7,217 \$12,220 \$18,995 7.40% \$4,237 \$5,639 \$7,233 \$12,234 \$19,009 7.45% \$4,258 \$5,656 \$7,249 \$12,249 \$19,023 7.50% \$4,279 \$5,673 \$7,265 \$12,263 \$19,037 7.55% \$4,300 \$5,691 \$7,281 \$12,278 \$19,051 7.60% \$4,321 \$5,708 \$7,297 \$12,292 \$19,065 7.65% \$4,342 \$5,726 \$7,313 \$12,307 \$19,079 7.70% \$4,363 \$5,743 \$7,329 \$12,321 \$19,093 7.75% \$4,384 \$5,761 \$7,345 \$12,336 \$19,107 7.80% \$4,406 \$5,778 \$7,361 \$12,351 \$19,121 7.85% \$4,427 \$5,796 \$7,377 \$12,365 \$19,136 7.90% \$4,448 \$5,813 \$7,393 \$12,380 \$19,150 7.95% \$4,469 \$5,831 \$7,409 \$12,395 \$19,164 8.00% \$4,491 \$5,849 \$7,425 \$12,409 \$19,178 8.05% \$4,512 \$5,866 \$7,441 \$12,424 \$19,192 8.10% \$4,533 \$5,884 \$7,458 \$12,438 \$19,206 8.15% \$4,555 \$5,902 \$7,474 \$12,453 \$19,220 8.20% \$4,576 \$5,919 \$7,490 \$12,468 \$19,234 8.25% \$4,598 \$5,937 \$7,506 \$12,483 \$19,249 8.30% \$4,619 \$5,955 \$7,523 \$12,497 \$19,263 8.35% \$4,641 \$5,973 \$7,539 \$12,512 \$19,277 8.40% \$4,662 \$5,991 \$7,555 \$12,527 \$19,291 8.45% \$4,684 \$6,009 \$7,572 \$12,541 \$19,305 8.50% \$4,706 \$6,027 \$7,588 \$12,556 \$19,319 8.55% \$4,727 \$6,045 \$7,604 \$12,571 \$19,334 8.60% \$4,749 \$6,063 \$7,621 \$12,586 \$19,348 8.65% \$4,771 \$6,081 \$7,637 \$12,600 \$19,362 8.70% \$4,793 \$6,099 \$7,654 \$12,615 \$19,376 8.75% \$4,815 \$6,117 \$7,670 \$12,630 \$19,390 8.80% \$4,836 \$6,135 \$7,686 \$12,645 \$19,405 8.85% \$4,858 \$6,153 \$7,703 \$12,660 \$19,419 8.90% \$4,880 \$6,171 \$7,719 \$12,674 \$19,433 8.95% \$4,902 \$6,189 \$7,736 \$12,689 \$19,447 9.00% \$4,924 \$6,207 \$7,753 \$12,704 \$19,461 9.05% \$4,946 \$6,226 \$7,769 \$12,719 \$19,476 9.10% \$4,968 \$6,244 \$7,786 \$12,734 \$19,490 9.15% \$4,990 \$6,262 \$7,802 \$12,749 \$19,504 9.20% \$5,013 \$6,280 \$7,819 \$12,764 \$19,518 9.25% \$5,035 \$6,299 \$7,836 \$12,779 \$19,533 9.30% \$5,057 \$6,317 \$7,852 \$12,793 \$19,547 9.35% \$5,079 \$6,335 \$7,869 \$12,808 \$19,561 9.40% \$5,101 \$6,354 \$7,886 \$12,823 \$19,576 9.45% \$5,124 \$6,372 \$7,902 \$12,838 \$19,590 9.50% \$5,146 \$6,391 \$7,919 \$12,853 \$19,604 9.55% \$5,168 \$6,409 \$7,936 \$12,868 \$19,618 9.60% \$5,191 \$6,428 \$7,953 \$12,883 \$19,633 9.65% \$5,213 \$6,446 \$7,969 \$12,898 \$19,647 9.70% \$5,236 \$6,465 \$7,986 \$12,913 \$19,661 9.75% \$5,258 \$6,483 \$8,003 \$12,928 \$19,676 9.80% \$5,281 \$6,502 \$8,020 \$12,943 \$19,690 9.85% \$5,303 \$6,521 \$8,037 \$12,958 \$19,704 9.90% \$5,326 \$6,539 \$8,054 \$12,973 \$19,719 9.95% \$5,348 \$6,558 \$8,071 \$12,988 \$19,733 10.00% \$5,371 \$6,577 \$8,088 \$13,003 \$19,748 | 5,204 | 10,399 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.578125 | 3 | CC-MAIN-2020-24 | latest | en | 0.775566 |
http://matplus.net/start.php?px=1581995330&app=forum&act=posts&fid=xshowe&tid=563&pid=3866 | 1,586,012,661,000,000,000 | text/html | crawl-data/CC-MAIN-2020-16/segments/1585370524043.56/warc/CC-MAIN-20200404134723-20200404164723-00369.warc.gz | 115,135,247 | 6,000 | MatPlus.Net
Website founded by
Milan Velimirović
in 2006
15:04 UTC
ISC 2020
Headlines Forum* Fellows Members DL Archive Links
Username:
Password:
Remember me
Forgot yourpassword?Click here! SIGN INto create your account if you don't already have one.
CHESS SOLVINGTournamentsRating lists1-Apr-2020
B P C F
MatPlus.Net Forum Endgame studies Waiting for an intro
You can only view this page!
### Waiting for an intro
Obviously I wasn't the first to notice that in Kc6 Bd5 Pa6/Kb8 Pa7 a second
bishop on White would be very beneficial. It wasn't hard either to set up
Kh1 Be8 Pa6 Pg7 - Kh6 Pa7 Ph7 (1.g8L!). A bit of recherche found exactly (?)
this position which might have benefitted from an intro.
Do you know other, even better, examples where White has to promote to
another bishop of the same color? Maybe even three?
Hauke
(Read Only) pid=3864
I had the same idea in an endgame published some time ago in Diagrammes. However it has a very short introduction, but perhaps worth exploring further.
The position is: Kb3 Rb8 Bd8 pc6 h6 / Ka6 Ra1 pa2 a7 h7.
Solution: 1.c7! Rb1+ 2.Kxa2 Rxb8 3.cxb8=B!! (i) etc.
(i) 3.cxb8=S? Kb7 4.Sd7 Kc8 5.Sf6/Sf8 Kxd8 6.Sxh7 Ke7 7.Sg5 Kf6 8.h7 Kg7 draw
There are also two tries - first trivial, second more interesting:
1.Bc7? Rb1+ 2.Kxa2 Rb2+ 3.Ka3 Rb3+ perpetual check or stalemate
1.Rc8!? Rb1+ 2.Kxa2 Rb8 3.Rc7 Rxd8 4.Rxh7 Rd6 5.c7 Kb7 6.Rh8 Ra6+ 7.Kb3 Rb6+ 8.Kc4 Rc6+ 9.Kd5 Rxc7 10.h7 Ka6 draw (at that time there was no Thompson database to check this line)
However, as I learnt later, this position was first shown by Pal Benko. I don't remember the source (Chess Life in sixties?), but I hope some better documented lectors will help you.
(Read Only) pid=3865
(3) Posted by Arpad Rusz [Saturday, Jun 20, 2009 19:45]
Here are some studies (there are many more):
A.Troitzky (1925)
(= 5+4 )
Win
1.b7 Rg4+ 2.Kf2 Rg8 3.d6 Kc4 4.d7 Kb5! 5.d8Q Rxd8 6.Bxd8 Ka6 7.b8B!! [7.b8N+? Kb7 8.Nd7 Kc8 9.Nf6 Kxd8 10.Nxh7 Ke7! 11.Ng5 (11.Kf3 Kf7=) 11...Kf6 12.h7 Kg7=; 7.b8Q? stalemate] 7...Kb7 8.Be5 Kc8 9.Be7 Kd7 10.B7d6 Ke6 11.Kf3 a5 12.Kf4 a4 13.Ba3 Kf7 14.Kf5 Kg8 15.Kf6 Kh8 16.Kf7#
V.Korolkov (1929)
(= 6+9 )
Draw (Cooked!)
1.f7! a1Q 2.h8B+!! [2.h8Q+? Kd3 3.Qxa1 Bd7+ 4.Kb4 a5+ 5.Kb3 Be6+ 6.Kb2 Bxf7 7.Qxb1 cxb1Q+ 8.Kxb1] 2...Kd3 3.Bxa1 Bd7+ [but 3...Be6! 4.f8Q Bc4+ 5.Kb4 a5#] 4.Kb4 a5+ 5.Kb3 Be6+ 6.Kb2 Bxf7 stalemate
H.Ginninger (1933)
(= 8+6 )
Win
1.d8B! [1.d8Q? Nf1 2.Qxc7 Ne2 3.b8B Nf4+ 4.Qxf4 Ng3+ 5.Qxg3 stalemate] 1...Nf1 2.Bxc7 Ne2 3.b8B! [3.b8Q? Nfg3+ (3...Neg3+) 4.Bxg3 Nxg3+ 5.Qxg3 stalemate] 3...fxg6+ 4.Kxg6 1–0
V.Smyslov (1936)
(= 9+7 )
Win
1.Bb1! a1Q+ 2.Kb5 Bg3 [2...Qa3 3.g7] 3.g7 Bb8! 4.g8B!! [4.g8Q? Qa4+ 5.Kxa4 stalemate] 4...Bf4 5.Bga2! Bxd2 6.f6! Bf4 7.f7 Bd6 8.Kc6 Bf8 9.Kc7 1–0
V.Troitzky, V.Korolkov (1938)
(= 11+6 )
Win
1.Qc3 Nxc3 2.d8B! [2.d8Q? f1N 3.Qxc7 Nde4 (3...Ne2) 4.Bf4 Ne2 5.b8B Nd6! 6.Qxd6 Neg3+ 7.Bxg3 Nxg3+ 8.Qxg3 stalemate] 2...Ne2 3.Bxc7 f1N! 4.b8B! [4.b8Q? Ne4=] 4...Ne4 5.B1f4 Nfg3+ 6.Bxg3 N2xg3+ 7.Bxg3 Nxg3+ 8.Bxg3 1–0
V.Korolkov (1941)
(= 10+7 )
Win
1.a8B!! [1.a8Q? Nc4 2.dxc4 d3 3.e5 Nc6 (3...Nd5) 4.Qxc6 Kh2 5.Qxf3 stalemate] 1...Nc4! 2.dxc4 d3 3.e5 Bxa8 4.c8B!! [4.c8Q? Bf3 5.Qb7 Nc6 (5...Nd5) 6.Qxc6 Kh2 7.Qxf3 stalemate] 4...Bf3! 5.Bb7 Nc6! 6.Bxc6 Bxc6 7.g8B!! [7.g8Q? Bf3 8.Qd5 Kh2! 9.Qxf3 stalemate] 7...Bf3 8.Bd5 Kh2 9.Bxf3 1–0
(Read Only) pid=3866
<hits himself repeatedly with chessboard>
How could I forget the last position when asking? I'm getting old :-)
Hauke
(Read Only) pid=3867
Some more (I found these in Nieuwe Schaakcuriosa by Tim Krabbe):
C. Bent, W. Veitch
(= 5+4 )
Win
1. Sh6 Kf8 2. c6 Rb4 3. c7 Rc4 4. Bc4 Bc2 5. Kh8 Bf5 6. Sf5 Se8 7. c8=B! and white wins
A. Troitski
(= 6+7 )
Win
1. Qg3 Qg3 2. ab8=B Kxd5 3. Bg3 (2. ab8=Q? 3... e1=Q!) Ke6 4. Ka5 (4. Ka4? Kd7 5. Ka5 Kc8 6. Kb6 e1=Q 7. Be1 Kb8=) Kd7 5. Kb6 Kc8 6. Ka7 Kd8 7. Kb8 Kd7 8. Kb7 Kd8 9. Kc6 Kc8 10. Bcd6 Kd8 11. Bh4 Kc8 12. Bh2 e1=Q 13. Be1 Kd8 14. Kb7 Ke7 15. Bh4 Kd7 16. Bg5 Ke6 17. Kc6 Kf5 18. Kb5 Ke6 19. Ka4 Kd7 20. Kb5 Kc8 21. Kb6+
V. Korolkov, A. Doluchanov
(= 7+6 )
Win
1. g8=Q ef2 2. Kf1 Rg8 3. hg8=B (3. hg8=Q? Bc4 4. Qc4=). In this position, black will draw if he can reach c7 and keep the bishop on the board. There are only two serious defences, in other cases the bishop is caught easily (e.g. 3... Bc8? 4. Bge6 Bb7 5. Bcd5).
A) 3... Bd7 4. Kf2 Kb4 5. Kf3 Kc5 6. Bge6 Be8 7. Kf4 Kd6 8. Kg5 Ke5 9. b3 Kd6 10. Bh3 Ke5 11. Bg4 Kd6 12. Kf6 Kc7 13. Bce2 Kd6 14. Bd3 Kc7 15. Ke7+
B) 3... Bf5 4. Kf2 Kb4 5. Kf3 Kc5 6. Kf4 Bh3 7. Ke5 Bd7 8. b3 Bg4 9. Bge6 Bd1 10. Bd7 Bf3 11. Ke6 Bg4 12. Ke7 Bf3 13. Bc6 Bg4 14. Be6 Bd1 15. Kd7 Be2 16. Kc7 Bd1 17. Kb7 (17. b4? Kb4 18. Kb6 Ba4!=) Bc2 18. Ka6 Bd1 19. Bc4 Bc2 20. B6d5 Bd1 21. Bd3!! zz Kd5 22. Kb6 Bb3 23. Kc7 Kc5 24. b6 Bd5 25. Ba6 Bf3 26. Bb7 Be2 27. Bg2 Ba6 28. Bf1 Bc8 29. Be2
(Read Only) pid=3868
http://rankzero.de/?p=4048
Not to forget this study by Teschke 2008
(Read Only) pid=3869
And a Troitski joke. Not entirely what OP wanted (the extra bishops are already present in the diagram), but white needs all 5 bishops to win!
A. Troitski
(= 6+2 )
Win
1. Bce5 a5 2. Ba1 a4 3. Bbe5 a3 4. Kd2 Ka2 5. Kc3 Ka1 6. Kb3 Kb1 7. Ba1 a2 8. Kc3 Ka1 9. Kc2
(Read Only) pid=3870
No more posts
MatPlus.Net Forum Endgame studies Waiting for an intro | 2,642 | 5,329 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.53125 | 3 | CC-MAIN-2020-16 | latest | en | 0.88282 |
http://www.chegg.com/homework-help/line-equation-x-t-l-y-3t-l-z-t-t-real-intersect-planes-x-y-chapter-7.5-problem-1e-solution-9780321046246-exc | 1,469,866,419,000,000,000 | text/html | crawl-data/CC-MAIN-2016-30/segments/1469257832942.23/warc/CC-MAIN-20160723071032-00201-ip-10-185-27-174.ec2.internal.warc.gz | 368,913,747 | 16,134 | View more editions
# TEXTBOOK SOLUTIONS FOR College Geometry A Discovery Approach 2nd Edition
• 862 step-by-step solutions
• Solved by publishers, professors & experts
• iOS, Android, & web
Over 90% of students who use Chegg Study report better grades.
May 2015 Survey of Chegg Study Users
Chapter: Problem:
A line has equation x = t - l, y = 3t + l, z = - t (t real). Does it intersect both planes x + y + z = 9 and 3x - y - 2z = 2? If so, find the coordinates of the point(s) of intersection.
STEP-BY-STEP SOLUTION:
Chapter: Problem:
• Step 1 of 3
Substituting
into the equation for the first plane gives us
so the line hits the plane when t = 3, or at the point (2, 10, -3).
• Chapter , Problem is solved.
Corresponding Textbook
College Geometry A Discovery Approach | 2nd Edition
9780321046246ISBN-13: 0321046242ISBN: David KayAuthors:
Alternate ISBN: 9780321830951 | 255 | 878 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.9375 | 3 | CC-MAIN-2016-30 | latest | en | 0.720624 |
https://www.coursehero.com/file/p4m1sebs/A-Random-sample-of-cases-B-Based-on-time-or-case-range-C-Use-filter-variable-D/ | 1,606,585,126,000,000,000 | text/html | crawl-data/CC-MAIN-2020-50/segments/1606141195687.51/warc/CC-MAIN-20201128155305-20201128185305-00667.warc.gz | 627,273,828 | 87,834 | A Random sample of cases B Based on time or case range C Use filter variable D
# A random sample of cases b based on time or case
This preview shows page 2 - 6 out of 6 pages.
A. Random sample of cases B. Based on time or case range C. Use filter variable D. If condition is satisfied Answer: D QUESTION: 51 26
As the sample size increases, the amount of variabilit9 in the distribution of sample means increases. A. True B. False Answer: B QUESTION: 52 Which interpretation is correct for the IndependentSamples T-Test table shown below? A. We did not meet the assumption of homogeneity of variance; however our two groups differed on the number of WWW HOURS PER WEEK. B. We did meet the assumption of homogeneity of variance and our two groups differedon the number of WWW HOURS PER WEEK. C. We did not meet the assumption of homogeneity of variance and our two groups did not differ on the number of WWW HOURS PER WEEK. We did meet the assumption of homogeneity of variance; however our two groups did not differ on the number of WWW HOURS PER WEEK. Answer: A QUESTION: 53 You have been asked to create a categorical variable from a scale variable, income, illustrated in the histogram below. The resulting categorical variable must have 5 categories with an approximately equal number of cases in each category. Which way would you accomplish this using the IBM SPSS Statistics Visual Binning dialog? 27
A. Use the automatic option Equal Width Intervals B. Use the automatic option Equal Percentiles Based on Scanned Cases C. Use the automatic option Outpoints at Mean and Selected Standard Deviations Based on Scanned Cases D. Specify Cut points manually at 10000, 20000, 30000, 40000 & 50000. Answer: B QUESTION: 54 The reason you would select the check box next to ¡°indicate case source variable¡± in the Add Cases dialog box is to: 28
A. Create a new case in your merged data. B. Highlight a specific case in one of your variables. C. Create a variable identifying the case data source. D. Create a variable identifying the variable data source. Answer: C QUESTION: 55 Which chart type is appropriate for viewing the association between two scale variables? A. Bar chart B. Area chart C. Pie chart D. Scatter plot Answer: D 29
For More exams visit http s ://killexams.com /vendors-exam-list Kill your exam at First Attempt .... Guaranteed!
#### You've reached the end of your free preview.
Want to read all 6 pages? | 555 | 2,429 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.03125 | 3 | CC-MAIN-2020-50 | latest | en | 0.865632 |
http://www.taxgirl.com/ask-the-taxgirl-sales-tax-classification/ | 1,487,704,884,000,000,000 | text/html | crawl-data/CC-MAIN-2017-09/segments/1487501170823.55/warc/CC-MAIN-20170219104610-00123-ip-10-171-10-108.ec2.internal.warc.gz | 626,390,728 | 12,838 | # Ask the taxgirl: Sales Tax Classification
In your articles about the states, you keep saying that sales tax is regressive. But since everybody is paying the same percent, doesn’t that make it a flat tax which means it’s not regressive? I’m confused.
Taxgirl says:
Good question!
Most sales taxes are flat rate taxes in that the same percentage is levied on the same kinds of items. So, if you and I both buy a package of gum in Philadelphia that costs \$1.00, we both pay 7% on that package of gum (at least this week).
Where the tax is considered regressive is as a percentage of income. Let’s assume that you make \$100,000 and I make \$20,000. If we both buy \$5,000 worth of taxable items for the year, we both pay \$350 in sales tax (assuming we’re still in Philly). Now, your effective tax rate is .35% and mine is 1.75%. In other words, I’m paying an effective rate of 5 times more than you are as a percentage of my income.
In some states, “essential” goods like grocery items, clothing and medicines are exempt from sales tax. But in many states, sales tax is imposed on essentials – in North Carolina, for example, clothing is taxed. While it probably follows that you’ll buy more expensive clothes because you have more money, it will likely still cost more as a percentage of income to pay the sales tax on my clothes because I make less money overall. Does that make sense?
That calculation changes a bit when you consider excise taxes. Those are taxes which are generally imposed on alcohol, cigarettes and other “luxury goods”, sometimes associated with “sin taxes.” Excise taxes are considered even more regressive than sales taxes because of the higher rates associated with those taxes. In most cases, those are taxed by volume or type and not by cost, which makes the excise tax difference between a very nice bottle of Mondavi and a bottle of Boone’s Farm non-existent.
A number of alternatives to the sales tax have been proposed, including the infamous Fair Tax, to address concerns about the regressive natures of sales taxes. To date, none of the alternatives have been implemented.
Like any good lawyer, I need to add a disclaimer: Unfortunately, it is impossible to give comprehensive tax advice over the internet, no matter how well researched or written. Before relying on any information given on this site, contact a tax professional to discuss your particular situation. | 519 | 2,412 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.578125 | 3 | CC-MAIN-2017-09 | longest | en | 0.973796 |
https://johannafaith.com/quebec/contribution-margin-behavioral-variable-income-statement-example.php | 1,627,967,829,000,000,000 | text/html | crawl-data/CC-MAIN-2021-31/segments/1627046154420.77/warc/CC-MAIN-20210803030201-20210803060201-00632.warc.gz | 339,356,831 | 7,326 | # Behavioral contribution statement example margin variable income
The Contribution Margin Income Statement – Accounting In Focus. Start studying chapter 12 & 16s. learn vocabulary, the contribution margin format income statement is an example of a cost that is likely to have a variable, calculate the weighted average contribution margin to find your which are found on the firm's income statement for example, if you have variable costs of.
### Contribution Margin Formula Calculator (With Excel Template)
CONTRIBUTION MARGIN INCOME STATEMENT blogspot.com. Acg 3 study guide by nency_quezada3 includes 27 questions covering vocabulary, terms and more. quizlet flashcards, activities and games help you improve your grades., this example merely covers net income contribution margin constitutes the variable costs of the differences between contribution margin, net income and.
Contribution margin = sales вђ“ variable costs. example: joe has a food truck from which he sells tacos. in contrast, with a contribution margin income statement, the profit is equal to the contribution margin minus the fixed costs. variable costs the total contribution margin is contribution-margin income statement.
... you start by looking at a traditional income statement and contribution margin = revenue в€’ variable are вђњquasi-variable.вђќ for example, a variable costing income statement is one in which all variable expenses are deducted from revenue to arrive at a separately-stated contribution margin , from which
Thus the production performance results reported on the income statement. cost behavior contribution margin or variable contribution margin formats. example the variable-costing or contribution margin format income statement is an are considered variable costs. for example, variable costing income statement,
The denominator of the break-even equation is the contribution margin. as an example, income statement, the gross profit margin variable. the contribution see the format of contribution margin income statement. to reduce variable cost of low contribution margin margin ratio with the help of an example?
Explanation of contribution margin income statement with the help of an example. 5.5 cost-volume-profit analysis in planning. analysis requires knowledge of costs and their fixed or variable behavior the contribution margin income
Contribution margin income statement. the income statement, for example, if variable cost is 60% of sales, then the contribution margin would be 40% of sales. this example merely covers net income contribution margin constitutes the variable costs of the differences between contribution margin, net income and
This is a guide to contribution margin while calculating the contribution, we deduct the total variable expenses from the income statement template the variable-costing or contribution margin format income statement is an are considered variable costs. for example, variable costing income statement,
Preparation of variable costing income statement; reconciliation of variable costing and absorption costing net operating income gross contribution margin and contribution margin in accordance with the behavior of variable and fixed costs, in totals on a contribution-type income statement.
### How to Figure Out the Weighted-Average Contribution Margin
Advantages or Disadvantages of Contribution Margin. The marginal income, or contribution margin, difference between the unit price and the variable costs per unit. in the example to calculate marginal income.", thus the production performance results reported on the income statement. cost behavior contribution margin or variable contribution margin formats. example.
### Contribution Margin Formula and Analysis AccountingVerse
The Contribution Margin Income Statement GitHub Pages. The denominator of the break-even equation is the contribution margin. as an example, income statement, the gross profit margin variable. the contribution ... variable) income statement for prepare a contribution margin (behavioral, variable) income statement for of income and leadership on. variables such.
• CONTRIBUTION MARGIN INCOME STATEMENT
• Acc 202 Module 3 Session Long Project Essay by Lhrod02
• Contribution Margin Business Literacy Institute
• Break even point and contribution margin for example, if variable costs the concepts of contribution margin and the contribution income statement have many this example merely covers net income contribution margin constitutes the variable costs of the differences between contribution margin, net income and
Cvp income statement is arranged to show variable expenses, contribution margin and fixed expenses allowing a business to make cost volume cvp statement example. variable selling and administrative. how much is the contribution margin for the year under the contribution-margin format of the income statement
Break even point and contribution margin for example, if variable costs the concepts of contribution margin and the contribution income statement have many variable selling and administrative. how much is the contribution margin for the year under the contribution-margin format of the income statement
A contribution margin income statement is a by the makerвђ™s variable costs, with the contribution able example, by analyzing your contribution margins the contribution margin per car lets you know that after the it needs to service in order to cover the company's fixed and variable income statement ; 13.
Here is an example of a contribution margin income statement the contribution margin income statement is a cost behavior using the same example, variable contribution margin = sales вђ“ variable costs. for example, statement makes understanding cost behavior and how contribution margin income statement is not
5.5 cost-volume-profit analysis in planning. analysis requires knowledge of costs and their fixed or variable behavior the contribution margin income what is contribution margin? in accounting contribution margin is defined as revenues minus variable expenses. contribution margin income statement:
... form of an income statement that is income items (revenue, contribution margin and operating income in this example), the flexible budget variance is see the format of contribution margin income statement. to reduce variable cost of low contribution margin margin ratio with the help of an example?
... affect net income: sales price sales volume variable cost contribution margin income statement. example company, plug the contribution margin a contribution margin income statement is an income statement in which all variable expenses are deducted from sales to arrive at a contribution margin , from which
5.5 cost-volume-profit analysis in planning. analysis requires knowledge of costs and their fixed or variable behavior the contribution margin income contribution margin is how much profit you are earning on your subtract variable costs from sales. example: looking for training on the income statement, | 1,224 | 7,044 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.5625 | 3 | CC-MAIN-2021-31 | latest | en | 0.846699 |
https://heatingsystemwiki.com/is-cooling-water-kinetic-or-potential/ | 1,725,791,145,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700650976.41/warc/CC-MAIN-20240908083737-20240908113737-00677.warc.gz | 283,768,614 | 46,218 | # Discover the Surprising 3 Reasons Why Cooling Water is Kinetic
Cooling water can exhibit both kinetic and potential energy, depending on the phase and context of the water. The kinetic energy of cooling water refers to the energy of motion of the water molecules, while the potential energy is related to the energy stored in the bonds between the water molecules.
## Kinetic Energy of Cooling Water
The kinetic energy of cooling water is directly related to the temperature of the water. As the water is cooled, the average kinetic energy of the water molecules decreases. This is because the water molecules move slower and collide with each other less frequently, resulting in a lower overall kinetic energy.
The kinetic energy of the water can be calculated using the formula:
``````K = 1/2 mv^2
``````
Where:
`K` is the kinetic energy
`m` is the mass of the water
`v` is the velocity of the water molecules
However, in the context of cooling water, the velocity of the water molecules is usually not directly measured. Instead, the kinetic energy is often expressed in terms of temperature using the formula:
``````K = 3/2 nkT
``````
Where:
`n` is the number of water molecules
`k` is the Boltzmann constant
`T` is the absolute temperature of the water
This formula allows the kinetic energy of the cooling water to be estimated based on the measured temperature.
## Potential Energy of Cooling Water
The potential energy of cooling water is related to the energy stored in the bonds between the water molecules. As the water cools and undergoes a phase change, such as from liquid to solid (ice), the potential energy of the water increases.
When water freezes, the water molecules form a crystalline structure, and the bonds between the molecules become more ordered and stable. This increase in potential energy is reflected in the energy required to break the bonds and melt the ice back into liquid water.
The potential energy of the water can be measured by comparing the energy required to break the bonds between the water molecules in different phases. For example, the energy required to melt ice is higher than the energy required to heat liquid water, indicating that the potential energy of the water increases during the phase change from ice to liquid.
## Technical Specifications of Cooling Water
The technical specifications of cooling water depend on the application and the desired properties of the water. In cooling towers, for example, the water is often treated with chemicals to prevent corrosion, scaling, and biological growth. The water quality specifications may include parameters such as pH, alkalinity, hardness, and conductivity, which can affect the efficiency and longevity of the cooling system.
In industrial processes, the cooling water may be recycled and reused, which requires careful monitoring and treatment to ensure that the water quality remains within acceptable limits. The design of the cooling system can also affect the kinetic and potential energy of the water, with factors such as flow rate, pressure drop, and turbulence influencing the heat transfer and energy consumption of the system. | 622 | 3,166 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.1875 | 3 | CC-MAIN-2024-38 | latest | en | 0.933095 |
https://www.coursehero.com/file/87862/Finite-Chapter-12/ | 1,498,134,950,000,000,000 | text/html | crawl-data/CC-MAIN-2017-26/segments/1498128319265.41/warc/CC-MAIN-20170622114718-20170622134718-00413.warc.gz | 958,285,663 | 49,275 | Finite Chapter 1.2
# Finite Chapter 1.2 - 1.2 Functions from the Graphical...
This preview shows page 1. Sign up to view the full content.
Math 120 SP08 SBrodnick 1 1 1.2 : Functions from the Graphical Viewpoint 2 1.2: Functions from the Graphical Viewpoint Examples : 1. (see graph) What is… f(-2)? f(0)? f(4)? 2.(see graph) What is… f(-4)? f(-2)? f(1)? f(5)? domain of f? range of f? domain of f? range of f? 3 * Reminder : a function has one (and only one) output for each input. (can’t input 4 and get two different outputs.) * Easy way to tell if graph is a function: it passes Vertical Line Test * Evaluating functions on your calculator… Enter equation into Y 1 2 nd TRACE Read Y-values on table
This is the end of the preview. Sign up to access the rest of the document.
Unformatted text preview: 1.2: Functions from the Graphical Viewpoint 4 Example : 3.Graph g(x) = -x² - 8x – 11 and evaluate a. g(-1) b. g(3) c. g(9) d. g(-8) + g(4) d. is g a function? 1.2: Functions from the Graphical Viewpoint 5 *Graphing Piecewise Functions: Examples : 4.Graph f(x) = 5.Graph f(x) = * Functions that you should know by heart : P. 50 & 51 x - 2 if x ≤ -1-2x² if x > -1 1.2: Functions from the Graphical Viewpoint 3x if x ≤ -2 x² if -2 < x ≤ 3-x + 1 if x > 3...
View Full Document
## This note was uploaded on 04/07/2008 for the course MAT 120 taught by Professor Brodnick during the Spring '08 term at Illinois State.
Ask a homework question - tutors are online | 468 | 1,465 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.4375 | 3 | CC-MAIN-2017-26 | longest | en | 0.795568 |
http://devmaster.net/forums/topic/14342-separatingsplitting-a-mesh-in-real-time/page__pid__76717 | 1,369,269,731,000,000,000 | text/html | crawl-data/CC-MAIN-2013-20/segments/1368702652631/warc/CC-MAIN-20130516111052-00052-ip-10-60-113-184.ec2.internal.warc.gz | 68,945,902 | 12,984 | # Separating/Splitting a Mesh in Real Time
6 replies to this topic
### #1Lokked
New Member
• Members
• 17 posts
Posted 18 March 2011 - 03:24 PM
What is the term for this, or what should I be searching for:
A 3D Object fragmenting into independant objects
Getting a limb blown off
Showing other physical dismemberments
To be calculated in Real Time.
Let me know if my description is too vague.
### #2TheNut
Senior Member
• Moderators
• 1701 posts
• LocationCyberspace
Posted 18 March 2011 - 03:56 PM
They're called giblets :happy:
Just take your mesh and break it down into parts. You most likely already did this if you created a skeleton for your mesh. If the part is already closed (no open holes for each part), then to simulate dismemberment you just have to render the part away from the body. If you want to do real-time slicing and dicing, then you need to loop-cut your mesh along the fracture or seam, close it (triangularize the open areas: see how to triangularize a polygon), provide UV coordinates and normals for the new triangles, and texture it. I don't think there's any tutorials on this. It's all mathematical.
http://www.nutty.ca - Being a nut has its advantages.
### #3Lokked
New Member
• Members
• 17 posts
Posted 21 March 2011 - 01:48 AM
I want to hack a limb off my model, and have it calculate in real time. The cut can be made anywhere, in any direction. Not necessarily at a bone joint.
My thoughts are:
1. Create verticies forming an elipse, equal to the plane the slice would form, around the limb.
2. Separate the cleaved Bone into 2 parts (I don't know how this is accomplished in real time. I could shorten the original bone and create another, but this would end up shortening the whole mesh, and/or I'm lost).
3. Triangulate any quads that were created.
4. Treat the Separated Mesh with 6 DOF.
Does this sound like an accurate procedure?
### #4rouncer
Senior Member
• Members
• 2722 posts
Posted 21 March 2011 - 05:40 AM
maybe it sounds ok? if a little unexplained just yet...
would be insanely cool for a medieval sword+shield game tho :)
you used to be able to fit a game on a disk, then you used to be able to fit a game on a cd, then you used to be able to fit a game on a dvd, now you can barely fit one on your harddrive.
### #5Lokked
New Member
• Members
• 17 posts
Posted 21 March 2011 - 04:32 PM
I haven't actually tried this out yet, just bouncing ideas around :p
Defining Vertices of a Solid where Intersected by a Plane:
1. Create a Transform T from the current coordinate system to a Frame A(x, y, z) where:
z = Slicing Plane's Normalized Velocity Vector Vn (Direction of Slicing Action)
y = Axis along which Plane intersects solid
x = Orthogonal to y and z
2. Create a Plane R, such that the Plane's equation in Frame A is:
R(x, y, z) = (0, 0, 0)x + (0, 1, 0)y + (0, 0, 1)z
for all Real x, y, z.
3. Calculate the points where the Plane R intersects lines of the Solid.
For each line, consisting of direction vector l extending from one end of the line lo, calculate the Point P where this line intersects the Plane R:
d = ( (0, 0, 0) - lo ) DOT Rn
_____________________
l DOT Rn
where Rn is a vector Normal to Plane R, which is (1, 0, 0), and d is the distance from lo to the Point P along the line vector l:
P(x, y, z) = lo + (Rn * d)
Each of these points can be applied T(inverse) to be represented by the original coordinate frame.
### #6TheNut
Senior Member
• Moderators
• 1701 posts
• LocationCyberspace
Posted 21 March 2011 - 07:38 PM
You're on the right track. All you need is a point on the plane that will sever the object and the plane normal. Transform the plane into object space. Then proceed with your 3rd step. You can speed things by finding the first intersection point and then follow neighbouring edges to find new intersection data rather than test for intersections against all edges in the mesh.
It helps to draw a diagram and illustrate what you want to do.
You will need to update your VBO to include new geometry data and you will also have to update any bone data (if there is one). I'm not sure what the best way of going about that is. The "upper" portion that was cut will need to fall down while the other half will have to play some sort of animation. You will need to find out which bone intersects the cutting plane and act accordingly on that. I would probably construct a new "hip bone" to replace the sliced bone and adjust the bone weights accordingly. I would then use the new hip bone to animate the part falling while the other half does whatever.
http://www.nutty.ca - Being a nut has its advantages.
### #7Lokked
New Member
• Members
• 17 posts
Posted 21 March 2011 - 09:14 PM
Thank you for providing the visual, TheNut!
I thought about how to determine through which lines the Plane would intersect, and all I could come up with was a brute force search :(.
In your proposed method of "finding the first intersection point and then follow neighbouring edges to find new intersection data", I am having touble understanding what this means.
The only sense I can make is to pick a direction (CW or CCW) from the Point of Contact (Known Vertex) and calculate the Plane created from the Triangle that's been sliced. Then it's simple algebra.
Programmatically, how do I determine the Vertices of a Triangle that I've intersected, using only 1 point on one of the lines of the Triangle? I'm using DirectX (in case there's a function for this).
If this is not the approach you had in mind, please let me know.
Thanks much.
**EDIT - I think I actually got this figured out. I'll get back to you :)
#### 1 user(s) are reading this topic
0 members, 1 guests, 0 anonymous users | 1,454 | 5,718 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.640625 | 3 | CC-MAIN-2013-20 | latest | en | 0.941053 |
http://orac.amt.edu.au/cgi-bin/train/problem.pl?problemid=450 | 1,638,315,228,000,000,000 | text/html | crawl-data/CC-MAIN-2021-49/segments/1637964359082.76/warc/CC-MAIN-20211130232232-20211201022232-00148.warc.gz | 61,447,670 | 3,188 | # Problem: Dating Site IT
Want to try solving this problem? You can submit your code online if you log in or register.
## Dating Site IT
Time Limit: 3 seconds
Memory Limit: 64 MB
You run an online dating site with many users. You keep detailed statistics for each user, including the number of times they visit your site this month. You would like to know how many visits your site gets in total this month. Unfortunately this is not as easy as it sounds – some of your users are spammers, who use your site to advertise their own products. You do not want to count the spammers' visits towards your total.
When a user registers with the site, they must supply many personal details including their age, height and weight. Spammers lie about these details, but they are very predictable and you can use their fake answers to spot them. For example, you might know that "any user whose age is between 18 and 30, whose height is between 80cm and 90cm, and whose weight is between 40kg and 50kg is a spammer".
Your task is to write a computer program that takes a number of statements like the above and a list of user statistics, and outputs the total number of visits your site has received this month.
### Input
Your program must read from standard input. In the description below, ai hi wi vi represent a user's age, height, weight and number of visits this month, respectively.
The first line will consist of two space-separated integers, S and U (1 ≤ S,U ≤ 1,000,000). Each of the following S lines will be of the form "aminamaxhminhmaxwminwmax", representing the statement "any user that satisfies amin ≤ aX ≤ amax and hmin ≤ hX ≤ hmax and wmin ≤ wX ≤ wmax is a spammer". (Of course, amin ≤ amax and so on). Following this will be U lines describes a single user, in the form "ai hi wi vi".
All ages, heights and weights are integers between 0 and 99 inclusive. Each user will make between 1 and 1000 visits, inclusive.
See the Scoring section for a breakdown of the marks awarded for different test cases.
### Output
Your program must write to standard output. The output should consist of a single integer: the number of visits made to your site this month by users who are not spammers.
### Sample Input
```2 3
18 24 30 60 80 85
21 30 40 50 0 99
18 30 80 3
25 35 86 5
23 45 82 7
```
```5
```
### Scoring
The score for each input scenario will be 100% if the correct answer is written to the output file, and 0% otherwise.
The following table lists the sizes of the inputs used in the test data. Here, N-1 is the maximum age, height and weight specified in the input.
N S U Percentage of marks 20 10 1000 10% 20 100 8000 10% 10 10000 100000 10% 30 10000 1000000 10% 50 100000 100000 20% 100 1000000 500000 20% 100 1000000 1000000 20%
Privacy statement
`Page generated: 1 December 2021, 10:33am AEDT` | 764 | 2,828 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.703125 | 3 | CC-MAIN-2021-49 | longest | en | 0.943366 |
http://www.ehow.com/how_8396281_determine-linear-feet.html | 1,474,842,758,000,000,000 | text/html | crawl-data/CC-MAIN-2016-40/segments/1474738660436.26/warc/CC-MAIN-20160924173740-00300-ip-10-143-35-109.ec2.internal.warc.gz | 437,325,016 | 19,786 | # How to Determine Linear Feet
Save
Unlike a square foot (which is a square with sides equaling 12 inches), a linear foot is just 12 inches in a straight line traveling in any direction. If you want to determine the number of linear feet in the length, width or height of an object, you can do so in a few minutes with any regular tape measure you happen to have access to.
### Things You'll Need
• Tape measure
• Lay the beginning of a tape measure at the point where you want your linear foot measurement to start. If you're measuring the height of something, for example, this end of the tape measure would rest on the floor.
• Stretch out your tape measure so that it reaches the end point of your measurement. If you're measuring the height of a table, for example, the end point would be the surface of the table.
• Look at how many feet are between your two points as displayed on the tape measure. If your table is 3 feet off the ground, your measurement would be 3 linear feet.
## References
Promoted By Zergnet | 228 | 1,028 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.390625 | 3 | CC-MAIN-2016-40 | longest | en | 0.932629 |
https://www.w3resource.com/php-exercises/php-basic-exercise-37.php | 1,657,025,725,000,000,000 | text/html | crawl-data/CC-MAIN-2022-27/segments/1656104576719.83/warc/CC-MAIN-20220705113756-20220705143756-00155.warc.gz | 1,138,780,575 | 29,297 | PHP Exercise: Compute sum of the prime numbers less than 100 - w3resource
# PHP Exercises: Compute sum of the prime numbers less than 100
## PHP: Exercise-37 with Solution
Write a PHP program to compute the sum of the prime numbers less than 100.
Note: There are 25 prime numbers are there in less than 100.
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97 and sum of all these numbers is 1060.
Sample Solution: -
PHP Code:
``````<?php
\$primes = array();
\$is_prime_no = false;
for (\$i = 2; \$i<100; \$i++) {
\$is_prime_no = true;
for (\$j = 2; \$j<=(\$i/2); \$j++) {
if (\$i%\$j==0) {
\$is_prime_no = false;
break;
}
}
if (\$is_prime_no) {
array_push(\$primes,\$i);
}
if (count(\$primes)==100) {
break;
}
}
echo array_sum(\$primes)."\n";
?>
```
```
Sample Output:
```1060
```
Flowchart:
PHP Code Editor:
Have another way to solve this solution? Contribute your code (and comments) through Disqus.
What is the difficulty level of this exercise?
Test your Programming skills with w3resource's quiz.
## PHP: Tips of the Day
Why shouldn't I use mysql_* functions in PHP?
The MySQL extension:
• Is not under active development
• Is officially deprecated as of PHP 5.5 (released June 2013).
• Has been removed entirely as of PHP 7.0 (released December 2015)
• This means that as of 31 Dec 2018 it does not exist in any supported version of PHP. If you are using a version of PHP which supports it, you are using a version which doesn't get security problems fixed.
• Lacks an OO interface
• Doesn't support:
• Non-blocking, asynchronous queries
• Prepared statements or parameterized queries
• Stored procedures
• Multiple Statements
• Transactions
• The "new" password authentication method (on by default in MySQL 5.6; required in 5.7)
• Any of the new functionality in MySQL 5.1 or later
Since it is deprecated, using it makes your code less future proof.
Lack of support for prepared statements is particularly important as they provide a clearer, less error-prone method of escaping and quoting external data than manually escaping it with a separate function call.
Ref : https://bit.ly/2BIIsF0 | 613 | 2,168 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.890625 | 3 | CC-MAIN-2022-27 | longest | en | 0.846843 |
https://terrificexterior.com/installation/how-much-does-a-square-of-shingles-weigh.html | 1,642,620,469,000,000,000 | text/html | crawl-data/CC-MAIN-2022-05/segments/1642320301488.71/warc/CC-MAIN-20220119185232-20220119215232-00347.warc.gz | 574,077,362 | 18,635 | # How much does a square of shingles weigh?
Contents
## How much does a square of 3-tab shingles weigh?
Roof Shingle Weight Calculator
A bundle of three-tab asphalt shingles weighs between 60 and 80 pounds, but this may vary depending on the quality and type of shingle. Generally, three bundles of shingles are enough to cover 1 square of roof (100 square feet), which can weigh anywhere from 180 to 240 pounds.
## How much does a square of asphalt shingle weigh?
A single square can weigh between 150-240 pounds, with a single bundle being between 50-80 pounds.
## How heavy is a shingle?
Asphalt shingles typically weigh 60-80 pounds per bundle.
## What is the heaviest shingle?
The heaviest GAF shingles are the Grand Canyon shake line at 450lbs per square, but most lines, including the best-selling residential shingle Timberline lines, weigh less than 240lbs per square.
## How much does 23 square of shingles weigh?
per bundle. On average, one square of shingles typically weighs 150 to 240 lbs. The thickest and most dense roofing shingles may weigh 320 to 400 lbs per square.
INTERESTING: What melts ice on roofs?
## How many squares of shingles will a 20 yard dumpster hold?
20-yard dumpster: 35 squares. 15-yard dumpster: 25 squares.
## What does 70 bundles of shingles weigh?
Most bundles of modern architectural shingles weigh between 60 pounds and 80 pounds. You can use these figures to calculate a weight range if you want to know how much your new shingles will weigh because most homeowners replace their roofs with architectural shingles these days.
## How much does built up roofing weight?
The weight of a built-up roofing system can range from about 2.5 pounds per square foot for a smooth surface to 6.5 pounds per square foot for a gravel surface. Though not nearly as heavy as a slate roof or a clay tile roof, built-up roofing is generally heavier than asphalt shingles, TPO, PVC, and metal roofs.
## How much do Owens Corning Duration shingles weight?
These Owens Corning laminated roofing shingles weigh about 200 lbs/square.
## What is 10 squares of shingles?
If you know how many bundles you need to buy, you are almost there. If you need to purchase 30 bundles of asphalt shingles you have a 10 square roof. (30 divided by 3 = 10) If you have 2 layers of asphalt shingles on your roof you have a total of 20 square.
## How many square feet are in a bundle of shingles?
You usually purchase shingles by the bundle. Standard shingles are 12 by 36 inches and come 29 to a package. Most shingles come 3 bundles to a square — which is equal to 100 square feet. So, each bundle provides about 33 square feet of coverage.
## How many shingles make a square?
How Many Shingles In A Square? For regular 3-tab, non-laminated shingles, you’ll have around 78 shingles per square. Some older styles of 3-tab shingles will have up to 87 shingles per square. Architectural shingles will have anywhere from 57 to 66 shingles per square.
## How many shingles are on a pallet?
There are 42 bundles on a pallet.
## How much does a shingle roof weight per square foot?
Asphalt Shingle: 2 – 3.5 pounds per square foot. Textured Asphalt Shingle: 3.5 – 5 pounds per square foot. Wood Shingles/Shakes: 3.5 – 4.5 pounds per square foot. Clay or Concrete Tile: 5.5 – 10 pounds per square foot. | 814 | 3,331 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.671875 | 3 | CC-MAIN-2022-05 | latest | en | 0.939695 |
https://brainmass.com/math/calculus-and-analysis/pg23 | 1,526,874,225,000,000,000 | text/html | crawl-data/CC-MAIN-2018-22/segments/1526794863923.6/warc/CC-MAIN-20180521023747-20180521043747-00023.warc.gz | 529,532,946 | 21,905 | Explore BrainMass
Share
# Calculus and Analysis
### Differential Equations : Variation of Parameters
Use variation of parameters to solve the differential equation y'''+4y'=cot2t.
### Linear PDE, Order, Homogeneous, Non-Homogeneous : Boundary Value Problems
A linear PDE can be written in differential operator notation L(u) = f. where L is the linear differential operator, u is the unknown function, and f is the right-hand side function. For each of the following PDEs, determine the linear operator and the right-hand side function, the order of the PDE, and whether the PDE is homog
### Inverse Laplace Transform Question
Find the inverse Laplace transform of exp(-s). Please help me with this problem.
### Solving the Differential Equation
Please give me a step-by-step solution to this attached ODE. x'' + x = d2(t) + u2(t) x(0) = 0 x'(0) = 0 Please see the attached file for the fully formatted problems.
### Decribe the region R in the xy-coordinate plane that corresponds to a domain.
1.) Describe the region R in the xy-coordinate plane that corresponds to the domain of the function. f(x,y)=e^x/y Describe the region R in the xy-coordinate plane that corresponds to the domain of the function. 2.) f(x,y)=sq rt 9-9x^2-y^2 3.) f(x,y)=x/y
### Differential Equation: Power Series
Trouble finding the power series to resolve the question.
### Differential Equation: Torricelli's Law
Please help with the following problem. Provide step by step calculations for each. (1) (a) Let h(t) and V (t) be the height and volume of water in a cylindrical tank at time t. If water leaks through a circular hole with area a at the bottom of the tank, Torricelli's law says that the rate of change of volume is given by the
### Work, Force, Consumer Surplus, Cost Functions and Maximum Profit
36. A holding tank has the shape of a rectangular parallelepiped 20ft by 30ft by 10 ft. a) How much work is done in pumping all the water to the top of the tank? b) How much work is done in pumping all the water out of the tank to a height of 2ft above the top of the tank? Please see the attached file for all nine questions
### Partial Differential Equation : Diffusion Equation and Explicit Series
Consider the diffusion equation ut = ku.xx for 0 < < pi and t > 0 with the boundary conditions ux(0, t) = 0 and u(pi, t) = 0 and the initial condition u(x,0) = 1. (a) Find the separated solutions satisfying the differential equation and boundary conditions. (b) Use these solutions to write an explicit series solution to t
### Word Problem : Minimizing Fencing
The math department is planning to build a park for calculus students along the riverbank. The park is to be rectangular with an area of 512 square yards and is to be fenced off on the three sides not adjacent to the river (draw a picture). a.) What is the least amount of fencing required for this job? b.) How long and w
### Finding the Second Derivative of a Function
How did the book get from here: -2X(1+x^2)^2 - 4X(1-x^2)(1+x^2) ______________________________ (1 + x^2)^4 to here? -2x (1+ x^2)[1+x^2+2(1-x^2] ___________________________ (1+x^2)^4 I have worked and reworked and I cannot get that numerator to become that. What is the deal? (This
### Word problem/sketch involving integrals
A high-tech company purchases a new computing system whose initial value is V. The system will depreciate at the rate f=f(t) and will accumulate maintenance costs at the rate g=g(t), where t is the time measured in months. The company wants to determine the optimal time to replace the system. a) Let C(t)=1/t the integral fr
### Differentials : Rate of Change, Δx and dx
Let x=1 and delta x= 0.01, find delta y. f(x)=5x^2 - 1 f(x)=sq rt 3x compare the values of dy and delta y y=x^3 x=1 delta x=dx=0.1 y=x^4+1 x=-1 delta x=dx=-0.1 Part 2 Use differentials to approximate the change in cost , revenue, or profit corresponding to an increase in sales of one
### Polar Forms : Cardinoid, Rose Curve, Lemniscate and Limacon
Questions: 4,6,10,12,18,22,26,30,34,36,42,44,46,48,50 on page 6.3. 2,8,22,14,18,12,24 on page 393 4. Identify each of the curves as a cardinoid, rose curve (state number of petals), lemniscate, limacon, circle, line of none of the above. Please see attached for all questions.
### Volume generated by rotation of area
52. The base of the solid is an isosceles right triangle whose legs are each 4 units long. Each cross section perpendicular to a side is a semicircle. Please see attached for all questions.
### Find the Volumes of Bounded Regions
Problems: 2, 6, 8, 12, 14,16,18,20,and 22, 28 done. Page 372: 2, 6,10,14,16,20,22,24,26,28,32,34 done. 28. Find the area of the region that contains the origin and is bounded by the lines 2y = 11 - x and y = 7x + 13 and the curve y = x² - 5. Please see attached for full question.
### Velocity & Acceleration
In science, we calculate the displacement of an object (how far it travels) and the velocity of an object (how fast it is moving) using the displacement equation and the velocity equation. Solving using the Method of substitution.
### Evaluating a Limit Involving a Riemann sum
Evaluate the limit by first recognizing the sum as a Riemann sum of a function: the limit as n goes to infinity of (4/n)(sqrt(4/n)+sqrt(8/n)+...+sqrt(4n/n))=___
### Find Derivatives using the Fundamental Theorem of Calculus
Use part I of the Fundamental Theorem of Calculus to find the derivatives of the following functions; answers must use correct variable. a. f(x)=the integral as pi goes to x of (1+cos[t])dt; f'(x)=___ b. f(u)=the integral as -1 goes to u of [1/(x+4x^2)]dx; f'(u)=___
### LaPlace Transformations with some Initial Value Problems
Problem 9.1 (Prob. 29. P. 252) Two particles each of mass m moves in the plane with co-ordinates (x(t), y(t)) under the influence of a force that is directed toward the origin and had magnitude k/(x2 + y2) an inverse-square central force field. Show that mx''=-kx/(r^3) and my''= -ky/(r^3) where r = sqrt(x2 + y2) Problem 9.2
### Differential Equations Variation of Parameters and Undetermined Coefficients and IVP
1. Find a Particular Solution using undetermined coefficients, then find a general solution y³ + y" - 6y' = 3e²ⁿ. 2. Find a particular solution using the method of variation of parameters then find a general solution y" + 9y = cos(3x). 3. Solve the Initial Value Problem x" + 4x = 6sin(3t). x(0)=4, x'(0) = 0. Ple
### Work Done by Force Field Along a Helix
Find the work done by the force field F(x,y,z)=... on a particle that moves along the helix... Please see the attached file for the fully formatted problems.
### Derivatives : Rate-of-Change Word Problem
A motorist, in a desert 5 km from point A, which is the nearest point on a long straight road, wishes to get to point B on the road. If the car can travel 30 km/ hr and 80 km/hr on the road, find the point where the motorist must meet the road to get to point B in the shortest possible time if point B is 5 km from point A. Use c
### Vectors, Equation of Sphere and Plotting Points (15 Problems)
Please assist me with the attached problems, including: 1. For the given vector find ... 2. Plot the given points 3. Find the standard form equation of the given sphere Please see attachment for complete list of questions. Thanks.
### Dot Product, Orthogonal Vectors, Angle Between Vectors
Please assist me with the attached problems, including: 1. Find the dot product 2. State whether the given points of vectors are orthogonal 3. Evaluate the expressions
### Polar Coordinates; Laplace's Equation; Boundary Conditions
I need some clues on figuring out these questions. Please see attachment for complete problems (regarding the below: "..." indicates an equation to be found in the attachment. Thanks!) (a) Using polar coordinates, find all the separated solutions of Laplace's equation satisfying the attached boundary conditions in the "wedge
### Differential Equations : Particular Solutions, Variation of Parameters and Resonance Frequency
Please see the attached files for the fully formatted problems.
### Brachistochrone Curves
What is it's origin? State the problem with picture. Explain how the cycloid relates to the solution.
### Vector Calculus - Maxwell's Equation
Hi, I'm having trouble figuring out how to solve this. I think I figured out some of it, but I don't understand it in general. I attached the problem as a jpeg. I'd appreciate seeing how to show the answer. You can ignore the pencil markings, they are notes to myself in trying to figure out the problem. Thanks.
### Find the slope of a line tangent to a curve.
Find the slope of the line tangent to the curve y=x^(x-1) at x=3. | 2,273 | 8,703 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.78125 | 4 | CC-MAIN-2018-22 | latest | en | 0.862327 |
http://mathhelpforum.com/pre-calculus/129058-3-4j-sqaure-roots-print.html | 1,527,439,485,000,000,000 | text/html | crawl-data/CC-MAIN-2018-22/segments/1526794869272.81/warc/CC-MAIN-20180527151021-20180527171021-00351.warc.gz | 191,057,919 | 2,704 | # 3-4j sqaure roots
• Feb 16th 2010, 03:16 AM
decoy808
3-4j sqaure roots
find the square roots of 3-4j
i used a software prog for the method, just want to check if it right?
-4j+3=0
-4j=-3
j=3/4
manny thanks(Cool)
• Feb 16th 2010, 03:25 AM
mr fantastic
Quote:
Originally Posted by decoy808
find the square roots of 3-4j
i used a software prog for the method, just want to check if it right?
-4j+3=0
-4j=-3
j=3/4
manny thanks(Cool)
Do you understand that 3 - 4j is a complex number and your job is to find two other complex numbers of the form $\displaystyle a + jb$ (where a and b are real) such that $\displaystyle (a + jb)^2 = 3 - 4j$?
Note for the uninitiated: j is the symbol for $\displaystyle \sqrt{-1}$ used by electrical engineers. | 263 | 751 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.390625 | 3 | CC-MAIN-2018-22 | latest | en | 0.851746 |
https://lavelle.chem.ucla.edu/forum/viewtopic.php?f=17&t=15631&p=39142 | 1,601,330,009,000,000,000 | text/html | crawl-data/CC-MAIN-2020-40/segments/1600401614309.85/warc/CC-MAIN-20200928202758-20200928232758-00301.warc.gz | 466,349,098 | 12,098 | ## quiz 1 fall 2014 prep #10
H-Atom ($E_{n}=-\frac{hR}{n^{2}}$)
Armo_Derbarsegian_3K
Posts: 35
Joined: Sat Jul 09, 2016 3:00 am
### quiz 1 fall 2014 prep #10
Hello,
I did #10 and I was looking at the answers in the back and noticed:
"USE BOHR EQU. FOR H ATOM (ANY 1e- H-LIKE ATOM, Li^2+):
En = -2.178x10^-18 J (Z^2/n^2) for n=1,2,3....
j=joules, z=atomic number, n=energy level"
What is the difference between that equation and using -hR? When do we need to plug in the Z and n?
I just wrote it as -7.55x10^-20J which I derived from the frequency given and set it equal to:
-7.55x10^-20J=-hR/4^2 -hR/n^2
-7.55x10^-20J=-hR(1/16-1/n^2)
----------------- ---
-hR -hR
and solved it that way. Is this work still valid? Is that what the answer key did and just didn't show the work? Where/when does the Z and n come into play?
Thanks!
Chem_Mod
Posts: 18400
Joined: Thu Aug 04, 2011 1:53 pm
Has upvoted: 435 times
### Re: quiz 1 fall 2014 prep #10
Ignore the above equation.
Here is the updated solution:
delta E = hv = (6.63 x 10-34J · s) (1.14 x 1014 s-1) = 7.56 x 10-20J
Since light is emitted delta E = - 7.56 x 10-20J
USE BOHR EQU. FOR H-ATOM:
En = -2.178 x 10 -18J ( 1/n2 ) for n = 1, 2, ...
WHERE, J: JOULES n: ENERGY LEVEL
So E = E4 - En (because light is emitted)
= - 7.56 x 10-20 J = -2.178 x 10-18J (1/42 - 1/n2 )
- 7.56 x 10-20J -2.178 x 10-18J = (1/42 - 1/n2 )
3.47 x 10-2 = 1/16 - 1/n2
1/n2 = 2.78 x 10-2
n = 6
Josh_Zhong_1F
Posts: 34
Joined: Fri Sep 30, 2016 3:02 am
### Re: quiz 1 fall 2014 prep #10
Hi,
Where does the number -2.178x10^-18J come from??
Chem_Mod
Posts: 18400
Joined: Thu Aug 04, 2011 1:53 pm
Has upvoted: 435 times
### Re: quiz 1 fall 2014 prep #10
404412260 wrote:Hi,
Where does the number -2.178x10^-18J come from??
(Planck's constant)x(Rydberg constant)
Jamie Huang 1L
Posts: 20
Joined: Fri Jul 15, 2016 3:00 am
### Re: quiz 1 fall 2014 prep #10
For this question, I got 7.56 x 10^-20 J for when freq is equal to 1.14 x 10^14 Hz, then using n=4, I plugged in -hR/n^2 and I got -1.36 x 10 ^-19 J. When I try to subtract the Energy of n=4 from Energy of freq, I got -2.12 x 10^-19 J. Using this Energy, I try to find n by plugging values into the formula E= -hR/n^2, but somehow I got the answer 3, and the correct answer is 6. Is there anything that I did wrong in my work? | 944 | 2,344 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 1, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.578125 | 4 | CC-MAIN-2020-40 | latest | en | 0.832198 |
https://brilliant.org/practice/challenging-brain-tanglers/ | 1,531,806,586,000,000,000 | text/html | crawl-data/CC-MAIN-2018-30/segments/1531676589573.27/warc/CC-MAIN-20180717051134-20180717071134-00361.warc.gz | 628,201,318 | 21,071 | # Challenging Brain Tanglers
Try this quiz to challenge yourself with some difficult (perhaps even brain-warping) puzzles that will tie your thoughts up in knots!
Be forewarned that most people get these answers wrong, even when they think about it hard and carefully.
If you get a question wrong, compare your work to our solution to improve your own strategies!
# Challenging Brain Tanglers
A variant of the famous Monty Hall Game Show Puzzle:
You're a contestant of a game show! There are 10 closed doors: 9 lead to nothing and 1 leads to an expensive car. You are allowed to pick a door and earn the car if it's behind the door you choose.
Stage 1: You choose a door.
Stage 2: The host tells you to choose from two helpful options:
Option 1: Open Five doors!
You choose four more doors in addition to the one you've already selected and open all 5. You win the car if it is behind any of the five doors you choose and open.
Option 2: The host eliminates 8 red herrings!
The host will open 8 empty doors that are not the door you chose initially that do not contain the car. This leaves two doors closed: your initial choice and one other door -- the car is definitely behind one of them. You can then choose to either open the original door you chose in stage 1 or open the only other remaining closed door.
What should you do to maximize your chances of winning the car?
# Challenging Brain Tanglers
When I put two marbles in this bag, I flipped a coin twice to determine their colors. For each flip,
• if it was heads $$\rightarrow$$ I put in a red marble;
• if it was tails $$\rightarrow$$ I put in a blue marble.
You reach into my bag and randomly take out one of the two marbles. It is red. You put it back in. Then you reach into the bag again. What is the chance that, this time, you pull out a blue marble?
# Challenging Brain Tanglers
When I put two marbles in this bag, I flipped a coin twice to determine their colors. For each flip:
• If it was Heads $$\rightarrow$$ I put in a red marble.
• If it was Tails $$\rightarrow$$ I put in a blue marble.
After I had the bag ready, I looked into the bag at both marbles and announced, "at least one of marbles in this bag is red." To prove it, I took a red marble out of the bag and set it aside. I then asked you to reach into the bag and remove the only remaining marble. What is the chance that it is blue?
Hint: The answer is not $$\frac{1}{2}.$$
# Challenging Brain Tanglers
Note: This picture is only an example of how the game might run.
In a game for two players, players take turns flipping a coin (they each have their own coin). Each round, if the flips match (HH or TT), they continue on. The game ends when the two flips in a round don't match (HT or TH). When the game ends:
• Player 1 wins if it's HT.
• Player 2 wins if it's TH.
An example game is pictured above. If this game is played with weighted coins that land heads 99% of the time and tails 1% of the time, which player would you rather be?
Note: "The game is fair," means that neither player has an advantage over the other.
# Challenging Brain Tanglers
For this puzzle, test your intuition by guessing without calculating, or do the calculation if you want.
Suppose you draw four cards at random from a 52 card deck, approximately how much more likely is a four-card flush, compared to four of a kind?
Definitions:
A four-card flush is four cards of the same suit (spades, hearts, diamonds, or clubs). For example:
Four of a kind is four cards of the same value (4 aces, 5s, jacks, etc.). For example:
# Challenging Brain Tanglers
Even if you got all 5 of the problems in this quiz wrong, don't fret. These were some tricky puzzles and they're exactly the kinds of situations that cause most people to slip up.
If you want more practice and more to learn, check out the remainder of this course! There are many quizzes that practice both simpler and more difficult variants of the techniques that have been called into play so far.
And there are many many more games to play and explore in depth, including some common casino games such as Blackjack and Craps. We'll help you master the skills needed for working with probability so that you can improve your strategy when playing these games and much more.
× | 1,006 | 4,283 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.03125 | 4 | CC-MAIN-2018-30 | longest | en | 0.951692 |
http://convertit.com/Go/ConvertIt/Measurement/Converter.ASP?From=pipe&To=static+moment+of+area | 1,653,017,780,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662531352.50/warc/CC-MAIN-20220520030533-20220520060533-00193.warc.gz | 12,464,716 | 3,821 | Partner with ConvertIt.com
New Online Book! Handbook of Mathematical Functions (AMS55)
Conversion & Calculation Home >> Measurement Conversion
Measurement Converter
Convert From: (required) Click here to Convert To: (optional) Examples: 5 kilometers, 12 feet/sec^2, 1/5 gallon, 9.5 Joules, or 0 dF. Help, Frequently Asked Questions, Use Currencies in Conversions, Measurements & Currencies Recognized Examples: miles, meters/s^2, liters, kilowatt*hours, or dC.
Conversion Result: ```pipe = 0.476961884784 volume (volume) ``` Related Measurements: Try converting from "pipe" to amphora (Greek amphora), board foot, cc (cubic centimeters), coomb, drop, dry gallon, dry quart, freight ton, gallon, hekat (Israeli hekat), jigger, liter, minim, nebuchadnezzar, noggin, oil arroba (Spanish oil arroba), peck (dry peck), pint (fluid pint), UK pint (British pint), vedro (Russian vedro), or any combination of units which equate to "length cubed" and represent capacity, section modulus, static moment of area, or volume. Sample Conversions: pipe = 4 barrel, 12,936 bath (Israeli bath), 202.13 board foot, .1315918 cord (of wood), .48125 displacement ton, 129,024 dram fluid (fluid dram), 108.28 dry gallon, 866.24 dry pint, 433.12 dry quart, 14 firkin, .42109375 freight ton, 100.02 hekat (Israeli hekat), 2 hogshead, 157.5 jeroboam, 7 kilderkin, 476.96 liter, 252 magnum, 84 rehoboam, .47696188 stere, 13.11 UK bushel (British bushel).
Feedback, suggestions, or additional measurement definitions?
Please read our Help Page and FAQ Page then post a message or send e-mail. Thanks! | 445 | 1,581 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.765625 | 3 | CC-MAIN-2022-21 | latest | en | 0.667055 |
https://testbook.com/question-answer/what-will-be-the-maximum-possible-uniformly-distri--609f79b937c9f3582578bd6c | 1,638,768,996,000,000,000 | text/html | crawl-data/CC-MAIN-2021-49/segments/1637964363290.39/warc/CC-MAIN-20211206042636-20211206072636-00476.warc.gz | 623,651,075 | 31,475 | # What will be the maximum possible uniformly distributed load (inclusive of self-weight) over the entire span of a simply supported beam of span ‘L’ such that the deflection at midspan at service condition is zero? The cross-section is rectangular. The Prestressing force ‘P’ is applied with uniform eccentricity ‘e’. Assume no losses.
This question was previously asked in
MPSC AE CE Mains 2017 Official (Paper 1)
View all MPSC AE Papers >
1. $$\frac{{8Pe}}{{{L^2}}}$$
2. $$\frac{{8.8Pe}}{{{L^2}}}$$
3. $$\frac{{9.6Pe}}{{{L^2}}}$$
4. $$\frac{{10.4Pe}}{{{L^2}}}$$
Option 3 : $$\frac{{9.6Pe}}{{{L^2}}}$$
## Detailed Solution
Concept:
Given:
Case(1):
For Simply Supported Beam with (UDL),
$$(\Delta _{max})_1=\frac{5wL^{4}}{384 EI}(Downword)\$$
Case(2):
Also, due to the prestressing force, there will moments at supports,
Maximum deflection for this case.
$$(\Delta _{max})_2=\frac{P.eL^{2}}{8 EI}(Upword)$$
Hence, for Zero Deflection,
$$(\Delta _{max})_2=(\Delta _{max})_1$$
$$\frac{{P.e\;}}{{8\;EI}} = \;\frac{{w{L^4}}}{{EI}} \times \frac{5}{{384}}$$
$$w = \;\frac{{48\;P.e\;}}{{5{L^2}}} = \;\frac{{9.6\;P.e}}{{{L^2}}}$$ | 399 | 1,138 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.765625 | 4 | CC-MAIN-2021-49 | latest | en | 0.655774 |
https://staxmobileapp.com/qa/question-does-wt-mean-weight.html | 1,606,979,206,000,000,000 | text/html | crawl-data/CC-MAIN-2020-50/segments/1606141723602.80/warc/CC-MAIN-20201203062440-20201203092440-00546.warc.gz | 461,331,714 | 8,597 | # Question: Does WT Mean Weight?
## What does Wut mean on Snapchat?
What you Up ToWhat you Up To.
Internet » Chat.
Rate it: WUT..
## How do I calculate my weight in kilograms?
Divide the number of pounds by 2.2046 to use the standard equation. For example, if you want to convert 50 pounds to kilograms, divide 50 by 2.2046, which is equal to 22.67985 kg. To convert 200 pounds to kilograms, divide 200 by 2.2046, which is equal to 90.71940 kg.
## What is Molality formula?
The unit of molality is, therefore, expressed in moles per kilogram. The formula for molality is m = moles of solute / kilograms of solvent. … One formula we need to be aware of is the formula for density, which is d = m / v, where d is density, m is mass and v is volume.
## What does WT WT mean?
Rating Weight by weight percentage1 Rating. Weight by weight percentage (wt/wt %) is defined as the ratio of weight of a solute to the total weight of the solution. It is also known as mass by mass percentage.
## What is 1m solution?
A 1 molar (M) solution will contain 1.0 GMW of a substance dissolved in water to make 1 liter of final solution. Hence, a 1M solution of NaCl contains 58.44 g.
## What is a 10% solution?
A 10% of NaCl solution by mass has ten grams of sodium chloride dissolved in 100 ml of solution. Weigh 10g of sodium chloride. Pour it into a graduated cylinder or volumetric flask containing about 80ml of water. … A 10% of alcohol solution by volume has ten ml of alcohol dissolved in 100ml of solution.
## What does WT mean in gaming?
Wrong TellWrong Tell (gaming chat) WT.
## How do I calculate ppm?
Parts Per Million (ppm) Concentration CalculationsWrite an equation representing the ppm concentration: ppm = mass solute (mg) ÷ volume solution (L)Extract the data from the question: mass solute (NaCl) = 0.0045 g. … Convert the mass in grams to a mass in milligrams: mass NaCl = 0.0045 g = 0.0045 g × 1000 mg/g = 4.5 mg.More items…
## How do you calculate weight?
To determine the weight per cent of a solution, divide the mass of solute by mass of the solution (solute and solvent together) and multiply by 100 to obtain per cent.
## What does WT mean on social media?
What the?”What the?” is the most common definition for WT on Snapchat, WhatsApp, Facebook, and Twitter.
## How many kg do I weight?
Pounds to Kilograms conversion tablePounds (lb)Kilograms (kg)Kilograms+Grams (kg+g)1 lb0.454 kg0 kg 454 g2 lb0.907 kg0 kg 907 g3 lb1.361 kg1 kg 361 g4 lb1.814 kg1 kg 814 g18 more rows
## When should I check my weight?
According to weight-loss experts and research, the best time to weigh yourself is first thing every morning—not just once a week.
## How do you prepare wt solution?
Since the density of water is 1 g/ml, the formula to calculate the amount of solute that must be mixed for a weight percent solution is: grams of solute = (wt% solution) x (ml of water) ÷ (100 – wt% solution)
## What is a 2% solution?
2% w / w solution means grams of solute is dissolved in 100 grams of solution. Weight / volume % 4% w / v solution means 4 grams of solute is dissolved in 100 ml of solution. Volume / weight % 3% v/ w solution means 3 ml of solute is dissolved in 100 grams of solution.
## How do you find weight of a fraction?
First, you need to find the mass of each component (given), the total mass (add them up). You’ll also need to calculate the moles of each component (divide mass by molecular weight) and the total moles. Now you have everything you need to calculate the composition fractions.
## How do you write weight percent?
Percentage by mass can also be expressed as percentage by weight, abbreviated wt%, or weight-weight percentage.
## What does WT mean in fitness?
Weight trainingWeight training is a common type of strength training for developing the strength and size of skeletal muscles. It utilizes the force of gravity in the form of weighted bars, dumbbells or weight stacks in order to oppose the force generated by muscle through concentric or eccentric contraction. | 1,031 | 4,031 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.734375 | 4 | CC-MAIN-2020-50 | latest | en | 0.910617 |
https://www.chegg.com/homework-help/definitions/analog-signal-4 | 1,560,675,152,000,000,000 | text/html | crawl-data/CC-MAIN-2019-26/segments/1560627998084.36/warc/CC-MAIN-20190616082703-20190616104703-00201.warc.gz | 738,493,444 | 50,565 | # Analog Signal
An analog signal is a continuous signal that contains time-varying quantities. Unlike a digital signal, which has a discrete value at each sampling point, an analog signal has constant fluctuations. The illustration below shows an analog pattern (represented as the curve) alongside a digital pattern (represented as the discrete lines).
An analog signal can be used to measure changes in some physical phenomena such as light, sound, pressure, or temperature. For instance, an analog microphone can convert sound waves into an analog signal. Even in digital devices, there is typically some analog component that is used to take in information from the external world, which will then get translated into digital form (using an analog-to-digital converter).
See more Electrical Engineering topics
Show Transcript
1:00
tutorial
1:00
tutorial
Impedance
1:00
tutorial
Voltage Dividers
## Need more help understanding analog signal?
We've got you covered with our online study tools
### Q&A related to Analog Signal
Experts answer in as little as 30 minutes
• Q:
1) Consider the circuit shown in Fig. 1a, if vg(t) is the input signal and vo(t) is the output signal. 5 Q vt) 250 mF 200 22 (b) Fig 1: Circuit (a) and input voltage (b) for Question 1. (a) Use the convolution integr...
A:
• Q:
5-16 Problems: 5.27. Two straight, parallel conductors, each of length 10 m, carry equal and opposite currents of 10 A. The separation 5 m 5 m 10 A 10 A between the conductors is 2 m. 2 m Calculate the magnetic vecto...
A:
• Q:
o 4-14 Problems: 4.34. The radius of the inner conductor of a coaxial cable is 10cm, and the radius of the outer conductor is 40 cm. There are two media. The inner one, extending from 10 com to 20 cm, has a conductiv...
A:
• Q:
5-16 Problems: 5.16. Two parallel conductors of infinite extent are carrying currents of 10 A and 20 A in opposite directions. If the separation between the conductors is 10 cm, calculate the force per unit length ex...
A:
• Q:
o 5-15 Exercises: 5.16. A very long, straight conductor located along the z axis has a circular cross section of radius 10 cm. The conductor carries 100 A in the z direction which is uniformly distributed over its cr...
A:
• Q:
Q) Explain the time and frequency domain characteristic properties of the voiced and unvoiced parts of the human speech signal
A:
• Q:
FACULTY OF ENGINEERING Q3) a) Write the definition of the sampling theorem. b) Describe and write the bandwidth of the human specech signal. c) What is the reasonable minimum sampling frequency of the human speech si...
A:
• Q:
HW #5 2. A large state university uses three-digit mail stops to code mail on campus. The initial step in sorting this mail is to sort according to the first digit (there are 10 possible), which signifies a general c...
A:
• Q:
Problem 5 Three messages mi, m2 and m3 are to be transmitted over an AWGN channel with noise power spectral density No/2. The messages are iif 0tT 81(t) 0 otherwise if 0
A:
• Q:
T1 T2 100 G2 G1 T3 T4 G3 100 G4 G1: S=100 MVA, UN 13 kV, XGI=1.3 p.u T1: SN-150 MVA, UN-13/150 kV, XTI 0.15 p.u G2: S 200 MVA, UN 20 kV, XG2=1.25 p.u T2: SN-250 MVA, UN-20/150 kV, X12-0.12 p.u G3: SN 150 MVA, UN 6.6 ...
A:
• Q:
Problem 4 A base-band digital communication system using binary signals shown in the Figure for transmission of two equiprob able messages. The transmitted signal is s(t), i e {1,2} and the recieved signal is r(t) s(...
A:
• Q:
Problem 2 Consider a general QAM scheme with transmitted symbol s(t) R { pulse shape p()71(7,/2). a(n) Apr(t - nT) exp (j2 fet)}, where the t-T./2 Let the constellation be a(n)e {2,-2,2j,-2j,0. 1. What is the appropr...
A:
• Q:
Example 13.6: For the figure below, a) Draw AC and DC load lines for both transistors b) Calculate the overall voltage gain Avs vo/v,. c) Find v(max) which produces maximum undistorted output voltage 9V 오 Q, Q2 1.3...
A:
• Q:
Problem 16 For the EA modulator shown in the figure below, assume ideal behaviour of the compara- tor, U, and D-type flip-flop, U2 R2 47k V in R1 47k 4 U2 4 U1 V bitstream CLB 5 C V ref 100nF C1 2.5V V_clock 3 NCLK Q...
A:
• Q:
Question 3 Determine the differential gain a MOSFET differential amplifier shown in Figure 3 biased by 0.2mA/V, Cx 0.1mA/V2, A = 0.1, VDD 10V and Vss -10V mA, (W/L)1,2=100, (W/L)3,4=2, HnCox a current source of I = V...
A:
• Q:
n tnller of an onecE t or than econter s drive stlearivewil aloe to open thdore, when thaaesis o S14ndls tEhL conttroler fu conttoller seats oft s off Question 2: (10 points) nt end tha sering wri close In the full r...
A:
• Q:
what is the complex power if frequency is infinite or zero??
A:
• Q:
For a negative edge-triggered J-K flip flop with the input signals in Figure P7-1, 1. draw the output waveform relative to the clock. Assume the Q is initially LOW CLK J K Figure P7-1
A:
• Q:
+O V w R. RB R2 R. + O Vaut R2 R3 Vre In the circuit above, provided that: R1 5 kOhm R2 200 kOhm R3 R4 = 10 kOhm What is the total differential Gain of the circuit?
A: | 1,485 | 5,015 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.5 | 4 | CC-MAIN-2019-26 | latest | en | 0.862326 |
https://www.physicsforums.com/threads/shape-of-universe-question.852134/ | 1,510,997,287,000,000,000 | text/html | crawl-data/CC-MAIN-2017-47/segments/1510934804680.40/warc/CC-MAIN-20171118075712-20171118095712-00568.warc.gz | 855,986,352 | 16,529 | # Shape of Universe question
Tags:
1. Jan 13, 2016
### Helios
I want to get this simplest cosmology question asked once and for all because I don't get it. We have "cosmologicial models" which have the curvature of the universe going from positive to negative ( or maybe visa-versa ) at some stage ( or not? ). Now elsewhere we hear that a negatively curved universe is infinite and a positive one is finite. Now any student is going to ask "How can finitude become infinite?" ( or visa-versa? ) . Is what I've said flawed? Is there a contradiction? I am the amateur so the fault is surely mine. This must be a page one cosmology question with an elementary answer so can someone please explain? Someone can throw in some names of different universe shapes if they feel like it. Thanks.
edit--send to cosmology pls
2. Jan 13, 2016
### phinds
In response to one part of your question, physical things that are finite cannot become infinite and things that are infinite cannot become finite. The universe either started out infinite or it started out finite. No one knows, but however it started out, that's how it is now. If it is finite, there is a very strong consensus that it is unbounded because a universe that is finite and bounded would have a center and an edge and our universe has neither.
3. Jan 13, 2016
### Helios
No one is ever going to see "bounds" regardless of consensus. I did not mention bounds.
4. Jan 13, 2016
### Staff: Mentor
Which models are you talking about? I'm not aware of any models where the sign of the spatial curvature of slices of constant time changes.
5. Jan 13, 2016
### Staff: Mentor
This is not correct the way you are thinking of it. A better way to say this is that there are a family of models where some have positive and some have negative curvature.
This is related to the fact that conic sections are a family of figures which include ellipses (positive curvature, finite) and hyperbolas (negative curvature, infinite).
6. Jan 13, 2016
### Staff: Mentor
And in each model in the family, the sign of the curvature is fixed; it doesn't change from one spatial slice to another. (I know you know this, but I want to make sure the OP understands it.)
7. Jan 13, 2016
### Helios
Thanks. It must be acceleration vrs deceleration that has the sign change. This
confused me because I read
"when curvature is crossing from negative to positive"
and I misconstrued the meaning. I take it that flat or negative curvature is the most popular belief. Now are there multiple negative shapes or one, because I've heard "saddle" and also "trumpet or horn" as descriptive of negative curvature?
8. Jan 13, 2016
### Staff: Mentor
The "curvature" referred to here is not spatial curvature; it refers to the curvature of the line on the graph describing our actual universe's deceleration/acceleration over time.
Our best current model is that the universe is spatially flat.
Multiple.
9. Jan 14, 2016
### Staff: Mentor
There aren't really good words in English for the shapes of 4D pseudo Riemannian manifolds. I am not sure that any word will convey the geometry correctly, that is why we use math.
Saddle refers to the spatial shape and horn refers to the time evolution, so both are legitimate descriptions. | 771 | 3,270 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.609375 | 3 | CC-MAIN-2017-47 | longest | en | 0.962695 |
https://www.codeproject.com/Articles/104931/Introduction-to-Android-development-TouchCalculato?msg=4480362 | 1,508,499,179,000,000,000 | text/html | crawl-data/CC-MAIN-2017-43/segments/1508187824068.35/warc/CC-MAIN-20171020101632-20171020121632-00470.warc.gz | 877,080,638 | 46,952 | 13,196,126 members (51,993 online)
alternative version
#### Stats
534.3K views
232 bookmarked
Posted 26 Aug 2010
# Introduction to Android development : TouchCalculator
, 13 Sep 2010
Rate this:
Android tutorial with sample styled calculator implementation
## Introduction
I have been designing and developing mobile applications for less than 1 year, though I'm a professional software developer for 10 years or so, and this new mobile era makes me feel excited. As of today there are two and a half major platforms gaining pretty well reputation by the mobile users. Two of them are iOS (formerly known as iPhone OS) and Android and the half is long debated Windows Phone 7.
In this tutorial article I will try to introduce you to the general development principles of Android by building a real calculator application (TouchCalculator). By the end of this tutorial you will be able to build Android applications with simple user interfaces and backing business logic.
## Organization of the article
1. Visualize (sketch or mock up) your app (beginner)
2. Write down what your application will do (beginner)
3. Code a first shot UI which is basic and mimics your mock up (beginner)
4. Design your data structures (Minimum Java experience needed but not a must)
5. Improve the UI to make it match to your initial mock up (Android specific beginner level code)
6. Implement the business logic (Java experience required, but you do not have to understand all of the code, just realize that you have to think separately about your business logic)
## Preparing Yourself and The Development Environment
Before you get started, if you are totally new to Android I would suggest you to read the What is Android? section from the Android Developers site and I would also suggest you to have a look at Android Developers Blog.
## TouchCalculator MockUp
TouchCalculator, our sample and simple calculator, is a standard calculator supporting four arithmetic operations and three mathematical functions (namely square root, reciprocal and percentage) along with a memory buffer.
Let's start with the mock up of our calculator. Below is a color coded sketch of our application. I've separated the UI into logical parts and each part is represented with a color highlight. There is a reasoning behind the conceptual separation and this will be evident in the next sections of the tutorial.
So, let us see what is intended with each region in our mock up.
1. We will display the subsequent user input until user presses (=) to calculate the result or C to clear the input buffer
2. Immediate user input and the result of the buffer will be displayed
3. Memory buffer value will be displayed in this area
4. Memory buffer operation buttons
5. Other operation buttons
6. Calculate button
7. Arithmetic operation buttons
9. Immediate input and buffer clear buttons
## TouchCalculator Use Cases
Our calculator shall be able to support the following use cases
• Calculator shall be initialized with input value of 0 and as soon as the user starts pressing numeric keypad buttons, input capture shall start
• User will press the numeric keypad buttons and we will append each numeric value to the current value of Area #2
• If user presses the decimal separator button placed in Area #5 we shall append the separator to the current value of Area #2
• When user presses an arithmetic operator button placed in Area #7 we shall display the input buffer content in Area #1. If input buffer has enough input to produce a result we shall also calculate the result and display the value in Area #2
• When user presses (=) button and if input buffer has enough input to produce a result we shall calculate the result and display it in Area #2, else do nothing.
• When user presses the backspace button (<-) we shall trim the last digit of the value displayed in Area #2
• When the user presses the CE button we shall reset the value displayed in Area #2 so that it becomes 0
• When user presses the C button we shall reset the input buffer and the value displayed in Area #2 so that it becomes 0
• When user presses (±) we shall toggle the sign of the user input value displayed in Area #2
• When user presses MC button we shall clear the memory buffer
• When user presses MR button we shall read the value in memory buffer and display that value in Area #2
• When user presses MS button we shall set the value of the memory buffer to the value displayed in Area #2
• When user presses M+ or M- buttons we shall add/subtract the value displayed in Area #2 with the existing value of the memory buffer
• When user presses SQRT button we shall calculate the square root of the value displayed in Area #2 and display the result in Area #2
• When user presses 1/x button we shall calculate the reciprocal of the value displayed in Area #2 and display the result in Area #
• When user presses % button we shall calculate the result of the input buffer and find the percent of the result and display in Area #2
## Creating The Bare Bones User Interface
Since we have our calculator mock up, we can start creating the bare bones Android user interface of our calculator. When you create a new Android project in Eclipse, you will have a default layout xml file named main.xml under res/layout folder. We will create the bare bones calculator user interface declaratively, not from code, inside this xml file. Using declarative xml files, layout files, while constructing the user interface has advantages. The primary advantage of using XML is that you separate the presentation of your application from the code used to control your applications behavior. In a team environment this separation enables designers and coders to work on the same application simultaneously. Designers familiar with HTML can easly design Android user interfaces once they get familiar with Android layout vocabulary.You can read more about Android layouts from here.
Now, lets see how we can accomplish an Android UI to represent different UI parts sketched in our TouchCalculator Mockup. Building blocks of Android UI are Views and ViewGroups. Views are basic user interface bits which provide screen layout and user interaction. For example Button, TextView and CheckBox are simple views extending the abstract View class. ViewGroups are composite user interface bits which can contain multiple Views and other ViewGroups. LinearLayout and GridView are two of the view groups we will use to construct our calculator.
In our mock up, we have actually four sections laid out in linear direction vertically. First three sections are for the areas labeled with 1,2 and 3 and the fourth section is for the keypad, containing sections labeled with 4,5,6,7,8 and 9. Thus, we will use LinearLayout ViewGroup so that we can place Views for each section. Here is our bare bones layout XML
```<?xml version="1.0" encoding="utf-8"?>
<LinearLayout xmlns:android="http://schemas.android.com/apk/res/android"
android:orientation="vertical"
android:layout_width="fill_parent"
android:layout_height="fill_parent">
<TextView
android:id="@+id/txtStack"
android:layout_width="fill_parent"
android:layout_height="wrap_content"
android:textSize="15sp"
android:gravity="right"
android:layout_marginTop = "3sp"
android:layout_marginLeft = "5sp"
android:layout_marginRight = "5sp"/>
<TextView
android:id="@+id/txtInput"
android:layout_width="fill_parent"
android:layout_height="wrap_content"
android:textSize="25sp"
android:gravity="right"
android:layout_marginLeft = "5sp"
android:layout_marginRight = "5sp"/>
<TextView
android:id="@+id/txtMemory"
android:layout_width="fill_parent"
android:layout_height="wrap_content"
android:textSize="15sp"
android:gravity="left"
android:layout_marginLeft = "5sp"
android:layout_marginRight = "5sp"/>
<GridView xmlns:android="http://schemas.android.com/apk/res/android"
android:id="@+id/grdButtons"
android:layout_width="fill_parent"
android:layout_height="fill_parent"
android:columnWidth="90dp"
android:numColumns="5"
android:verticalSpacing="10dp"
android:horizontalSpacing="10dp"
android:stretchMode="columnWidth"
android:gravity="center"/>
</LinearLayout>```
We will use TextView to represent areas labeled with 1,2 and 3 in our mock up. We will use GridView ViewGroup for the keypad. We will place our keypad buttons inside the cells of the GridView at run time by using an Adapter.
Most of the View and ViewGroup attributes are self explanatory. You can infer easily what an attribute is used for, actually Eclipse xml editor will also help you if you press Ctrl+Space you will be presented a list of attributes. I will mention id attribute explicitly since it has special importance. Any view or view group can have an id attribute, but this is not a must. If you want to get reference to the View or ViewGroup from your code, you should set the id attribute of your Views and ViewGroups. id attribute has some sort of special notation which you can read more about here.
If you press on the Layout tab in Eclipse XML editor where our layout is defined, you will see the bare bones UI as shown in the image below. Note that by using the LinearLayout we have managed to put each logical section in linear direction vertically.
The XML layout we have defined is not enough by itself, since the users can not get into interaction with our application through the layout directly. As the terminology implies layout XML is used just for defining the placement and visual aspects of the UI bits. What we need in order to enable user interaction is the Activity class, which controls the behavior of our UI and enables user interaction.
When you create a new Android project with Eclipse, you will be asked for the details of your project and one of them is the optional Create Activity check box along with a name for your first Android activity class. For all practical purposes we have named our activity to be main. Eclipse will automatically create a "main.java" file under the src/package node. Here is the initial contents of our main activity class
```package com.pragmatouch.calculator;
import android.app.Activity;
import android.os.Bundle;
public class main extends Activity {
/** Called when the activity is first created. */
@Override
public void onCreate(Bundle savedInstanceState) {
super.onCreate(savedInstanceState);
setContentView(R.layout.main);
}
}```
As you can see, we override the onCreate (Line 10) method of the base Activity and perform activity initialization, loading layout is part of our initialization process, inside the overriden method.
setContentView method called on Line 12 belongs to base Activity class and is used to load the UI layout from a resource (main.xml) identified by an integer. Please note how we get the integer identifier of our main.xml. When Android builds your application, it automatically generates a class named R (can be found under /TouchCalculator/gen/com/pragmatouch/calculator/R.java) and generates identifier constants for your resources, since main.xml is a resource Android generates a constant for us and we can use that constant from our code to load our layout.
If you run the application you will see an empty UI with two linear TextViews placed on top with no keypad.
In this section, we will model our keypad buttons using Java enum type. Java enums are interesting for a guy like me. Spending too many years with C# I must confess that Java enums are much more capable than the C# enums since the Java enum class body can include methods and other fields.
To model the keypad buttons we will declare a KeypadButton enum class, which will also hold button text and category information.
```package com.pragmatouch.calculator;
CharSequence mText; // Display Text
mText = text;
mCategory = category;
}
public CharSequence getText() {
return mText;
}
}```
Each keypad button shown in our mockup is represented with an enum constant and each constant also holds a text and a category value. We also use Java enums to represent the keypad button categories and declare a KeypadButtonCategory enum class.
```package com.pragmatouch.calculator;
MEMORYBUFFER
, NUMBER
, OPERATOR
, DUMMY
, CLEAR
, RESULT
, OTHER
}```
We will utilize KeypadButtonCategory enums for applying different styles for each category so that our sample calculator seems more colorfull.
As I mentioned in the previous sections, we will use GridView to display our keypad. We will use a five column GridView and we will declare an Adapterwhich extends the BaseAdapter class and is responsible of providing data to our AdapterView that is a GridView in our case.
```package com.pragmatouch.calculator;
import android.widget.*;
import android.content.*;
import android.view.*;
import android.view.View.OnClickListener;
private Context mContext;
mContext = c;
}
public int getCount() {
return mButtons.length;
}
public Object getItem(int position) {
return mButtons[position];
}
public long getItemId(int position) {
return 0;
}
// create a new ButtonView for each item referenced by the Adapter
public View getView(int position, View convertView, ViewGroup parent) {
Button btn;
if (convertView == null) { // if it's not recycled, initialize some attributes
btn = new Button(mContext);
// Set CalculatorButton enumeration as tag of the button so that we
// will use this information from our main view to identify what to do
}
else {
btn = (Button) convertView;
}
btn.setText(mButtons[position].getText());
return btn;
}
// Create and populate keypad buttons array with CalculatorButton values
}```
Adapters are responsible for providing data to AdapterViews, in our case the data we will provide to our GridView is keypad button instances. To be able to create these button instances, we define an array of KeypadButton enums on Line 47-52.
Our KeypadAdapter provides keypad button instances to our GridView with the getView (Line 28-44) method implementation where we instantiate or revoke our keypad buttons and set their properties based on their position on the GridView.
Please note what Line 36 does in the code. We set KeypadButton enumeration instance as the tag of our Button and we will use that tag value during business logic implementation to identify what to do when the user presses a keypad button.
Now, we have defined our Adapter and it is time to wire-up the GridView with our KeypadAdapter. Here is our main.java file.
```package com.pragmatouch.calculator;
import android.app.Activity;
import android.os.Bundle;
import android.widget.GridView;
import android.view.View;
import android.view.View.OnClickListener;
public class main extends Activity {
/** Called when the activity is first created. */
@Override
public void onCreate(Bundle savedInstanceState) {
super.onCreate(savedInstanceState);
setContentView(R.layout.main);
// Get reference to the keypad button GridView
});
public void onItemClick(AdapterView<?> parent, View v,int position, long id) {
// This will not help us catch button clicks!
}
});
}
}```
Note that we create an instance of our KeypadAdapter on Line 25 and set this instance as the adapter of our GridView on Line 28. Another thing I want you to notice in the code above is the findViewById call on Line 21. As I noted in previous section, we use the value of the id attribute we have assigned to our GridView in our layout XML (main.xml).
When you run the TouchCalculator at this point, you will see the following UI which is almost the same as our mock up.
Now it is time to implement the business logic of our calculator. We will utilize Java Stack class in order to implement our calculation logic. We will have two Stack instances; the first instance will hold the user input and the second stack will hold the intermediate calculation results. We will wrap our business logic as an instance method inside our main class. Here is our ProcessKeypadInput method along with some utility methods.
```private void ProcessKeypadInput(KeypadButton keypadButton) {
// Toast.LENGTH_SHORT).show();
String currentInput = userInputText.getText().toString();
int currentInputLen = currentInput.length();
String evalResult = null;
double userInputValue = Double.NaN;
case BACKSPACE: // Handle backspace
// If has operand skip backspace
if (resetInput)
return;
int endIndex = currentInputLen - 1;
// There is one character at input so reset input to 0
if (endIndex < 1) {
userInputText.setText("0");
}
// Trim last character of the input text
else {
userInputText.setText(currentInput.subSequence(0, endIndex));
}
break;
case SIGN: // Handle -/+ sign
// input has text and is different than initial value 0
if (currentInputLen > 0 && currentInput != "0") {
// Already has (-) sign. Remove that sign
if (currentInput.charAt(0) == '-') {
userInputText.setText(currentInput.subSequence(1,
currentInputLen));
}
// Prepend (-) sign
else {
userInputText.setText("-" + currentInput.toString());
}
}
break;
case CE: // Handle clear input
userInputText.setText("0");
break;
case C: // Handle clear input and stack
userInputText.setText("0");
clearStacks();
break;
case DECIMAL_SEP: // Handle decimal seperator
if (hasFinalResult || resetInput) {
userInputText.setText("0" + mDecimalSeperator);
hasFinalResult = false;
resetInput = false;
} else if (currentInput.contains("."))
return;
else
userInputText.append(mDecimalSeperator);
break;
case DIV:
case PLUS:
case MINUS:
case MULTIPLY:
if (resetInput) {
mInputStack.pop();
mOperationStack.pop();
} else {
if (currentInput.charAt(0) == '-') {
} else {
}
}
dumpInputStack();
evalResult = evaluateResult(false);
if (evalResult != null)
userInputText.setText(evalResult);
resetInput = true;
break;
case CALCULATE:
if (mOperationStack.size() == 0)
break;
evalResult = evaluateResult(true);
if (evalResult != null) {
clearStacks();
userInputText.setText(evalResult);
resetInput = false;
hasFinalResult = true;
}
break;
userInputValue = tryParseUserInput();
if (Double.isNaN(userInputValue))
return;
if (Double.isNaN(memoryValue))
memoryValue = 0;
memoryValue += userInputValue;
displayMemoryStat();
hasFinalResult = true;
break;
case M_REMOVE: // Subtract user input value to memory buffer
userInputValue = tryParseUserInput();
if (Double.isNaN(userInputValue))
return;
if (Double.isNaN(memoryValue))
memoryValue = 0;
memoryValue -= userInputValue;
displayMemoryStat();
hasFinalResult = true;
break;
case MC: // Reset memory buffer to 0
memoryValue = Double.NaN;
displayMemoryStat();
break;
case MR: // Read memoryBuffer value
if (Double.isNaN(memoryValue))
return;
userInputText.setText(doubleToString(memoryValue));
displayMemoryStat();
break;
case MS: // Set memoryBuffer value to user input
userInputValue = tryParseUserInput();
if (Double.isNaN(userInputValue))
return;
memoryValue = userInputValue;
displayMemoryStat();
hasFinalResult = true;
break;
default:
if (Character.isDigit(text.charAt(0))) {
if (currentInput.equals("0") || resetInput || hasFinalResult) {
userInputText.setText(text);
resetInput = false;
hasFinalResult = false;
} else {
userInputText.append(text);
resetInput = false;
}
}
break;
}
}
private void clearStacks() {
mInputStack.clear();
mOperationStack.clear();
mStackText.setText("");
}
private void dumpInputStack() {
Iterator<String> it = mInputStack.iterator();
StringBuilder sb = new StringBuilder();
while (it.hasNext()) {
CharSequence iValue = it.next();
sb.append(iValue);
}
mStackText.setText(sb.toString());
}
private String evaluateResult(boolean requestedByUser) {
if ((!requestedByUser && mOperationStack.size() != 4)
|| (requestedByUser && mOperationStack.size() != 3))
return null;
String left = mOperationStack.get(0);
String operator = mOperationStack.get(1);
String right = mOperationStack.get(2);
String tmp = null;
if (!requestedByUser)
tmp = mOperationStack.get(3);
double leftVal = Double.parseDouble(left.toString());
double rightVal = Double.parseDouble(right.toString());
double result = Double.NaN;
result = leftVal / rightVal;
result = leftVal * rightVal;
result = leftVal + rightVal;
result = leftVal - rightVal;
}
String resultStr = doubleToString(result);
if (resultStr == null)
return null;
mOperationStack.clear();
if (!requestedByUser) {
}
return resultStr;
}
private String doubleToString(double value) {
if (Double.isNaN(value))
return null;
long longVal = (long) value;
if (longVal == value)
return Long.toString(longVal);
else
return Double.toString(value);
}
private double tryParseUserInput() {
String inputStr = userInputText.getText().toString();
double result = Double.NaN;
try {
result = Double.parseDouble(inputStr);
} catch (NumberFormatException nfe) {}
return result;
}
private void displayMemoryStat() {
if (Double.isNaN(memoryValue)) {
memoryStatText.setText("");
} else {
memoryStatText.setText("M = " + doubleToString(memoryValue));
}
}```
ProcessKeypadInput method is called each time user presses a keypad button and we decide what to do with a swtich/case code block. We also have some helper methods
• clearStacks, is used to clear our stacks and the user input TextView
• dumpInputStack, is used to dump the input stack as a single line string to the TextView represented as Area #1 in our mockup
• evaluateResult, is called when user presses an artihmetic operation keypad button or the (=) keypad button. Inside this method we try to calculate a result by popping values from our operation stack and we push the result as the first item to the operation stack if we were able to calculate a result
• doubleToString, utility method which is used to convert a double value to String
• tryParseUserInput, utility method where we try to parse the user input, represented as Area #2 in our mockup, as a valid double value
• displayMemoryStat, utility method used to dump the memory buffer status and value to the Area #3 in our mockup
## The Right Place To Call ProcessKeypadInput Method
In "Displaying The Keypad" section please take a look at the comment placed on Line 34. If you read the GridView Sample in Android Developers site, you might think that this line is the right place to put the ProcessKeypadInput method call since the user will click on the keypad buttons which are in turn items of our GridView that in turn will trigger the OnItemClick event. This assumption is absolutely wrong in our case. If you put the call to ProcessKeypadInput method on that line and run your application OnItemClick of our GridView will not be fired even though a button is pressed. The reason for this misconception is this : Since Button views placed in the cells of the GridView are clickable, when user clicks over a button the Button view handles that click and the action is not propagated to the GridView.
Solution to this problem is pretty straight forward; we have to set OnClickListener of our keypad Button views and we will do that in our KeypadAdapter class. Below is the modified version of our KeypadAdapter class.
```package com.pragmatouch.calculator;
import android.widget.*;
import android.content.*;
import android.view.*;
import android.view.View.OnClickListener;
private Context mContext;
// Declare button click listener variable
private OnClickListener mOnButtonClick;
mContext = c;
}
// Method to set button click listener variable
public void setOnButtonClickListener(OnClickListener listener) {
mOnButtonClick = listener;
}
public int getCount() {
return mButtons.length;
}
public Object getItem(int position) {
return mButtons[position];
}
public long getItemId(int position) {
return 0;
}
// create a new ButtonView for each item referenced by the Adapter
public View getView(int position, View convertView, ViewGroup parent) {
Button btn;
if (convertView == null) { // if it's not recycled, initialize some
// attributes
btn = new Button(mContext);
btn.setOnClickListener(mOnButtonClick);
// Set CalculatorButton enumeration as tag of the button so that we
// will use this information from our main view to identify what to
// do
} else {
btn = (Button) convertView;
}
btn.setText(mButtons[position].getText());
return btn;
}
// Create and populate keypad buttons array with CalculatorButton enum
// values
}```
We declared mOnButtonClick field on Line 12 and defined a setter method for this field on Line 19-21. Then we set OnClickListener of our Button views to mOnButtonClick value on Line 43-44.
In order to catch button clicks and call ProcessKeypadInput, we also have to modify our main class.
```package com.pragmatouch.calculator;
import android.app.Activity;
import android.os.Bundle;
import android.widget.GridView;
import android.view.View;
import android.view.View.OnClickListener;
public class main extends Activity {
/** Called when the activity is first created. */
@Override
public void onCreate(Bundle savedInstanceState) {
super.onCreate(savedInstanceState);
setContentView(R.layout.main);
// Get reference to the keypad button GridView
@Override
public void onClick(View v) {
Button btn = (Button) v;
// Get the KeypadButton value which is used to identify the
// keypad button from the Button's tag
}});
});
public void onItemClick(AdapterView<?> parent, View v,int position, long id) {
// This will not help us catch button clicks!
}
});
}
}```
## Are we done yet?
We have a fully functional (actually I left implementaton of SQRT, 1/x and % to you as an excercise) standard calculator but there is always room for improvement and visual styling. In this last section I will try to show you a simple sample for styling our keypad buttons and the TextViews we have used in our UI. For more information about Using Styles And Themes please visit this link.
### Applying Style To Our Keypad
Android has lots of different resource types and it is possible to style your Android application's UI at different levels by utilizing these resources. As a simple example, we will use Drawable resource type (to be more specific State List drawable resource type) for styling. You can check out this link for more resource types though.
First of all we have to define a State List drawable as an XML file under res/drawable. If you installed the latest Android SDK you will see drawable-hdpi, drawable-ldpi under res folder but there is no drawable folder. You can safely create a drawable folder if you do not already have one. After ensuring that drawable folder exists, add an XML file with name keypadclear1.xml. Inside keypadclear1.xml you will have the following markup code which defines a style for Button views.
```<?xml version="1.0" encoding="utf-8"?>
<selector
xmlns:android="http://schemas.android.com/apk/res/android">
<item android:state_pressed="true" >
<shape>
android:startColor="#ff8c00"
android:endColor="#FFFFFF"
android:angle="270" />
<stroke
android:width="2dp"
android:color="#dcdcdc" />
<corners
android:left="10dp"
android:top="10dp"
android:right="10dp"
android:bottom="10dp" />
</shape>
</item>
<item android:state_focused="true" >
<shape>
android:startColor="#ffc2b7"
android:endColor="#ffc2b7"
android:angle="270" />
<stroke
android:width="2dp"
android:color="#dcdcdc" />
<corners
android:left="10dp"
android:top="10dp"
android:right="10dp"
android:bottom="10dp" />
</shape>
</item>
<item>
<shape>
android:startColor="#ff9d77"
android:endColor="#ff9d77"
android:angle="270" />
<stroke
android:width="2dp"
<corners
android:left="10dp"
android:top="10dp"
android:right="10dp"
android:bottom="10dp" />
</shape>
</item>
</selector>```
keypadclear1.xml contains seperate style definitions for each of the three possible states of a Button view. Now that we have our State List drawable resource ready, we have to write some code to make use of this resource. We will set the background of keypad buttons of KeypadButtonCategory.CLEAR to be styled according to the definitions of keypadclear1.xml. We will modify getView method of our KeypadAdapter class slightly
```// create a new ButtonView for each item referenced by the Adapter
public View getView(int position, View convertView, ViewGroup parent) {
Button btn;
if (convertView == null) { // if it's not recycled, initialize some attributes
btn = new Button(mContext);
btn.setOnClickListener(mOnButtonClick);
// Set CalculatorButton enumeration as tag of the button so that we
// will use this information from our main view to identify what to do
} else {
btn = (Button) convertView;
}
btn.setText(mButtons[position].getText());
return btn;
}
```
On Line 13, we set the background resource of our Button views if they are categorized as KeypadButtonCategory.CLEAR and that is all, we have pinky rounded buttons sketched as Area #9 in our mockup.
## Accomplishment
We got familiar with Android application development and evaluate different aspects of an Android application's UI. We developed a styled calculator which looks like the image atatched below
## Is There Room For Improvement In TouchCalculator?
Yes. There is always room for improvement and I intentionally left some business logic implementation to you. Here is the list of possible improvements
• Implement SQRT
• Implement 1/x (reciproc)
• Implement % (percent)
• Handle division by zero cases properly
• Implement different styles and provide "Switch Theme" dialog to the user
• Implement Scientific, Programmer and Statistics mode and allow user to switch modes
## Other Notes
How to fix Eclipse SDK 3.6 null pointer exception appearing when you try to edit res/values/strings.xml resource?
Open res\values\strings.xml with Text Editor and replace <resources> with <resources xmlns:android="http://schemas.android.com/apk/res/android">
## Share
- Software developer
- Has BS degree in Computer Engineering
- Has MBA degree
- Programmed with C, C++, Delphi, T-SQL and recently C#
- Little educational experience with Prolog
- Feel enthusiasm about NHibernate and LINQ
- Love to develop on Cuyahoga Web Framework
- Developer of PragmaSQL Editor
(Code Project Members Choice Winner for 2009 and 2010)
- Developed JiraTouch and MoodleTouch for iPhone
## You may also be interested in...
Pro Pro
First PrevNext
Finally Evan Mason16-Nov-15 23:46 Evan Mason 16-Nov-15 23:46
error Puneet Baranwal15-Nov-15 11:17 Puneet Baranwal 15-Nov-15 11:17
Button location Member 116971805-Jul-15 12:17 Member 11697180 5-Jul-15 12:17
good futurejo21-Oct-14 7:04 futurejo 21-Oct-14 7:04
My vote of 2 webluke20-Jul-14 16:55 webluke 20-Jul-14 16:55
Thanks for sharing. mijan9320-Apr-14 0:25 mijan93 20-Apr-14 0:25
How to implement VAT calc Member 1044976513-Mar-14 3:19 Member 10449765 13-Mar-14 3:19
Why??? Member 1060786518-Feb-14 20:01 Member 10607865 18-Feb-14 20:01
keys display mixed up getView fixes Member 1046539620-Dec-13 8:49 Member 10465396 20-Dec-13 8:49
change text color of gridview buttons Member 1020606415-Oct-13 21:20 Member 10206064 15-Oct-13 21:20
Is this the right logic on how to commit the improvements? MaddieA22-Aug-13 20:09 MaddieA 22-Aug-13 20:09
how to implement SQRT function upulwijayantha14-Aug-13 0:07 upulwijayantha 14-Aug-13 0:07
My vote of 5 computervirus349-Jun-13 16:43 computervirus34 9-Jun-13 16:43
My vote of 5 muratcantuna28-May-13 10:09 muratcantuna 28-May-13 10:09
My vote of 5 VitorHugoGarcia20-May-13 0:38 VitorHugoGarcia 20-May-13 0:38
Question about the code Dani21215-Mar-13 13:01 Dani2121 5-Mar-13 13:01
Re: Question about the code Phat (Phillip) H. VU21-Apr-13 5:03 Phat (Phillip) H. VU 21-Apr-13 5:03
problem Member 98731643-Mar-13 12:00 Member 9873164 3-Mar-13 12:00
what is the code for sqrt,percentage and reciprocal in this article? Member 98151326-Feb-13 0:10 Member 9815132 6-Feb-13 0:10
Re: what is the code for sqrt,percentage and reciprocal in this article? robzzzzz6-Feb-13 5:40 robzzzzz 6-Feb-13 5:40
Business Logic Confusion Endbringer4224-Jan-13 17:06 Endbringer42 24-Jan-13 17:06
I was doing pretty good until I got to the business logic section. There isn't an explanation as to what file all that code goes into nor where in the file. I'm assuming it goes in the Main.java file. Also, while typing the code in that section I keep getting the error "userInputText cannot be resolved". I don't see where this is defined anywhere in the file. `String text = keypadButton.getText().toString();` Is the string "text" in the line above supposed to be userInputText? This is my first Android app and Java app, so I could just be missing something simple.
My vote of 5 VitorHugoGarcia8-Jan-13 22:35 VitorHugoGarcia 8-Jan-13 22:35
Thank you, usefull example. Nap_BlownApart21-Nov-12 1:56 Nap_BlownApart 21-Nov-12 1:56
My vote of 5 csharpbd3-Oct-12 18:51 csharpbd 3-Oct-12 18:51
awesome iRakeshJha22-Sep-12 5:52 iRakeshJha 22-Sep-12 5:52
My vote of 5 iRakeshJha22-Sep-12 5:51 iRakeshJha 22-Sep-12 5:51
nice article vamp.bkstha12-Sep-12 7:37 vamp.bkstha 12-Sep-12 7:37
Works Properly parkavikarthi15-Jul-12 23:06 parkavikarthi 15-Jul-12 23:06
My vote of 5 wasiuddin8-Jul-12 6:12 wasiuddin 8-Jul-12 6:12
one error please see urgently Akshit Jain27-Jun-12 21:18 Akshit Jain 27-Jun-12 21:18
Well explained anjali john20-May-12 21:34 anjali john 20-May-12 21:34
sqrt is not working veereshbabu20-Feb-12 20:45 veereshbabu 20-Feb-12 20:45
TOUCHCALCULATOR Vaibhav17891-Feb-12 17:57 Vaibhav1789 1-Feb-12 17:57
need help compiling it code00130-Jan-12 4:26 code001 30-Jan-12 4:26
My vote of 5 darkagent2925-Dec-11 21:42 darkagent29 25-Dec-11 21:42
My vote of 5 Habaner04-Dec-11 1:54 Habaner0 4-Dec-11 1:54
where to place Key process cig779821-Oct-11 15:06 cig7798 21-Oct-11 15:06
My vote of 5 Ernesto Herrera23-Jun-11 7:22 Ernesto Herrera 23-Jun-11 7:22
Great tutorial! One minor suggestion... Goalstate19-May-11 13:39 Goalstate 19-May-11 13:39
My vote of 5 joe_mycostech14-May-11 0:52 joe_mycostech 14-May-11 0:52
Error, perhaps? DavidCrow7-Mar-11 10:12 DavidCrow 7-Mar-11 10:12
How to get started in Android Developement Mick Leong28-Feb-11 17:05 Mick Leong 28-Feb-11 17:05
Re: How to get started in Android Developement DavidCrow7-Mar-11 9:59 DavidCrow 7-Mar-11 9:59
My vote of 4 Mick Leong28-Feb-11 16:59 Mick Leong 28-Feb-11 16:59
My vote of 5 thatraja25-Feb-11 15:17 thatraja 25-Feb-11 15:17
My vote of 5 chandu999928-Dec-10 1:22 chandu9999 28-Dec-10 1:22
My vote of 5 paulsasik23-Dec-10 3:05 paulsasik 23-Dec-10 3:05
My vote of 5 Zorance17-Dec-10 8:20 Zorance 17-Dec-10 8:20
Last Visit: 31-Dec-99 18:00 Last Update: 20-Oct-17 1:32 Refresh 12 Next » | 8,172 | 34,415 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.6875 | 3 | CC-MAIN-2017-43 | latest | en | 0.909052 |
https://mailman.ntg.nl/pipermail/ntg-context/2016/087097.html | 1,638,416,466,000,000,000 | text/html | crawl-data/CC-MAIN-2021-49/segments/1637964361064.69/warc/CC-MAIN-20211202024322-20211202054322-00599.warc.gz | 448,219,457 | 2,230 | # [NTG-context] Question about natural tables
Fabrice Couvreur fabrice1.couvreur at gmail.com
Sun Oct 9 10:42:31 CEST 2016
Hello,
I do not succeed in having two sub-columns of the same width in the third
column.
Thank you.
Fabrice
\useMPlibrary[dum]
\startsetups[table:initialize]
\setupTABLE[start][align={middle,lohi},offset=0.8ex]
\setupTABLE[column][2][width=0.5\textwidth]
\setupTABLE[column][3][width=0.4\textwidth]
\setupTABLE[column][first][width=1.5cm]
\setupTABLE[1][1,2,3][frame=off]
\stopsetups
\starttext
\startlinecorrection[blank]
\startmidaligned
\bTABLE[setups=table:initialize]
\bTR
\bTD \eTD
\bTD Algébriquement \eTD
\bTD [nc=2] Graphiquement \eTD
\eTR
\bTR
\bTD \eTD
\bTD[nr=2] L'équation \math{ax^2+bx+c=0} \eTD
\bTD[nc=2] La parabole d'équation \math{y=ax^2+bx+c} \eTD
\eTR
\bTR
\bTD \eTD
\bTD Cas où \math{a\geqslant 0} \eTD
\bTD Cas où \math{a\leqslant 0} \eTD
\eTR
\bTR
\bTD \math{\Delta >0} \eTD
\bTD admet deux solutions distinctes :
\startformula
x_2=\frac{-b+\sqrt{\Delta}}{2a}
\stopformula
\eTD
\bTD[nc=2] coupe deux fois l'axe des abscisses
\dontleavehmode\startcombination[2*1]{\externalfigure[dummy][scale=900]}{}{\externalfigure[dummy][scale=900]}{}
\stopcombination \eTD
\eTR
\bTR
\bTD \math{\Delta=0} \eTD
\bTD admet une unique solution :
\startformula
x_0=-\frac{b}{2a}
\stopformula
\eTD
\bTD[nc=2] coupe l'axe des abscisses en un seul point
\dontleavehmode\startcombination[2*1]{\externalfigure[dummy][scale=900]}{}{\externalfigure[dummy][scale=900]}{}
\stopcombination \eTD
\eTR
\bTR
\bTD \math{\Delta<0} \eTD
\eTD
\bTD [nc=2] ne coupe pas l'axe des abscisses
\dontleavehmode\startcombination[2*1]{\externalfigure[dummy][scale=900]}{}{\externalfigure[dummy][scale=900]}{}
\stopcombination \eTD
\eTR
\eTABLE
\stopmidaligned
\stoplinecorrection
\stoptext
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://mailman.ntg.nl/pipermail/ntg-context/attachments/20161009/3c03d616/attachment.html> | 746 | 2,241 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.328125 | 3 | CC-MAIN-2021-49 | latest | en | 0.293525 |
chippewavalleyconceptualphysics.weebly.com | 1,571,067,543,000,000,000 | text/html | crawl-data/CC-MAIN-2019-43/segments/1570986653876.31/warc/CC-MAIN-20191014150930-20191014174430-00504.warc.gz | 41,483,874 | 8,100 | Name: Chapter 2 Pre-Test
Multiple Choice
Identify the choice that best completes the statement or answers the question.
1.
Speed is
a. a measure of how fast something is moving. b. always measured in terms of a unit of distance divided by a unit of time. c. the distance covered per unit time. d. all of the above. e. none of the above.
2.
One possible unit of speed is
a. miles per hour. b. light years per century. c. kilometers per hour. d. all of the above. e. none of the above.
3.
When you look at the speedometer in a moving car, you can see the car's
a. average distance traveled. b. instantaneous acceleration. c. average speed. d. instantaneous speed. e. average acceleration.
4.
A train travels 6 meters in the first second of travel, 6 meters again during the second second of travel, and 6 meters again during the third second. Its acceleration is
a. 0 m/s2. b. 6 m/s2. c. 12 m/s2. d. 18 m/s2. e. none of the above
5.
A car starts from rest and after 7 seconds it is moving at 42 m/s. What is the car’s average acceleration?
a. 0.17 m/s2 b. 1.67 m/s2 c. 6 m/s2 d. 7 m/s2 e. none of the above
6.
As an object falls freely in a vacuum, its
a. velocity increases. b. acceleration increases. c. both A and B. d. none of the above.
7.
In the absence of air resistance, objects fall at constant
a. speed. b. velocity. c. acceleration. d. distances each successive second. e. all of the above
8.
If you drop a feather and a coin at the same time in a tube filled with air, which will reach the bottom of the tube first?
a. The feather b. Neither—they will both reach the bottom at the same time. c. The coin
9.
Suppose you take a trip that covers 180 km and takes 3 hours to make. Your average speed is
a. 30 km/h. b. 60 km/h. c. 180 km/h. d. 360 km/h. e. 540 km/h.
10.
Suppose a car is moving in a straight line and steadily increases its speed. It moves from 35 km/h to 40 km/h the first second and from 40 km/h to 45 km/h the next second. What is the car's acceleration?
a. 5 km/h·s b. 10 km/h·s c. 35 km/h·s d. 40 km/h·s e. 45 km/h·s
11.
A ball is thrown straight up. At the top of its path its instantaneous speed is
12.
A ball is thrown straight up. At the top of its path its acceleration is
13.
A freely falling object starts from rest. After falling for 6 seconds, it will have a speed of about
a. 6 m/s. b. 30 m/s. c. 60 m/s. d. 300 m/s. e. more than 300 m/s.
14.
If you drop a feather and a coin at the same time in a vacuum tube, which will reach the bottom of the tube first?
a. Neither-they will both reach the bottom at the same time. b. The coin c. The feather
True/False
Indicate whether the statement is true or false.
15.
The rate at which distance is covered is called speed.
16.
Average speed is defined as the time it takes for a trip divided by the distance.
17.
Velocity is different from speed in that velocity is speed in a given direction.
18.
The rate at which velocity changes with time is called acceleration.
19.
When a car rounds a corner at a constant speed, its acceleration is zero.
20.
Even though a car is slowing down, it is still accelerating, in the most general definition of acceleration. | 881 | 3,193 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.734375 | 4 | CC-MAIN-2019-43 | latest | en | 0.885408 |
https://proofwiki.org/wiki/Category:Examples_of_Chinese_Remainder_Theorem | 1,721,836,661,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763518304.14/warc/CC-MAIN-20240724140819-20240724170819-00120.warc.gz | 398,542,700 | 11,118 | # Category:Examples of Chinese Remainder Theorem
This category contains examples of use of Chinese Remainder Theorem.
Let $b_1, b_2, \ldots, b_r \in \Z$.
Let $n_1, n_2, \ldots, n_r$ be pairwise coprime positive integers.
Let $\ds N = \prod_{i \mathop = 1}^r n_i$.
Then the system of linear congruences:
$\ds x$ $\equiv$ $\ds b_1$ $\ds \pmod {n_1}$ $\ds x$ $\equiv$ $\ds b_2$ $\ds \pmod {n_2}$ $\ds$ $\vdots$ $\ds$ $\ds x$ $\equiv$ $\ds b_r$ $\ds \pmod {n_r}$
has a solution which is unique modulo $N$:
$\exists ! a \in \Z_{>0}: x \equiv a \pmod N$
## Pages in category "Examples of Chinese Remainder Theorem"
The following 2 pages are in this category, out of 2 total. | 242 | 679 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.734375 | 3 | CC-MAIN-2024-30 | latest | en | 0.416088 |
https://fr.scribd.com/document/437401730/kupdf-net-eec-233-theory-pdf | 1,590,991,731,000,000,000 | text/html | crawl-data/CC-MAIN-2020-24/segments/1590347414057.54/warc/CC-MAIN-20200601040052-20200601070052-00487.warc.gz | 372,442,023 | 108,323 | Vous êtes sur la page 1sur 75
# UNESCO-NIGERIA TECHNICAL &
VOCATIONAL EDUCATION
REVITALISATION PROJECT-PHASE II
NATIONAL DIPLOMA IN
ELECTRICAL ENGINEERING TECHNOLOGY
C A B
Ic Ia Ib
ELECTRICAL MACHIENS I I
COURSE CODE: EEC233
THEORY
## Version 1: December 2008
1
Chapter 1: Basic Principles of electric machines: ............................... keeW1
1.1 Introduction .........................................................................................1
1.2 Electro- mechanical energy convertion ........................................... 2
## 1.6 Work Examples ....................................................................................... 8
1.7Electromagnets ...................................................................................... 11
## Chapter 3: Synchronous Machine: ....................................................... keeW5
3.1 Introduction ........................................................................................... 18
3.2 Stator construction .............................................................................. 18
## Chapter4:Control & protection of electric motors ............................. keeW6
4.1 Need for Circuit Protection ............................................................... 22
## 4.3.2 Contactors ....................................................................... 31
4.3.3Pushbuttons ............................................................Week10
## Chapter 5: Energy convertion ............................................................. keeW11
5.1 Electro-mechanical energy convertion .......................................... 37
## 5.2 Energy convertion ................................................................................ 39
5.3 Linked energy system ............................................................................ 40
## 5.11.3 General Condition
1. Basic Principles of Electric Machines Week 1
1.1 Introduction
It may be necessary to define what we mean by the term electrical machines. A machine is a
device that does useful work in a predictable way according to some physical laws. It acts as
## An electromagnetic machine, in the essential conversion process, uses energy in an
intermediate magnetic form. As a motor the machine takes in electrical energy and converts
it into mechanical work, such as driving a machine tool or a lift, or operating a loudspeaker.
## An electro-magnetic machine is usually reversible and cab, as a generator, producer
electrical energy form some other kind, such as the mechanical energy of prime- movers or
## the a caustic energy of microphones and gramophone pickups.
Electrical energy is versatile and controllable. Its special lie in that can be transfer
## processing), and applied to indicate an supervise production systems (control,
instrumentation and computation). It is readily converted into sound, light, heat and useful
## forms of energy. In particular it is easily converted to or from mechanical energy in the
electromagnetic machines
1
1. Basic Principles of Electric Machines Week 1
## i The development of magneto-mechanical forces and
ii. The induction of emf (electromotive force) by the rate of change of the linkage.
Thus, electromagnetic energy conversion is based on three bask principles namely (i)
## induction (ii) interaction and (iii) alignment
1. Principle of induction
It is known that when electrons are in motion, they produce a magnetic field. Conversely,
when, a magnetic field embracing a conductor moves relative to the conductor, it produce a
## flow of electrons in the conductor.
The phenomenon whereby on e.m.f and hence current (i.e flow of electrons) is induced in
any conductor which is cut across or is cut by a magnetic flux is known as electromagnetic
induction
dt
## Ø = flux in webers linking the coil
T = time in seconds
2
1. Basic Principles of Electric Machines Week 1
This is the equation for the induced emf when the magnetic flux moves relatively to the
conductor.
## L = effective length of conductor in metre , U = velocity of the conductor in m/s
And this is the equation for the induced emf when the conductor moves relatively to the flux.
## 1.2.2 Sketchmatic explanation of the induction principle
Fig:1.1a. Voltage & Current induced in the secondary Fig: 1.1b Conductor stationary, while the
circuit due to flux linkage with the primary winding. field moves (current will be induced on the
galvanometer)
Fig: 1.1c Conductor moves, while the field stationary (current will be induced on the
galvanometer)
3
1. Basic Principles of Electric Machines Week 1
Fig. 1.1 (a) shows an irobn- cored solenoid with a permanent magnetic place adjascent ot it. If the
magnet‟s position is changed from position CD to position AB, the flux linking with the
coils of the solenoid will change, leading to an induced emf in the coil which can be
## detected by the sensitive galvanometer G. in this arrangement, the conductor (coil) i
stationary whilst the filed (magnet) moves as in alternators i.e a.c generators.
Fig 1.1 (b) shows a filed arrangement that is stationary while the conduct a-b is free to move about
the vertical axis. An emf, detectable by galvanometer G, will be induced in the conductor as
it cuts through the flux through the flux. This principle is employed in the construction of
d.c. generator,.
F ig 1.1(c) when a coil (Ni) is made to carry an alternative current (ii) it produces an alternative flux
(g). if a second coil (N2) is now placed in a region whereby the alternative flux produced by
the first coil links with the second coil, an emf ( usually of the some frequency) will be
induced in the second coil. This is the principle of the transformer and the induction motors
2. Principle of interaction
## An electric current flowing in a direction making an angle (preferably a right-angle) with a
magnetic filed produced by another current ( or a magnet) experience a force fe, the relative
## Fig: 1.2 Principle of interaction.
4
1. Basic Principles of Electric Machines Week 1
The force, fe, arises from the interaction of the flux (created by the current l‟ flowing in the
conductor with the flux produced by a second current or magnet. Since lines of flux do not
cross, the two fluxes will realign. Resulting in a stronger fie ld one side. The conductor and
weaker filed on t6he other side. The conductor then tends to move from the region of
## stronger field to the region of weaker filed. Employed in electric motors.
3. Principle of alignment
## A pieces of ferromagnetic materials in a magnetic field experience of force urging it towards
a region where the field is stronger, or tending to align it so as to shorten the magnetic flux
## path as shown in fig: 1.3
Fig: 1.3a Moving coil meter Fig: 1.3b The force „fe‟ on shaped high
## Fig: 1.3c Polar attraction & repulsion on separately magnetized bodies
5
1. Basic Principles of Electric Machines Week 1
## 1.3 Alignment devices
(a) The lifting magnet: Attract ferromagnetic loads such as beams, plates, and scrap-
iron.
(b) The relay: the coil current causes the armature to be attracted towards the cover
against a spring load: Millions of such relays do useful work in automatic telephone
## (c) The telephone receivers: has a ferromagnetic diaphragm attracted by a permanent
magnet, the field is caused to fluctuated by the speech currents in the coil, so varying
the deflection of the claptrap and producing sound waves in the air.
(d) The moving- iron indicator, uses the force between the fixed and moving irons to
## deflect a pointed against a spring.
(e) The Reluctance motor- the forces urge a displaced rotor in alignment with the
magnetized stator.
(f) The actuator-the current-carrying coil “suck” a displaced ferromagnetic plunger into
## a position of symmetry: this is a useful and forceful device.
6
1. Basic Principles of Electric Machines Week 1
## (g) Electromagnetic pump: current passed through a conducting liquid in an enclosed
channel forces the liquid to move by interaction with a magnetic cross field; liquid
sodium-potassium or lithium can be pumped in thy way for the extraction of heat
## from a nuclear reactor.
(h) Loudspeaker: alternating current in the coil flow in the radial magnet filed of the port
magnet,. And the consequent movement of the attached diaphragm sets up sound
## waves. This is the same essential arrangement as a “generator‟ of mechanical
vibrations
(i) Moving –coil indicator-current (normally direct) in the coil of the indirect develops a
force in the radial permanent- magnet filed to move pointed against a control spring.
(k) Industrial rotating machines: Current caused to flow in conductors the surface of a
rotor, mounted within a magnetic stator develop interaction forces tending to turn the
rotor.
## 1.5 Induced voltage devices
Recalling that a conductor moving or cutting magnetic lines of flux or that the flux
moves relative to the conductor will proan induced voltage, the following devices
## employ the induced voltage arrangement.
(i) The transformer- an alternating current flowing in the primary coil (winding) set up
an alternating flux that links with the secondary coil inducing a voltage in the latter.
(m) The generatopr-usually constructed like (k) but with the rotor mechanical energy (via
the prime –mover) will have emf induced in the stator coils. ( the stator is slotted to
house conductors)
7
1. Basic Principles of Electric Machines Week 1
(n) The induction motor- the stator usually carried one or htree –phawindings whilst the
rotor may have a similar arrangement of coil as the stator or just carry or alirmium
bars. Electrical energy supplied to the stator windings produced a rotating magnetic
field with cuts the rotor conductors and hence induced voltages in them. A complete
rotor circult will have current flowing in the rotor conductors (caused by the induced
## 1.6 Work Examples
Examples 1
A conductor carries a current of 800 A at right- angle to magnetic field having a density of
Solution
## The force F is given by F = Bli
= 0.5 X 1 X 800
= 400N
Example 2
A four –pole generator has a magnetic flux of 12 mnb /pole calculated the average value of
the emf generated in one of the armature conductors while it is moving through the
## magnetic flux of one pole, if armature is driven at 900 r.p.m
Solution
When a conductor moves through the magnetic field of one pole, it cuts a magnetic flux of
12 x 10-3 wb.
## Time taken for a conductor to move through one revolution
= 60 = 1 second
8
1. Basic Principles of Electric Machines Week 1
900 15
Since the machine has 4 poles, time taken for a conductor to move through the field of one
## :. Average emf generated in one conductor rate of change of flux
= Ø = 12 x 10-3 1/60
## = 0.012 – 0.01667 = 0.72v
= 0.72v
Example 4
A magnetic flux of 400 uwb passing through a coil of 1200 turns is reversed in 0.1s calculate
## the average emf induced in the coil.
Solution
The magnetic flux has to decrease form 400 uwb to zero and then increase to 400wwb in the
reverse direction, hence the increase of flux is 400 (-400-400) uwb = -800 x 10-6 wb.
## = (change in flux x No of turns) = NdØ
Time taken. Dt
9
1. Basic Principles of Electric Machines Week 1
1.7 Electromagnets
Anything with an electrical current running through it has a magnetic field. Figure1 shows different
sources of magnetic field.
## Figure1.4: Different sources of magnetic field
The most common forms of electromagnets are the Solenoids .When the wire is shaped into a coil
as shown in Figure1.1, all the individual flux lines produced by each section of wire join together to
form one large magnetic field around the total coil.
As with the permanent magnet, these flux lines leave the north of the coil and re-enter the coil at its
south pole. The magnetic field of a wire coil is much greater and more localized than the magnetic
field around the plain conductor before being formed into a coil. This magnetic field around the coil
can be strengthened even more by placing a core of iron or similar metal in the center of the core.
The metal core presents less resistance to the lines of flux than the air, thereby causing the field
strength to increase. (This is exactly how a stator coil is made; a coil of wire with a steel core.) The
advantage of a magnetic field which is produced by a current carrying coil of wire is that when the
current is reversed in direction the poles of the magnetic-as shown in Figure1.2- field will switch
positions since the lines of flux have changed direction. Without this magnetic phenomenon
existing, the AC motor as we know it today would not exist.
10
1. Basic Principles of Electric Machines Week 1
Iron Core
Magnetic field Lines
N S
The Current
Battery
S N
Figure1.5: Reversing the polarity of the solenoid by reversing the current direction
Faradays law states whenever the magnetic flux linked with a circuit changes, an e.m.f. is always
induced in it, or Whenever a conductor cuts magnetic flux, an e.m.f. is induced in that conductor.
The phenomenon of inducing a current by changing the magnetic field in a coil of wire is known as
electromagnetic induction.
Figure1.3 shows an electromagnet which is connected to an AC power source. Another
electromagnet is placed above it. The second electromagnet is in a separate circuit. There is no
physical connection between the two circuits. Voltage and current are zero in both circuits at Time1.
At Time2 voltage and current are increasing in the bottom circuit
11
1. Basic Principles of Electric Machines Week 1
0 0 0
## Figure 1.6: Experment showing the electromagnetic induction phenomena
A magnetic field builds up in the bottom electromagnet. Lines of flux from the magnetic field
building up in the bottom electromagnet cut across the top electromagnet. A voltage is induced in
the top electromagnet and current flows through it. At Time 3 current flow has reached its peak.
Maximum current is flowing in both circuits. The magnetic field around the coil continues to build
up and collapse as the alternating current continues to increase and decrease. As the magnetic field
moves through space, moving out from the coil as it builds up and back towards the coil as it
collapses, lines of flux cut across the top coil. As current flows in the top electromagnet it creates its
own magnetic field.
## 1.9 Lenz's Law
Lenz's law enables us to determine the direction of the induced current: "The direction of the
induced current is such as to oppose the change causing it." The Figure 1.4a shows the north pole of
a bar magnet approaching a solenoid. According to Lenz's law, the current which is thereby
generated in the coil must cause an effect which opposes the approaching magnetic field.
12
1. Basic Principles of Electric Machines Week 1
N N
Iron Core
Ammeter
a
N S N
## Figure1.7: Experiment demonstrating Lenz's law
This is achieved if the direction of the induced current creates a north pole at the end of the
solenoid closest to the approaching magnet, as the induced north pole tends to repel the approaching
north pole. The Figure1.4b shows the north pole of a bar magnet withdrawing from a solenoid.
According to Lenz's law, the current which is thereby generated in the coil must cause an effect
which opposes the departing magnetic field. This is achieved if the direction of the induced current
creates a south pole at the end of the solenoid closest to the departing magnet, as the induced south
pole tends to attract the departing north pole
13
1. Basic Principles of Electric Machines Week Two
## 1.4 Rotating magnetic field
The three-phase induction motor also operates on the principle of a rotating magnetic
field. The following discussion shows how the stator windings can be connected to a three-
phase ac input and have a resultant magnetic field that rotates.
Figure 1.5 shows how the three phases are tied together in a Y-connected stator. The dot in
each diagram indicates the common point of the Y-connection. You can see that the
individual phase windings are equally spaced around the stator. This places the windings
120° apart.
C A B
Ic Ia Ib
## Figure 1.5:- Three-phase, Y-connected stator.
Using the left-hand rule the electromagnetic polarity of the poles can be determined at any
given instant.
5
1. Basic Principles of Electric Machines Week Two
The results of this analysis are shown for voltage points 1 through 7 in figure 2. At point 1,
the magnetic field in coils A is maximum with polarities as shown. At the same time,
negative voltages are being felt in the B and C windings. These create weaker magnetic
fields, which tend to aid the A field. At point 2, maximum negative voltage is being felt in
the C windings. This creates a strong magnetic field which, in turn, is aided by the weaker
fields in A and B. As each point on the voltage graph is analyzed, it can be seen that the
resultant magnetic field is rotating in a clockwise direction. When the three-phase voltage
completes one full cycle (point 7), the magnetic field has rotated through360°.
6
1. Basic Principles of Electric Machines Week Two
10
-5
-10
1 2 3 4 5 6 7
## Point4 Point 5 Point6
Point7
5
1. Basic Principles of Electric Machines Week 2
## 1.5 Synchronous speed:
The speed of the rotating magnetic field is referred to as synchronous speed (Ns). Synchronous
speed is equal to 120 times the frequency (f), divided by the number of poles (P).
120 f
Ns
p
If the frequency of the applied power supply for the two-pole stator used in the previous example is
50 Hz, synchronous speed is 3000 RPM.
120 50
Ns 3000 RPM
2
The synchronous speed decreases as the number of poles increase. The following table shows the
synchronous speed at 50 Hz for the corresponding number of poles.
## No of poles Synchronous speed
2 3000rpm
4 1500rpm
6 1000rpm
8 750rpm
Table 1.1: Different speeds for different number of poles
6
2. Three phase induction motor Week 3
2.1 Introduction
Three-phase AC induction motors are widely used in industrial and commercial applications. They
are classified either as squirrel cage or wound-rotor motors.
These motors are self-starting and use no capacitor, start winding, centrifugal switch or other
starting device.
They produce medium to high degrees of starting torque. The power capabilities and efficiency in
these motors range from medium to high compared to their single-phase counterparts.
Popular applications include grinders, lathes, drill presses, pumps, compressors, conveyors, also
printing equipment, farm equipment, electronic cooling and other mechanical duty applications.
## Simple and rugged construction
Low cost and minimum maintenance
High reliability and sufficiently high efficiency since there is no losses in brush contacts
or mechanical friction
Needs no extra starting motor and need not be synchronized
Need only one source of power
## 2.2 Construction of Induction Motor:
An Induction motor has basically two parts, Stator and Rotor. Also some of other parts were
acknowledged in the following section
1
2. Three phase induction motor Week 3
## Figure2.1: Diagram construction of the stator
The stator is made up of several thin laminations of aluminum or cast iron. They are punched and
clamped together to form a hollow cylinder (stator core) with slots as shown in Figure 2.1. Coils of
insulated wires are inserted into these slots.
The iron core on the figure has paper liner insulation placed in some of the slots.
Each grouping of coils, together with the core it surrounds, forms an electromagnet (a pair of poles)
on the application of AC supply. The number of poles of an AC induction motor depends on the
internal connection of the stator windings. The stator windings are connected directly to the power
source. Internally they are connected in such a way, that on applying AC supply, a rotating magnetic
field is created
## 2.2.2 Rotor construction:
There are two main types
2
2. Three phase induction motor Week 3
Squirrel cage type
Wound rotor
## 2.2.2.1 Squirrel cage rotor:
This rotor has a laminated iron core with slots(Figure2.2), and is mounted on a shaft. Aluminum
bars are molded in the slots and the bars are short circuited with two end rings. The bars are skewed
on a small rotor to reduce audible noise. Fins are placed on the ring that shorts the bars. These fins
also work as a fan and improve cooling.
Most motors use the squirrel-cage rotor because There are no commutators, slip rings or brushes.
Hence this is a most rugged and maintenance-free construction.
End ring
## 2.2.2.2 Wound rotor:
3
2. Three phase induction motor Week 3
Wound Rotor
Brush
External Rotor
Slip Rings Resistances
Figure 2.3: Schemtic diagram showing Induction motor, wound rotor type
The wound rotor or slip-ring induction motor differs from the squirrel-cage motor only in the rotor
winding. The rotor winding consists of insulated coils, grouped to form definite polar areas of
magnetic force having the same number of poles as the stator. The ends of these coils are brought
out to slip-rings. By means of brushes, a variable resistance is placed across the rotor winding
(Fig.2.3). By varying this resistance, the speed and torque of the motor is varied. The wound rotor
motor is an excellent motor for use on applications that require an adjustable-varying speed (an
Terminals
Shaft
Slip rings Laminated core
Bearings Fan
Coils
Figure 2.4:Wound rotor
2.2.3 Enclosure
## Enclosure or the frame (Figure2.5) ,its main
application to hold the parts together. also it Helps
with heat dissipation. In some cases, protects internal
4
2. Three phase induction motor Week 3
components from the environment. A cooling fan is attached to the shaft at the left-hand side. This
fan blows air over the ribbed stator frame
## Figure2.5:Induction Motor enclosure
2.2.3 Bearings:
There are two main types, the sleeve bearings and ball bearings .Ball (Roller) Bearings
(Figure2.6a) Support shaft in any position. Its Grease lubricated and required no maintenance
The Sleeve Bearings(figure2.6b) are Standard on most motors. They are only used with horizontal
shafts and its oil lubricated.
(a) (b)
b
Figure2.6: a)Ball Bearings
b)Sleeve bearings
2.2.5 Conduit Box
Point of connection of electrical power to the motor’s stator windings.
## 2.2.6 Eye Bolt
Used to lift heavy motors with a hoist or crane to prevent motor damage, as it can be seen in the
following figure.
5
2. Three phase induction motor Week 3
## Figure2.7: Sectional view of Induction Motor
6
2. Three phase induction motor Week 4
## 2.2 The principle of operation of the Induction Motor:
The three-phase current with which the motor is supplied establishes a rotating magnetic
field in the stator. This rotating magnetic field cuts the conductors in the rotor inducing
voltages and causing currents to flow. These currents set up an opposite polarity field in the
rotor(Lenz's law). The attraction between these opposite stator and rotor fields produces the
torque which causes the rotor to rotate. This simply is how the squirrel-cage motor works
Figure2.8:The magnetic field created in the stator and the rooted in the squirrel cage induction motor
## 2.3 The Slip:
There must be a relative difference in speed between the rotor and the rotating magnetic
field. If the rotor and the rotating magnetic field were turning at the same speed no relative
motion would exist between the two, therefore no lines of flux would be cut, and no voltage
would be induced in the rotor. The difference in speed is called slip. Slip is necessary to
produce torque. Slip is dependent on load. An increase in load will cause the rotor to slow
down or increase slip. A decrease in load will cause the rotor to speed up or decrease slip.
Slip is expressed as a percentage and can be determined with the following formula.
( Ns Nr ) 100
Slip (%)
Ns
1
2. Three phase induction motor Week 4
Where Nr is the actual speed of the rotor
For Example, a four-pole motor operated at 60Hz has a synchronous speed (Ns) of
1800 RPM. If the rotor speed at full load is 1765 RPM (Nr), then the slip will be
calculated
(1800 1765) 100
Slip (%) 1.9%
1800
2.4 Name Plate:
It is essential that all motors have nameplates with certain information useful in the
identification of the type of motor, The following Table explain the indication of each code
used on the shown nameplate
Name Of Manufacturer
ORD. No. IN123456789
TYPE HIGH EFFICIENCY FRAME 286T
SERVICE
H.P. 42 FACTOR 1.10 3PH
## R.P.M 1790 HERTZ 60 4POLE
DUTY CONT DATE 01/15/2003
NEMA B NEMA 95
CLASS INSUL. F Design NOM. EFF.
## Figure2.9:Typical Nameplate of an AC induction motor
Term Description
Volts Rated Supply voltage
HP Rated motor output
RPM Rated full load speed of the motor
2
2. Three phase induction motor Week 4
## Hertz Rated supply frequency
Frame External dimensions based on NEMA Regulations
Date Date of manufacturing
Class Insulation Specifies the max. limit temperature of the winding
NEMA Design Types of NEMA design, A,B,C etc
Service factor Factor by which the motor can be overloaded beyond the full load.
NEMA Nom Motor efficiency at rated load
Efficiency
PH Number of phases
Pole Number of poles
Motor safety standard
## Y The connection either star or delta
Table 2.1:Explanation of the codes used on AC motor nameplates
3
3. Synchronous machine Week 5
3.1 Introduction:
Synchronous motors are motors that always run at the same speed regardless of load.
Synchronous motors are somewhat more complex than squirrel-cage and wound rotor motors and,
hence, are more expensive. There is no slip in a synchronous motor, that is, the rotor always moves
at exactly the same speed as the rotating stator field.. The machine consists of three main parts:
Stator, which carries the three phase winding,
Rotor, with one DC winding or permanent magnets
Slip rings or excitation machine (exciter) (in case of electrical excitation).
Synchronous motors are used whenever exact speed must be maintained or for power factor
correction. Synchronous motors are more expensive than other types for the lower horsepower
ratings, but may possibly be more economical for 100 hp and larger ratings.
## 3.2 Stator construction:
The stator of a synchronous generator holds a three-phase winding where the individual phase
windings are distributed 120° apart in space and is sometimes called the armature winding. The
stator must be made of laminated iron sheets in order to reduce eddy currents.
## 3.3 Rotor construction:
The rotor holds a field winding,which is magnetized Metal frame
## by a DC current( the field current). The rotating Laminated iron
core with slots
field winding can be energized through a set of slip
rings and brushes (external excitation), or from a Insulated copper
bars are placed in
the slots to form
diode-bridge mounted on the rotor (self-excited). The the three-phase
winding
rectifier-bridge is fed from a shaft-mounted
alternator, which is itself excited by the pilot exciter.
In externally fed fields, the source can be a shaft-
driven dc generator, a separately excited dc generator, or a solid-state rectifier. Several variations to
these arrangements exist. There are two types of rotors:
Salient-pole rotor (Fig.2) for low-speed machines (e.g.hydro-generators)
Cylindrical rotor (Fig.3) for high-speed machines (e.g. turbo-generators).
1
3. Synchronous machine Week 5
## 3-Phase Stator Winding
Rotor Field
Winding
Brushes
- +
Slip Rings
Cylindrical
Pole Rotor Field current
Steel
retaining
ring
Shaft
Shaft
Wedges
DCcurrent
DC current
terminals
terminals
## Figure3.1: cylindrical rotor of a synchronous machine
2
3. Synchronous machine Week 5
## 3-Phase Stator Winding
Rotor Field
Winding
Brushes
- +
Slip Rings
Salient Pole
Rotor Field current
Slip
rings
Pole
DC excitation
winding
Fan
## b- salient-pole rotor of a synchronous machine
Figure3.2: Salient-Pole rotor of a synchronous machine
## 3.4 Principle of operation of the synchronous generator:
When the 3phase rotor is rotated (by an external prime-mover) the rotating magnetic
flux(induced by DC current) induces voltages in the stator windings. These voltages are sinusoidal
with a magnitude that depends on the field current, and also differ by 120° in time and have a
frequency determined by the angular velocity of the rotation.
3.5 Principle of operation of the synchronous motor:
The stator is supplied with three phase supply in order to develop a rotating magnetic field. Also
the rotor is supplied with DC supply to produce constant
magnetic field. As a result of the interaction of these two fields, the rotor will start to move.
However, the synchronous motor is not self started. Consequently, it usually equipped with squirrel
cage windings that mounted on the pole faces of the synchronous motor rotor. These rotor windings
3
3. Synchronous machine Week 5
are frequently referred to as damper or amortisseur windings. Thus, the synchronous motor starts as
an induction motor. When the motor accelerates to near synchronizing speed (about 95%
synchronous speed), DC current is introduced into the rotor field windings. This current creates
constant polarity poles in the rotor, causing the motor to operate at synchronous speed as the rotor
poles "lock" onto the rotating AC stator poles.
## 3.6 Excitation Methods
Two methods are commonly utilized for the application of the direct current (DC) field current to
the rotor of a synchronous motor.
Brush-type systems apply the output of a separate DC generator (exciter) to the slip rings of the
rotor.
Brushless excitation systems utilize an integral exciter and rotating rectifier assembly that
eliminates the need for need for brushes and slip rings.
## 3.7 Method of Synchronization
There are three basic method of synchronizing two or more machine:
. Bright lamp method
. Dark lamp method
. automatic method
4
3. Protection & control of electric motors Week 6
## 4.1 Need for Circuit Protection
Current flow in a conductor always generates heat(Figure1). The greater the current flow, the
hotter the conductor. Excess heat is damaging to electrical components. For that reason, conductors
have a rated continuous current carrying capacity or ampacity. Overcurrent protection devices, such
as circuit breakers, are used to protect conductors from excessive current flow. These protective
devices are designed to keep the flow of current in a circuit at a safe level to prevent the circuit
conductors from overheating.
## Figure4. 1:The effect of current flowing in conductors
overcurrent is defined as any current in excess of the rated current of equipment of a conductor. It
may result from overload, short circuit, or ground fault
Overloads: An overload occurs when too many devices are operated on a single circuit, or a piece of
electrical equipment is made to work harder than it is designed for. For example, a motor rated for
10 amps may draw 20, 30, or more amps in an overload condition.
1
3. Protection & control of electric motors Week 6
Good Insulation
Damaged Insulation
## Figure4. 2: Insulation of electric conductors
Conductor Insulation Motors, of course, are not the only devices that require circuit protection for
an overload condition. Every circuit requires some form of protection against overcurrent. Heat is
one of the major causes of insulation failure of any electrical component. High levels of heat can
cause the insulation to breakdown and deteriorated, exposing conductors (Figure4.2).
Short Circuits When two bare conductors touch, a short circuit occurs (Figure4.3).
When a short circuit occurs, resistance drops to almost zero. Short circuit current can be thousands
of times higher than normal operating current.
The heat generated by this current will cause extensive damage to connected equipment and
conductors. This dangerous current must be interrupted immediately when a short circuit occurs.
2
3. Protection & control of electric motors Week 6
## Short Circuit conductor
Insulation
Figure4. 3: Short circuit fault between two condu
3
4.Protection & control of electric motors Week 7
## 4.2 Types of Overcurrent Protective Devices
Circuit protection would be unnecessary if overloads and short circuits could be eliminated.
Unfortunately, overloads and short circuits do occur. To protect a circuit against these currents, a
protective device must determine when a fault condition develops and automatically disconnect the
electrical equipment from the voltage source. An overcurrent protection device must be able to
recognize the difference between overcurrents and short circuits and respond in the proper way.
Slight overcurrents can be allowed to continue for some period of time, but as the current magnitude
increases, the protection device must open faster. Short circuits must be interrupted instantly.
Several devices are available to accomplish this.
4.2.1 Fuses
A fuse is a one-shot device (Figure1). The heat produced by overcurrent causes the current
carrying element to melt open, disconnecting the load from the source voltage. There are three types
of fuses, namely
Semi-enclosed (Rewireable) fuse
Cartridge fuses
High Breaking Capacity(HBC)
Fuse Cap
Good Element
Glass or Ceramic
Body
Open
Element
## Figure 4.4: Plug fuse
4.2.1.1 Cartridge
The cartridge type have fuses which look similar to those you would
find in a standard household plug. This type is improvement of the
rewirable fuse type. It is main advantages, is easy to replace, totally
1
4.Protection & control of electric motors Week 7
enclosed and its current rating is very accurate
## Figure 4.5: A cartridge fuse and its holder
4.2.1.2 HBC
HBC stands for "high blow current (sometimes described as HRC = high rupture current). HBC
fuses are designed not to explode when failing under currents
many times their normal working current (e.g. 1500 amps in a 10
amp circuit). They are therefore to be preferred for the
protection of main voltage circuits where the power source may
be capable of providing very high currents. HBC types can
usually be recognized by being sand filled though they may have
a thick ceramic body.
## Figure 4.5: A HBC fuse
4.2.1.3 Semi-enclosed(Rewireable) fuses
As the name indicates, the rewireable type have a fuse wire held at both
ends by a small retaining screw. Once the fuse is blown, the fuse wire is
the only pieces to be replaced. It is cheap, but replacing a wrong size of
element can cause catastrophic consequences.
## Figure 4.6: Rewireable fuses
2
4. Protection & control of electric motors Week 8
## Figure 4.7:Miniature circuit breakers with different poles
The problem with fuses is they only work once. Every time you blow a fuse, you
have to replace it with a new one. A circuit breaker(Figure 4.7) does the same thing
as a fuse .It opens a circuit as soon as current climbs to unsafe levels ,but you can
use it over and over again.
The basic circuit breaker consists of a simple switch,(see figure 4.8) connected to
either a bimetallic strip or an electromagnet. The diagram below shows a typical
electromagnet design.
## Figure4.8: Cut view of a miniature circuit breaker
27
4. Protection & control of electric motors Week 8
## circuit breakers generally employ a bimetal strip to sense overload
conditions(Figure4.9b). When sufficient overcurrent flows through the circuit
breaker’s current path, heat build up causes the bimetal strip to bend. After bending
a predetermined distance the bimetal strip makes contact with the tripper bar
activating the trip mechanism.
A bimetal strip is made of two dissimilar metals bonded together(Figure4.8). The
two metals have different thermal expansion characteristics, so the bimetal bends
when heated. As current rises, heat also rises. The hotter the bimetal becomes the
more it bends, until the mechanism is released.
Material 1
Material2
} Bi-metal
Heat source
Figure 4.8:The effect of heat on a bimetal strip
## Short circuit protection is accomplished with an electromagnet (Figure4.8a). The
electromagnet is connected in series with the overload bimetal strip. During
normal current flow, or an overload, the magnetic field created by the
electromagnet is not strong enough to attract the armature. When a short circuit
current flows in the circuit, the magnetic field caused by the electromagnet attracts
the electromagnet’s armature. The armature hits the tripper bar rotating it up and to
the right. This releases the trip mechanism and operating mechanism, opening the
contacts. Once the circuit breaker is tripped current no longer flows through the
electromagnet and the armature is released. (See figure 4.9).
28
4.Protection & control of electric motors Week 8
## Magnetic Circuit Breaker(a)
Magnetic
Current in coil Magnetic
Current in coil
Electrical
contacts Electrical
contacts
Current Current
out out
Spring Spring
Latching
Latching mechanisim
mechanisim
## Thermal-magnetic Circuit Breaker(b)
Magnetic
coil
Current in Magnetic
coil
Electrical
contacts
Electrical
contacts
Current out
Current in
## Spring Current out
Latching
Spring
mechanisim
Latching
Normal Conditions mechanisim
## Figure4.9: The principle of operation of circuit breakers
29
4.Protection & control of electric motors Week 9
## 4.3 Control devices
4.3.1 Relay:
Iron Core
Iron Core
Switch
Switch
Relay Coil
Relay Coil Battery
Contacts
Contacts
To Power Circuit
To Power Circuit
## Relay Open Relay Close
Figure4.10:The principle of operation of the relay
The relay is a remotely controlled switch. In the diagram above, a power circuit contains a
switch which is opened and closed by operation of a
relay. The relay is activated by a magnetic core which is
energised when a controlling switch is closed. As the
core is energised, it lifts and closes a pair of contacts in a
second circuit - usually a power circuit. The current
required for the relay is usually much lower than that used
for the power circuit so it can be provided by a battery
In the left hand of figure4.10,the diagram shows the
controlling switch is open, so the relay is de-energised and Figure4.11: a relay the
power circuit contacts are open. If the controlling switch is
closed, as in the right hand diagram, the relay is therefore energised and its core magnet lifts
to close the contacts in the power circuit.
1
4.Protection & control of electric motors Week 9
4.3.2 Contactors:
(a) ( b)
## Figure4.12: a)Construction of a contactor ,b) A contactor
Figure4.12a shows the interior of a basic contactor. There are two circuits involved with the
operation of a contactor, the control circuit and the power circuit. The control circuit is
connected to the coil of an electromagnet, and the power circuit is connected to the
stationary contacts.
When the control circuit supplies power to the coil, a magnetic field is produced,
magnetizing the electromagnet. The magnetic field attracts the armature to the magnet,
which, in turn, closes the contacts. With the contacts closed, current flows through the power
circuit from the line to the load. Figure(4.13)
When current no longer flows through the control circuit, the electromagnet's coil is de-
energized, the magnetic field collapses, and the movable contacts open under spring
pressure.
2
4.Protection & control of electric motors Week 9
## Figure4.13:Principle of operation of the contactor
Overload relays (Figure4.14)are designed to meet the special protective needs of motor
control circuits. Overload relays allow harmless temporary overloads that occur when a
motor starts.
Overload relays trip and disconnect power to the motor if an overload condition persists.
Overload relays can be reset after the overload condition has been corrected.
3
4.Protection & control of electric motors Week 9
## 4.3.2.2 Contactors and Overload Relays
Contactors are used to control power in a variety of applications. When used in motor-
control applications, contactors can only start and stop the motors. Contactors cannot sense
Most motor applications require overload protection, although some smaller motor, such as
household garbage disposals, have overload protection built into the motor. Where overload
protection is required, overload relays (such as the one shown here) provide such protection.
## 4.3.2.3 Motor Starter
Contactors and overload relays are separate control devices. When a contactor is combined
with an overload relay, it is called a motor starter.Figure4.15
4
4.Protection & control of electric motors Week 10
4.3.3Pushbuttons
A pushbutton is a control device used to manually open and close a set of contacts. Pushbuttons may
be illuminated or non-illuminated and are available in a variety of configurations and actuator
colors.
## Figure 4.16: Different types of pushbuttons
i) Normally Open Pushbuttons
Pushbuttons are used in control circuits to perform various functions such as starting and stopping a
motor. A typical pushbutton uses an operating plunger, a return spring, and one set of contacts.
This illustration shows a pushbutton with normally open contacts. Pressing the button causes the
contacts to close (figure4.17). This pushbutton has momentary contacts which means that the
contacts will open when the pushbutton is released.
ii) Normally Closed Pushbuttons
Pushbuttons with normally closed contacts, such as the one shown here, are also used in control
circuits. The contacts remain in the closed position allowing current to flow through them until the
pushbutton is pressed(figure4.17). Pressing the pushbutton opens the contacts and interrupts current
flow. The pushbutton shown here also has momentary contacts; however, normally open and
normally closed pushbuttons with maintained contacts are also available.
.
1
4.Protection & control of electric motors Week 10
## Normally Close Pushbutton
Figure 4.17: The mechanism of the pushbuttons
## 4.3.4 Selector Switches
Selector switches are another means to manually open and close contacts and are commonly used
to select one of two or more circuit possibilities.
Selector switches may be maintained, spring return, or key operated and are available in two-
position, three-position, and four-position types.
The basic difference between a pushbutton and a selector switch is the operator mechanism. A
selector switch operator mechanism is rotated to open and close contacts.
2
4.Protection & control of electric motors Week 10
## Figure 4.18: Different types of selector switches
4.3.5 Indicator Lights:
Indicator lights, often referred to as pilot lights, provide a visual indication of a circuit's operating
condition. An indicator light may be wired to turn on for any predetermined condition. Indicator
lights are available in round designs with 16 mm, 22 mm, or 30 mm mounting diameters as well as
in square designs.
## Figure 4.19: Different types of push buttons switch
3
5. energy conversion Week 11
## 5.1 Electro-mechanical energy conversion
Energy is converted to electrical form because of the advantages listed in the introductory
part of the note. It is seldom available or used in electrical form, but converted into electrical
form at the input to a system and back to non-electrical form at the output of a system. A
typical example is the processing of energy from and hydro generating plant. It is converted
into electrical form at the power plant. Transmitted through transmission lines and
distribution lines, and converted to mechanical energy in an electric motor are the point use.
A second example is in the conversion of the energy in sound pressure waves, and the
transmission in electrical form from the taker to the listener in a telephone system. Few more
## Theoretically, only a sourceless current is needed to develop a mechanical force
magnetically. But in a machine the production of force is hardly enough: something must
move in order to do useful work done demands a corresponding energy supply form
somewhere.
In a device energized only by a permanent magnet, the only energy source is the magnet
itself. If the displacable part of the machine moves under force and does work, this can only
be at the expense of the field energy of the permanent magnet, which must decrease. Such an
5. energy conversion Week 11
arrangement has obvious limitations. It may also be inconvenient a permanent magnet”
lifting magnet, for example would not e capable of releasing its load. Where the magnetic
affected by the movement is produced by a current circuit, changes of field energy have to
be supplied electrically from a source. This implies the appearance in the circuit of an
electromotive force e, which, with the current I, represents the delivery or absorption by the
source of energy at the rate ei consider the elementary system of fig 2.1 A sources of voltage
## conversion process results in the appearance of an e.f.m.
The effective resistance of the circuit is represented by R. if current flows into the circuit
form the positive terminal of the source, and the input power p = Vi Rl + el, has the
direction as shown at (a). However¸ if e >, the current reverses and we can now call it –e. the
power input from the now p = v (-i) = Rl2 + e (-l), which is negative, i.e it is an output from
the device into the source, as at (b). to illustrate this simple but fundamental point, suppose
## The current o = v-e = 10-8 =2A
R 1
And the source provides an input power p = 10 x 2 = 20w The converting device accepts 8
## x 2 W as a motor And power loss due to plissipation = 1 x RT2 = 4W Conversely, if e
12V, The current again is 10 -12 -2A (I.e reversed) The device produces 12 x 2 = 24 W as
## a generator of which RT2 22 x 1 = 4W is dissipated in R, and 10 x 20W is delivery as an
output to the source. In the case of the electromagnetic machine, the relationship between
the emf and the magnetic field is obtained from the faraday induction law (which had been
mentioned in 1.1)
5. energy conversion Week 11
## An electromechanical machine forms a coverting link between an electrical energy system (
such as a main power –supply network) and a mechanical one (such as a prime- mover or a
train). In action a machine is not an isolated things, but has a behavious strongly influenced
by its terminal systems. A relay, for instance, will be affected if its operating battery
## becomes discharged; a loudspeaker will behave very differently it enclosed in an evacuated
vessels with the air loading thus removed; a hydro electric generator, suddenly short-
## circuited, will react severely on the turbine and pipe-line.
A machine can, of course, be studies initially in isolation, but the engineering interest
begins in fact when the complete linked system is considered. Again, the steady-state
## Fig 2.1 Electro–mechanical linked energy system
System analysis can be complicated. Fig 2.2 shows diagrammatically a typical electric
## supply system feeding a mechanical load through an electromechanical machine. In some
cases we might simplify the analysis by assuming, say, that the terminal voltage and
frequency of the machine were constant. This is good enough if the machine is a small
contactor but if it is a 25MW motor the effects of its behaviour reach for back through even
an extensive supply system. Methods are available for evaluating such a complex for any
5. energy conversion Week 11
given stimulus, such as the occurrence of a transmission- line fault or starting of a large
motor.
## 5.4 Energy storage
We now consider how a flux is established and energy is stored in simple toroidal magnetic
Circuit of cross sectional area A, path length L, and of material of constant permeability u,
## The flux is to be established by a current i, in a uniformly wound coil of N-turns. In order
To concentrate on energy storage we neglect the coil resistance. With i initially zero, let a
Voltage V, be applied to the coil terminals, what happen thereafter depends on Faraday’s
## Law of electromagnetic induction.
5. energy conversion Week 12
## Fig: 2.1 Electromechanical machine conventions
A machine accepts energy in a variety of forms from its attached terminal systems. By
conversion we take energy input as positive, so that an output is regarded as a negative input.
The machine internally electrical energy- mechanical energy is a motor mechanical energy to
electrical energy is a generator converts some energy, stores some, and dissipates the rest:
these energies are positive if they increase with time. As the prime object of a machine is
conversion to useful output, one of the terminal inputs will normally be negative. Recalling
the principle of conservation of energy which states that energy is neither created nor
destroyed and combining it with the laws of electric and magnetic fields, electric circuits and
## Newtonian mechanics, the energy balance can be expressed as:-
Total terminal energy input internal energy + Dissipation 2.1 for an electromechanical
machine using a magnetic field as the means of conversion, the balance can be stated in more
## = stored magnetic –field energy + stored mechanical energy + Dissipation
5. energy conversion Week 12
Reckoned from an initial condition of zero energy, w = o.A comparable relation must apply
to energy changes dw, and also to energy rate dw/dt i.e to power, P. in corresponding
## Energy rate Pe + pm = dwf + dws + p 2.2(c)
dt dt
The rates of change of stored field energy wf and stored mechanical energy, ws, are left in
differential form because there is always a practical limit to storage. A magnetic field can not
grow in strength indefinitely when ferromagnetic materials is employed; and if the kinetic
energy in a flywheel is continually increased, the speed must rise and the wheel may burst
## under centrifugal force.
We shall now examine the electromechanical machine in more detail with fig 2.3. The
machine links an electric source of voltages supplying a current; and a mechanical sources
represented by a bar moving to positive directions, thus both vi and fmu are inputs ( The
## mechanical source could alternatively be a shaft rotated at angular speed wr by a tongue mm
to give an input power mnwr ). The electrical end of the machine is precisely that of fig 2.1
(a), with opposing v. the mechanical end has the magnetically developed force fe opposing
fm > fm it can reverse speed w so that the mechanical system is driven and absorbs a
mechanical output.
The behavior can now be summarized. With the machine operating in the steady state as a
motor, the applied voltage u drive +I against e to give a total electrical power input pe =
u(+e), of which the part ei is converted. The outcome of conversion is the force fe which
drives the bar against fm to develop the mechanical input pm = fm (-u) which, being
5. energy conversion Week 12
negative, is actually an output. With the machine as a generator; the bar is driven at speed u
by the force fm to provide the mechanical input pm = fm ( +u), as a result which e now
exceeds u and reverse the current to provide the negative electrical input (i.e output (i.e
output) pe = u (-i) the sum of the inputs (pe +pm) must be rate of rise of internal energy
## storage plus the rate of energy dissipation.
A real electromagnetic machine has fairly obvious points of attachment (e.g the electrical
terminals and the shaft) by which it is connected to the electrical and mechanical sources to
form a link between them. But it is very to concentrate source to from link between them.
But it is very convenient attention on the conversion region enclosed by the chain- dotted
line in fig 2.3, for it contains only the essential quantities e and i,. U and fe. Various losses,
and the mechanical storage, are excluded so that attention can be directed on to the physical
process if useful energy conversion by electromagnetic means outside the conversion region
we can account for conduction and core losses associated with the electrical end and
represented rough by the resistance R in fig 2.3, and friction and similar losses on the
mechanical side. It is to be noted that the externally applied force fm is not necessarily equal
to –fe because there may be force-absorbing components of inertial and elasticity in the
## mechanical working parts of the machine itself, as well as internal friction.
The machine has new been reduced to an analyzable form. Its behaviors under specified
conditions involves the forces and movement of the mechanical parts, the voltages and
current at the electrical terminals and processes of energy conversion and storage and
dissipation going on inside. Evaluation is based on the well-established principles and laws
## summarized in the following table.
5. energy conversion Week 12
Part of system Quantities Principles
Kirchhoff laws
Mechanical
## 5.5.1 Block diagram for energy balance equation
The energy balance equation is given by equation 2.2 as electrical energy input mechanical
energy input
## The dissipation (energy lossess) arise from three main causes
(ii) Part of electrical energy is converted directly to heat in the resistance of current path.
(ii) Part of mechanical energy developed with the device is absorbed in friction ad
## windage and converted to heat.
(iii) Part of the energy absorbed by the coupling field is converted to heat in magnetic
core losses (for magnetic coupling ) or dielectric loss) for electric coupling).
if we associate the various losses with the corresponding energies, equation 2.2 be written as
## Resistance losess and windage losses plus associated losses
5. energy conversion Week 12
Equation 2.3 is obtained ( for a motor) with the mechanical energy transferred to the R.H.S
of the equality sign and neglecting the energy mechanical stored energy ( for a machine
without a flywheel and neglecting the mass of the shaft). If there is a flywheel, the stored
## w = angular velocity of rotating wheel
Equation 2.3 may be represented in the form of a block diagram as shown in fig 2.4
Fig 2.4 General representation of electromagnetic energy conversion. Fro a generator action, the
positions of the electrical system and that or the mechanical system will be interchanged.
5. energy conversion Week 13
## completely described by the energy balance equation, we need to be able to determine
qualitatively the energy of the magnetic field and the associated force.
## 5.6.1 Magnetic field
A magnetic field is a region of space in which certain physical effects occurs in particular
the development of mechanical force. A pictorial model of the field can be made by drawing
closed loops of magnetic flux, such that their direction and spacing at any point are a
measure of the flux density. The magnetic circuit in the present context is composed partly
of ferromagnetic material such as iron, and partly of an airgap. The iron serves to “guide” the
flux in a desired path; the airgap is necessary to make useful magnetic effects readily
accessible.
The lines in a flux plot have no real existence. In a given region a magnetic field may change
## 5.6.2 Magnetic circuit n/a
Engineers look upon magnetic flux (Weber) as produced by electric current. A current I
develops around any path that links it a magneto motive force (M.M.F) F = I (ampere). The
effect of a current can be multiplied. By coiling the electric circuit into N turns so that
around a path linking all N turns the m.m.f is N times as great, giving F =- ampere- turn.
The m.m.f is distributed along the path, to give along a path element of length dx the
magnetic field intensity h (ampere-turn/ metre). The summation of Hdx around a single loop
## closed with F i.e F = Hdx = m.m.d.
5. energy conversion Week 13
At any point, H gives rise to a flux density B = NH (tesla or Weber/m2) our Henry/meter]
Flux summation of the flux density over the area available to the flux path given the total
flux [ i.e Ø i.e. BA. (Weber).-2.6 where A is the are of flux path.
The „ law of the magnetic circuit relates the total flux Ø to the mmf f through the
expression.
I = V
## And = 1/s = total permeance [ weber per ampere-turn]
For a path- length x of materials of absolute permeability U, and having a uniform cross-
sectional area A over which the density B is everywhere the same, the mmf f require = N x x
= Hx…………..2.8
## For a succession of parts , x, y, z 2.11
F = fx + fy + f2 + and S = SX + SY + SZ + 2.12
If, however the parts are in parallel and share the flux
## F = fx =fy =fz and
For fields in ferromagnetic materials U is very much greater, and the relative permeability Nr
## =u =Uo 4 /107 1/80000
5. energy conversion Week 13
Which means that H = Ub = 800000B
## Ad the relative permeability Ur = U
Uo
Since, usually Ur is large, then it is convenient ( it simplies analysis) to assume that the
whole mmf is required for the excitation of the air gap i.e the whole of the field energy is
## 5.7 Magnetic field energy
With the assumption that the magnetic filed energy is concentrated within the air gap. It
## becomes easy to calculated the magnetic field energy.
A magnet attract on iron bar. If the iron bar is light enough and the magnet filed is enough,
the bar will be seen to move up to get attached to the magnet. The movement of the bar
signifies that work is done, since the iron bar has mass and covered some distance
(work done = force x distance). This means that the space that the file occupies (the field
region) can demonstrated or has on attribute of force. And hence, the filed region must
process some energy. If can be easily noticed that the force is strong when the air gap is short
## Fig 2.5 maxwell forces
Maxwell formulated the concept that the forces is transmitted across the gap between a pair
of magnetized surface as a result of two stresses. If at a point in the gap the flux density is B
and the corresponding field intensity is H =B/U,. then there is a tensile stress of magnitude
5. energy conversion Week 13
1.2 BH along the direction of a flux line and a compressive stress ½ BH along all directions
## at right angles to a flux line.
Fig 2.5 shows two iron bars forming part of magnetic circuit when, as at (a), the polar
surfaces are close together, the flux is mainly concentrated between the surfaces. The density
## B is large, and so therefore is H, and ½ BH represented a strong tensile force of attraction
between the faces. Not all the flux is useful; some, of the leakage flux, exists at the sides of
each bar. Flux crossing the boundary between air and a high permeable materials must enter
or leave the boundary between air and a high permeable materials must enter or leave the
boundary almost at right angles, so that the tensile stress due to faces. All the comprehensive
## stresses balance out by symmetry.
In case (b), the greater reluctance of the long air gap reduces the total flux, the useful flux
density of the pole faces is smaller while the leakage flux is much greater hence the forces of
attraction between the pole faces is much less than in case (a)
In most practical applications, the air gap is small enough to enable us assumes a uniform
flux density over the polar area. i.e in the air gap.
.
5. energy conversion Week 14
## 5.9 ENERGY DENSITY
The Maxwell stress concept is another way of saying that the energy to the value
½ BH is stored in a unity cube of the space occupied by = magnetic, thus ½ BH is the energy density
## Fig 2.6 magnetic energy.
Consider an air gap, initially unmagnetized. Apply a magnetic force to the gap, an increase of H
from zero causes the flux density B = μoH to increase proportionately, Fig 2.6(o). The energy (m 3
is [HdB, and for and values Bi and H1 the final energy density (shaded area) is clearly ½ B 1H1 . The
some summation applies to a filed set up by in a ferromagnetic matter, with similar result Fig. 2.6
(b0, if the permeability U is constant; but for the same and density B1 a much smaller magnetizing
## force Hii is need and much less energy is stored.
If the ferromagnetic materials is subjected to saturation, the stored energy is as shown in Fig 2.6(c0
and is calculated by piece-wise approximation to composite area of DOAD plus area of trapezium
AB,CD.
5. energy conversion Week 14
When the flux 4 associated with an electric increase in time at by amount d4, an emf, e = de/dt
appears in the circuit. The minus sign implies that the direction of the emf is such that a current
## produced by it in the circuit opposes the change d4.
Flux-linkage 4 (weber- turn] is the product of a magnetic flux and the number of turns through
which it passes in the same direction. Since the current is proportional the flux,
## then flux likage Ų = NQ
Since we are neglecting the coil resistance, then around the electric circuit loop formed by the
voltage source and the N turns of coil on the toroid, the KVL gives
## The instantaneous electric power input to the coil
P =vi = (dw/dt)i
The total energy required to establish from zero a flux Q1 and a linkage Q1, (corresponding to a
## Since the core of the toroid has constant permeability.
Which is represented by the shaded area in Fig, 2. 6 (d). this magnetically stored energy can be
assumed to be uniformly distributed through the active volume Al of the core. Then because
## [f =1/24I =1/2QF =1/2Q2S =1/2 F2S =1/2Q / 1/2F2 =1/2Li2]
5. energy conversion Week 14
Also, since Q BA and F =Hl and H =B/U
## Then wf =1/2 QF =1/2 BAHL =1/2AL
U
But al = volume
Wf = Vol. B2
2U
Any expression for the energy of the field wf in equation 2.32 and 2.23 may be employed
## Fig. 2.7 Energy change with position
Fig 2.7 (a) shows airgap region and existing coil of a magnetic circuit, the ferromagnetic
core of which has a high. Permeability, the plane parallel polar faces. Have an area A and are
spaced x apart. The n-turn coil carrying current I magnetic the system. The problem is to find
## the magnetic force of alteraction between the polar faces.
In the comparable system Fig 2.7 (b), with a rotatable part (rotor) port (stator), the problem is
## to find the tongue.
Insight into the inteplay of energy can be obtained from a study of finite mobvements, say
from an initial position (1) to afinal direction position (2). At (a0. this movement -∆x (i.e
5. energy conversion Week 14
against the positive direction of x) of the right-hand member’ are ( b) it is a rotation -∆Q of
the rotor. The static 4/I relations for the two positions are shown in Fig 2.7 © differ because
the gap reluctance for (2) is less than for (1). Clearly the filed energy will differ too. How it
changes depends on the conditions wholly in the gap, and the effect of coil resistance will
initially be ignored.
## (1) CONSTANT CURRENT
Let the current be held constant at is throughout, as shown at Fig 2.7 (d). for
position the linkage is 41 and the filed energy is ½ Fig 4. to reach position (2) a
linkage 42 with constant current, an electrical energy input + ∆we =(Ų2-Ų1 ) i0 must
be fig 2.7 (d). the current sources. This is represented by the hatched area at Fig
2.7(d0. Now, the increase in field energy is ∆WF =1/2 (Ų2-Ų1)io, which, comparing
the expressions or the hatched areas at (d), is only one-half of∆we. What has
## happened to the other half?
Writing the energy balance and excluding the loss and mechanical storage terms:
∆we + ∆wf
## As 41 the mechanical input is negative: it is in fact an output work
(force x displacement). A precisely similar consideration gives for the rotary case (b)
the output work (torgue x angular displacement). For constant current, therefore, the
source provides ∆we, of which one-half is taken as energy into the filed and the
## other half is converted into mechanical energy output.
5. energy conversion Week 14
## (2) CONSTANT FLUX
Let the flux be kept constant so that linkage is always . the condition implies that the
current fall from Li to i1 to compensate for the rise in permeance in Fig (e). there is
no electrical energy transfer between the source and system for with constant linkage
there is no induced e.m.f to be balance. Hence ∆we =o. but there is change of filed
energy ∆wf =1/2Ų0 (l2-l1) which is negative because l2 <l1. the energy balance is
## Hence ∆wm =fm (-∆x) =1/2 Ų0 (l2 –l1)
For constant flux, therefore, the mechanical work done comes from an equal
## (3) GENERAL CONDITION
In a practical device neither of condition (1) and (2) is likely to apply consistently.
The transition will follow some arbitrary contour, such as that in Fig 2.7 (f), with
changes in both 4 and i. the energy balance is then some combination of cases (1) and
(2). The change in field energy is the shaded area ∆wf, and this will correspond, as
## before in magnitude to the mechanical energy ∆wm even, if owing to saturation
effect, the Q/I relation is non- linear, they are ∆wf can still be found by graphical
∆x
## The mean torgue ∆wf, = mm 2.29
5. energy conversion Week 14
## (4) DIFFENTIAL FORM
IF ∆ AND ∆Q are reduced to the infinitesimal differentials dx and dq, the force and
torgue are obtained for a single position x or Q. Then
Force, fm = dwf 2.30
dx
torgue, mm = dwf 2.31
dQ
5. energy conversion Week 15
## Fig: 2.8 Reluctance motor
The reluctance motor shown in figure above depend on the tendency of the rotor to
Align itself magnetically with the stator. A flux plot for the machine shows that,
provided there is ad equate ove4rlop, all the active flux and all the field energy can be
assumed to occupy the overlap regions. The active gap volume changes with angle Q
between the two magnetic exes, and the torgue is d e f/dQ eqtn 2.31 using equation
2.22 a basis. An angular increase Dq others the active volume of each gap by - rlg
## me = dwe = B2Lrlg 2.24
Dq uo = 4π x10-7 (const.)
## The minus sign indicating that the force acts to reduce Q.
Example 1
With the rotor dimentions shown and a coil of 400 turns carrying 1.6A, calculated the
## torgue acting on the rotor.
5. energy conversion Week 15
Solution
Uo
## :. B =640 x UO 640 X 4π X 190-7 = 0.40 tesla
2lg 2 x 10-3 0.43
## :. me = -0.42 X 0.025 X0.03 X0.001 X107 = 0.0955N-M
-B2l/g4 π
Example 2
The 4-l characteristics of a magnetic circuit are frequently described with straight
segments as shown below. The act is considered linear up to pt. a and in saturation
## from a to 5 find the field energy
Example 3
A dynamic phonograph pickup consists of a 20-turn coil length of each coil =1cm)
## calculated the output voltage at 100-HZ and at 100Hz
Solution
5. energy conversion Week 15
A dynamic phonograph pickup for vertical recording the effective length of
2 2
= 0.0036v =3.6mv
## And r.m.s value of output voltage = 0.2 x 0.2 x 4 π x 10-3
2
= 0.00036v =0.36mv
5. energy conversion Week 15
Example4.
In a d.c machine, shown above, the armature is wound on a laminated iron cylinder
15cm long and 15cm in diameter. The N and S role faces are 15cm long (into the
paper) and 10cm along the circumference the average flux density in the air gap
under the pole faces is 1T. If there are 80 conductors in series between the brushes
and the machine turning at N =1500rpm, calculated the no-load terminal voltage
Solution
## E =NS ∆Ø wb =Ns Ø wb P poles n rev No 2 conductor in sec)
∆t s pole rev 60 sec
= Ns Øpn volts
## Where the flux per pole Ø = BA = 1 x0. 15 x 0.1 = 0.015 wb.
:. E = 80 x 0.015 x 2 x 1500
60
= 60 volts
Example 5.
5. energy conversion Week 15
A magnetic circuit is completed through a soft –iron rotor as shown in the figure
above. Assuming (1) all the reluctance of the magnetic circuit is in the air gaps of
length L
(ii) There is no fringing so the effective area of each gap is the area
Solution
## R = 2l (since Ur =1 for air) R = F =1L
UOA Q A
= 2L
Urwq
For an N-turn coil, the inductance is
L = NØ = NF N2I = N2 trwØ
I IR IR 2L
## Since torgue =1/2 I2 dL = Uo N2rw
dØ 2L
The torgue is independent of Ø under the assume conditions.
Example 6
## (a) Wiring diagram (b)Steady state model
A commutator machine, with the wiring diagram and steady-state model showed
above, is rated 5KW , 250V, 2000rmp. The armature resistance RA is 1. Drive from
the electrical and at 2000rmp, the no-load powder input to the armature is IA = 1.2A
at 250V with the field winding (RE =250) excited by IF =1A. Calculate the efficiency
of this machine.
5. energy conversion Week 15
Solution
In fig (a), input power IF 2RF = 12 X 250 =250W is required to provide the necessary
## In no-load steady operation, there is no output and no change is all loss
[The armature cooper loss at no load is negligible (1.22 x 1=1.44w) and most of the
input power at no- load goes to supply air, bearing brush friction, eddy cumenty and
hystersis losses] the losses are associated with flux changes in the rotting armature
## And rotational loss = IAV = 300w p =iv :.i = p1
v
At full-load of 5KW, IA =5000W = 20A
## Mech. Energy + field elect = increase energy
:input input output energy stored converted
Field to heat
i.e
less less less
## Hence efficiency = output = elect output
Input mech. output + elect input
## = 5000 = 0.84. or 84%
5700 + 250
5. energy conversion Week 15
Example 7
In the relay shown above, the contacts are held open by the spring excerting a force
of 0.1N . The gap length is 4mm when the contacts are open and 1mm when
closed. The coil of 5000 turns would on core 1cm2 in cross- section. Assuming | 16,690 | 69,810 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.640625 | 3 | CC-MAIN-2020-24 | latest | en | 0.315384 |
https://www.thefreelibrary.com/Cartwheeling+through+CamMotion-a018667830 | 1,552,976,943,000,000,000 | text/html | crawl-data/CC-MAIN-2019-13/segments/1552912201904.55/warc/CC-MAIN-20190319052517-20190319074517-00095.warc.gz | 910,892,124 | 13,347 | Cartwheeling through CamMotion.
To many students, mathematics has only tenuous connections to their everyday lives and personal concerns. Therefore, current educational reform emphasizes teachers adopting curriculum activities that connect mathematics to students' lives. But what kinds of activities might there be? And how can students' concerns be integrated into mathematics instruction?
The view project at the Technical Education Research Center (TERC) combines new video and computer tools to bring math and students together in previously impossible ways. With these tools, students explore and analyze their own experiences by making measurements on videos of real phenomena. Video allows them to slow down or speed up time; associated computer tools let them analyze events they have actually observed. By making measurements on single frames of video, students can explore the "fine structure" of actions that take place quickly, like bouncing balls or flying paper airplanes. They can examine patterns of motion through video analysis of their own bodies in such activities as sports and dance.
The innovation that makes this vision possible is called CamMotion. Using CamMotion to make measurements on the video, students construct meaningful connections between their own motions and conventional mathematical representations. We have coined a general term for such tools: video-based labs, or VBL.
A Data Question
The easiest way to see CamMotion's potential is to work through a simple example.
Two students, Kathy and Nadia, practice gymnastics. Kathy uses a camcorder to videotape Nadia doing cartwheels in the school auditorium, then digitizes the video into a machine-readable movie that CamMotion can read. Now they are ready to use CamMotion to explore how Nadia does a cartwheel.
To analyze Nadia's cartwheel, Kathy and Nadia start by tracking the positions of Nadia's left hand. While advancing through the frames of the movie, they click on Nadia's left hand in each frame to mark its position. Clicking causes CamMotion to store the position of Nadia's hand in (x, y) coordinates, along with the current time in the movie.
In addition to position data, CamMotion supports measurements of distances, angles, and areas, among others. Just as position data are used to track an object's motion over time, distance data track the distance between two objects over time, such as Nadia's two hands. Angle data can track the rotation of objects, such as a hamster's wheel, or examine the changing angle of parts of a moving object, such as Nadia's legs.
However, the process of mapping the real world to coordinates on the screen is not always straightforward. Like any robust measuring system, CamMotion has a set of tools that facilitate connecting the observed world to mathematical representations in a way that makes sense to the user. Two of these many tools allow the user to set the origin at any point on the movie and to change the scale of the coordinate system.
In all but a few cases, the size of an image on the screen will be significantly different from the size of the object in the world. CamMotion provides a scale tool that allows the user to specify the relationship between the two sizes. To set an appropriate scale, Kathy and Nadia indicate on the video a line that reflects a length they know in the world, then enter the real-world length as a scale factor. In examining the cartwheel, the girls use Nadia's arm, which they know is half a meter long, as their calibration length.
Viewing the Data
After Kathy and Nadia collect their samples, they can display their data as either a table or a graph. They choose to first use the table window to view their data in a spreadsheet, with each row representing measurements at a specific time. In looking at their data, Kathy and Nadia notice something strange: six rows with the very same data. They wonder if they might have made a mistake during data collection, or if a sequence of frames in the video really generated these data. What can this mean? Kathy and Nadia select these rows and request that the corresponding video frames be played in the replay window. They notice that the selected piece of video shows Nadia upside-down with both hands on the floor. Now they understand these numbers are not errors; Nadia's left hand did not move during this half second.
Kathy and Nadia are now eager to continue their exploration of Kathy's hypothesis: that at some point in her cartwheels Nadia has only one hand on the floor. They go through a similar process to collect data on Nadia's right hand, then build a graph combining the two datasets so they can compare the motion of her two hands.
The figure illustrates the graph that shows the motion of Nadia's right and left hands. As the girls examine it, Kathy says, "Look, Nadia, there's a small piece of the graph where you have only one hand on the floor!" As indicated by the arrow, a single data point shows where Nadia's left hand is on the floor and her right hand is off. But what part of the cartwheel corresponds to this part of the graph?
To find out, the girls select the graph segment that shows only one hand on the floor and use the replay button to see the corresponding video frames.
Having found the answer to their first question, the girls are off on another investigation. Observation, hypothesizing, and experimentation have led Kathy and Nadia to ponder other questions about the cartwheel. How fast are Nadia's hands and feet moving? Are her feet and hands always the same distance apart? Is there any part of her body that stays the same vertical distance from the floor during the entire cartwheel? With CamMotion, the fleeting seconds it takes Nadia to do a cartwheel can be stilled, and she and her friend can ask and answer questions they might have never thought of without such a tool.
Andee Rubin is a senior scientist and Scott Bresnahan is a programmer at Technical Education Research Centers in Cambridge, Mass. Ted Ducas teaches physics at Wellesley College in Wellesley, Mass.
COPYRIGHT 1996 Association for Computing Machinery, Inc.
No portion of this article can be reproduced without the express written permission from the copyright holder. | 1,259 | 6,246 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.609375 | 4 | CC-MAIN-2019-13 | latest | en | 0.939717 |
http://www.perlmonks.org/index.pl/jacques?node_id=300236 | 1,527,296,033,000,000,000 | text/html | crawl-data/CC-MAIN-2018-22/segments/1526794867254.84/warc/CC-MAIN-20180525235049-20180526015049-00099.warc.gz | 449,669,317 | 6,675 | Just another Perl shrine PerlMonks
### How to sort hash tables alpha-numeric
by juo (Curate)
on Oct 18, 2003 at 05:27 UTC Need Help??
juo has asked for the wisdom of the Perl Monks concerning the following question:
```\$keys{'C10'}->{'C10-1'}=1;
\$keys{'C10'}->{'C10-2'}=1;
\$keys{'C10'}->{'C10-20'}=1;
\$keys{'C10'}->{'C10-3'}=1;
\$keys{'C200'}->{'C200-1'}=1;
\$keys{'C200'}->{'C200-20'}=1;
\$keys{'C200'}->{'C200-3'}=1;
\$keys{'C200'}->{'C200-21'}=1;
\$keys{'C30'}->{'C30-1'}=1;
\$keys{'C30'}->{'C30-2'}=1;
\$keys{'C30'}->{'C30-30'}=1;
\$keys{'C30'}->{'C30-4'}=1;
# Result should be :
'C10' => HASH(0x1832a58)
'C10-1' => 1
'C10-2' => 1
'C10-3' => 1
'C10-20' => 1
'C30' => HASH(0x1832b30)
'C30-1' => 1
'C30-2' => 1
'C30-4' => 1
'C30-30' => 1
'C200' => HASH(0x1835318)
'C200-1' => 1
'C200-3' => 1
'C200-20' => 1
'C200-21' => 1
Replies are listed 'Best First'.
Re: How to sort hash tables alpha-numeric
by Aragorn (Curate) on Oct 18, 2003 at 17:48 UTC
Here's a solution using the so-called Schwartzian transform for sorting the keys (the leading "C" is stripped off, and the the key list is sorted by the number before the dash, and then by the number after the dash:
```#!/usr/bin/perl
use warnings;
use strict;
my %keys;
\$keys{'C10'}->{'C10-1'}=1;
\$keys{'C10'}->{'C10-2'}=1;
\$keys{'C10'}->{'C10-20'}=1;
\$keys{'C10'}->{'C10-3'}=1;
\$keys{'C200'}->{'C200-1'}=1;
\$keys{'C200'}->{'C200-20'}=1;
\$keys{'C200'}->{'C200-3'}=1;
\$keys{'C200'}->{'C200-21'}=1;
\$keys{'C30'}->{'C30-1'}=1;
\$keys{'C30'}->{'C30-2'}=1;
\$keys{'C30'}->{'C30-30'}=1;
\$keys{'C30'}->{'C30-4'}=1;
sub sorted {
return map { \$_->[0] }
sort {
\$a->[1] <=> \$b->[1] ||
\$a->[2] <=> \$b->[2]
} map { [ \$_, split("-", substr(\$_,1)) ] } @_;
}
foreach my \$key (sorted(keys %keys)) {
print "'\$key' => ", \$keys{\$key}, "\n";
foreach my \$subkey (sorted(keys %{\$keys{\$key}})) {
print " '\$subkey' => \$keys{\$key}->{\$subkey}\n";
}
}
Arjen
This works perfect although I don't understand yet 100% how the Schwartzian transform works. Their is one small problem that I have with the code is that it should look for all leading characters to be split because now it substr only one but it could be more. (CR30-1 for example) So I tried to modify the code but no success.
```sub sorted {
return map { \$_->[0] }
sort {
\$a->[1] <=> \$b->[1] ||
\$a->[2] <=> \$b->[2]
} map { [ \$_, split("-", s/^[A-Z]+//) ] } @_;
}
foreach my \$key (sorted(keys %keys)) {
print "'\$key' => ", \$keys{\$key}, "\n";
foreach my \$subkey (sorted(keys %{\$keys{\$key}})) {
print " '\$subkey' => \$keys{\$key}->{\$subkey}\n";
}
}
The Schwartzian Transform is explained here by the person after who this sorting technique is named.
A modified version of the sorted routine which also takes the leading letters into account:
```
sub sorted {
return map { \$_->[0] }
sort {
\$a->[1] cmp \$b->[1] ||
\$a->[2] <=> \$b->[2] ||
\$a->[3] <=> \$b->[3]
} map { [ \$_, (/([A-Z]+)(\d+)(?:-(\d+)){1,2}/) ] } @_;
}
The split function is replaced by a regex which returns a list of letters and the numbers.
Arjen
Create A New User
Node Status?
node history
Node Type: perlquestion [id://300236]
Approved by davido
help
Chatterbox?
and all is quiet...
How do I use this? | Other CB clients
Other Users?
Others pondering the Monastery: (2)
As of 2018-05-26 00:50 GMT
Sections?
Information?
Find Nodes?
Leftovers?
Voting Booth?
World peace can best be achieved by:
Results (192 votes). Check out past polls.
Notices? | 1,259 | 3,472 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.109375 | 3 | CC-MAIN-2018-22 | latest | en | 0.652011 |
http://crypto.stackexchange.com/questions/2292/rsa-finding-the-inverse-of-the-public-exponent | 1,469,434,438,000,000,000 | text/html | crawl-data/CC-MAIN-2016-30/segments/1469257824217.36/warc/CC-MAIN-20160723071024-00250-ip-10-185-27-174.ec2.internal.warc.gz | 53,199,317 | 19,028 | # RSA finding the inverse of the public exponent
I have a very basic doubt in RSA key generation and its usage.
In RSA key generation you choose two large prime numbers of a very large order. Then you multiply them.(eq $p \cdot q = N$) Now, $\phi(N)=(p-1)(q-1)$. Now you find a number $0 < e < \phi(N)$ such that $e$ and $\phi(N)$ are coprime. {$e,N$} becomes your public key. Now you compute $d$(private key) such that $ed \equiv 1 \bmod{\phi(N)}$.
Now suppose you encrypt something (say $m$) with your the public key: $c=m^e\bmod{N}$. To decrypt with the private key, you do $c^d\bmod{N}$.
Now my doubt is that you found out the inverse of $e$ modulo $\phi(N)$, but when you are decrypting you are doing it in modulo $N$. How is this possible?
-
## migrated from security.stackexchange.comApr 6 '12 at 13:48
This question came from our site for information security professionals.
I fixed the public key you had noted. It should be {$e,N$} not {$e,\phi(N)$} – mikeazo Apr 6 '12 at 14:23
The answer comes from Euler's Theorem. Note: math below is done modulo $N$ unless otherwise specified and draws heavily from group theory.
That theorem says that any element of a group (say $m$) raised to the order of the group, in this case $\phi(N)$ is congruent to $1$ (i.e., $m^{\phi(N)}\equiv 1\bmod{N}$). Furthermore, this holds for multiples of $\phi(N)$ (i.e., $c\cdot\phi(N)$ where c is an integer).
In the case of RSA, you find $e,d$ such that $ed\equiv 1\bmod{\phi(N)}$. Note then that $ed=c\cdot\phi(N)+1$, where $c$ is some integer.
Thus $c^{d}=m^{ed}=m^{c\cdot\phi(N) + 1}=m^{c\cdot\phi(N)}\cdot m^1$. From the Euler's Theorem, $m^{c\cdot\phi(N)}=1$, so that term goes away and you are left with the original message.
-
You can say that Euler's theorem forms the basis for PKI. – Ashwin Nov 21 '12 at 15:32
That's not altogether accurate, since there are several different signature algorithms used in PKI. – pg1989 Nov 11 '15 at 1:17
Euler's work formed the basis of most of modern group theory, though, so in that way it forms the basis for PKI. – pg1989 Nov 11 '15 at 1:18
I'm not sure that I understand your question, so I might give you an answer that is not accurate.
Anyways, this happens because you encrypt your message using N (N is one of the two parts of the public key, not $\phi(N)$), this way: $c = m^e mod N$, like you said. So, as you can see, it's N that you are using to encrypt your message, and so you need N to decrypt it.
If this is not the answer you were looking for, just ignore it :D
-
Another way to look at it is that you are working in the ring ZmodN, but the multiplicative group of units, U(N) has (p-1)(q-1) elements. You still do the math mod N, but e and d are inverses in U(N) x^(ed) = 1 mod N for any unit x in U(N).
- | 831 | 2,777 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.53125 | 4 | CC-MAIN-2016-30 | latest | en | 0.884155 |
https://present5.com/100-100-200-200-300-300-400-400-3/ | 1,556,129,077,000,000,000 | text/html | crawl-data/CC-MAIN-2019-18/segments/1555578655155.88/warc/CC-MAIN-20190424174425-20190424200425-00130.warc.gz | 532,219,739 | 12,424 | Скачать презентацию 100 100 200 200 300 300 400 400
• Количество слайдов: 69
\$100 \$100 \$200 \$200 \$300 \$300 \$400 \$400 \$500 \$500
Writing Expressions, Equations, & Inequalities
Evaluating Expressions
Formulas and Word Problems
Domain and Range
Rules for Functions
Writing Expressions, Equations, & Inequalities Evaluating Expressions Formulas & Word Problems Domain and Range Functions \$100 \$100 \$200 \$200 \$300 \$300 \$400 \$400 \$500 \$500
Writing Expressions, Equations, & Inequalities- \$100 c 2 – 1 when c = 4
Writing Expressions, Equations, & Inequalities- \$200 Five times the sum of 6 and x is no more than 35. Write the inequality. Then, test to see is x = 0 is a solution.
Writing Expressions, Equations, & Inequalities- \$300 Write 5 k as a product. Then, evaluate for k=1.
Writing Expressions, Equations, & Inequalities- \$400 Twice m plus three to the power of zero. Write the inequality. Then, evaluate for m=4.
Writing Expressions, Equations, & Inequalities- \$500 5 n + 7 n when n=4. 2
Evaluating Expressions- \$100 (4 + 2 6)
Evaluating Expressions- \$200 3(6) – 5 + 2 (2 – 2)
Evaluating Expressions- \$300 7[(18+7)÷ 5]
Evaluating Expressions- \$400 ab+(5 -b) if a = 2 and b = 3
Evaluating Expressions- \$500 The formula for determining the interior angle measures of a regular polygon with n sides is… Find the interior angle measures of a regular polygon with 10 sides.
Formulas and Word Problems- \$100 What is the simple interested earned on \$500 invested for 10 years earning an interest rate of 3%?
Formulas and Word Problems- \$200 Corey is putting up a fence around his yard. If his yard is 25 ft long and 15 feet wide, how much fencing should he purchase?
Formulas and Word Problems- \$300 Blake drove for 4. 5 hours at an average speed of 50 miles per hour. How far did he travel?
Formulas and Word Problems- \$400 Carrie wants to put all of her shoes on a shoe rack. She has 280 pairs of shoes. If one shoe rack holds 15 pairs and costs \$10, how much will it cost Carrie to put all of her shoes on a shoe rack?
Formulas and Word Problems- \$500 Lady Gaga is redoing her kitchen. If the dimensions of the room are 14 x 20 feet, how many 1 foot square tiles should she purchase?
Domain and Range- \$100 1) Identify the Domain and Range: Input 4 5 6 4 Output 3 4 5 6 2) Determine if this is a function.
Domain and Range- \$200 Identify the Domain and Range
Domain and Range- \$300 1. Identify the Domain and Range: Input Output 3 5 1 4 0 2. Determine if this is a function.
Domain and Range- \$400 1. Identify the Domain and Range: Input Output 0. 5 3 1 1 1. 5 0 2. Determine if this is a function.
Domain and Range- \$500 Make a table for the function. Then, identify the range. y=2 x+1 Domain {0, 1, 2, 3}
Rules for Functions- \$100 Write a rule for the function: 1 2 3 Input 0 Output 8 9 10 11
Rules for Functions - \$200 Write Input for the a rule Output function: 7 3 4 9 5 11
Rules for Functions - \$300 Write a rule for the function:
Rules for Functions - \$400 Graph the function Domain {2, 4, 6}
Rules for Functions- \$500 Write a rule for the function: { (3, 2), (6, 3), (9, 4), (12, 5)}
Writing Expressions, Equations, & Inequalities- \$100 15
Writing Expressions, Equations, & Inequalities- \$200 5(6+x)≤ 35 Yes, it is a solution.
Writing Expressions, Equations, & Inequalities- \$300 k*k*k 1
Writing Expressions, Equations, & Inequalities- \$400 0 2 m+3 9
Writing Expressions, Equations, & Inequalities- \$500 50. 4
Evaluating Expressions- \$100
Evaluating Expressions- \$200 15
Evaluating Expressions- \$300 35
Evaluating Expressions- \$400 8
Evaluating Expressions- \$500 144°
Formulas and Word Problems- \$100 i=prt \$150
Formulas and Word Problems- \$200 P = 2 l + 2 w 80 ft
Formulas and Word Problems- \$300 d=rt 225 miles
Formulas and Word Problems- \$400 \$190 Since you can’t have 18. 6666… shoe racks, you would need to round up to 19 shoe racks so that all the shoes are on a rack. 19 x 10 = 190
Formulas and Word Problems- \$500 A=lw 280 tiles
Domain and Range- \$100 Domain {4, 5, 6} Range {3, 4, 5, 6} Not a function!
Domain and Range- \$200 Domain {1, 2, 4, 6} Range {2, 3, 4, 7}
Domain and Range- \$300 Domain {3, 4, 5} Range {0, 1} Yes it is a function!
Domain and Range- \$400 Domain {0. 5, 1, 1. 5} Range {0, 1, 3} Not a function!
Domain and Range- \$500 Input 0 1 2 3 Output 1 3 5 7
Rules for Functions - \$100 y=x+8
Rules for Functions- \$200 y = 2 x + 1
Rules for Functions - \$300 y = 3 x - 1
Rules for Functions - \$400
Rules for Functions- \$500
Process Writing Question
Process Writing Question Is y = x² a function? Support your answer.
Process Writing Question Through creating a table, you can determine that no item in the domain is paired with more than one item in the range. By graphing this function, you will notice it passes the vertical line test. This function is known as the parent quadratic function.
END OF GAME Daily Doubles and usage notes follow. . .
JEOPARDY! Slide Show Notes • • The font for the question & answer slides is “Enchanted; ” a copy of this font in located in the “REAL Jeopardy Template” folder. (This font will need to be installed in the C: /WINDOWS/FONTS folder of the computer running the show. ) In order to keep all of the sounds and fonts together, copy the entire “REAL Jeopardy Template” folder. To change the categories: – – • 1. Go to “Edit” and “Replace…” 2. In the Find box, type CATEGORY 1 (all caps) 3. In the Replace box, type the category in all caps (for example, PRESIDENTS) 4. Click Replace All. . . To use the Daily Double: – 1. Choose which dollar values to set as Daily Double – 2. Link that dollar value to one of the DD slides – 3. Link the arrow on the DD slide to the correct question slide (so dollar/category match)
Running the JEOPARDY! Slide Show • • On the game board with the categories on top, click on the desired dollar value. (The first game board is used only to blink in the dollar values like the show. ) ICONS: – – ? Go to the answer screen. House Go back to the game board. Right Arrow (on Daily Doubles) Go to the question screen. Turned-up Arrow Reload question screen after incorrect guess | 1,823 | 6,208 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.765625 | 4 | CC-MAIN-2019-18 | longest | en | 0.846465 |
https://brainly.my/tugasan/80206 | 1,487,836,400,000,000,000 | text/html | crawl-data/CC-MAIN-2017-09/segments/1487501171162.4/warc/CC-MAIN-20170219104611-00138-ip-10-171-10-108.ec2.internal.warc.gz | 689,643,733 | 9,937 | # What is the formula to find diameter of a circle
2
dari tkk
## Jawapan
2015-08-07T21:51:28+08:00
Diameter of a circle = 2r
D=C/π
C refers to what?
radius tu lah.. in malay.. jejari...
2015-08-07T22:08:04+08:00
Radius circle tu darab dgn 2.. | 99 | 245 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.59375 | 3 | CC-MAIN-2017-09 | latest | en | 0.370971 |
https://de.slideshare.net/RakshaSharma6/types-of-quadrilaterals-62952450 | 1,576,078,626,000,000,000 | text/html | crawl-data/CC-MAIN-2019-51/segments/1575540531917.10/warc/CC-MAIN-20191211131640-20191211155640-00270.warc.gz | 332,938,649 | 38,435 | Diese Präsentation wurde erfolgreich gemeldet.
Wir verwenden Ihre LinkedIn Profilangaben und Informationen zu Ihren Aktivitäten, um Anzeigen zu personalisieren und Ihnen relevantere Inhalte anzuzeigen. Sie können Ihre Anzeigeneinstellungen jederzeit ändern.
Nächste SlideShare
×
85 Aufrufe
Veröffentlicht am
Guys in this ppt u get information on Types of Quadrilaterals.The animation and designs of my ppt i think is best for me and i suggest u guys first u see my ppt then u ultimately impressed by my ppt .Then, u know guys what to do just download my ppt,like my ppt etc.
Veröffentlicht in: Bildung
• Full Name
Comment goes here.
Are you sure you want to Yes No
• To learn more about the Fibroids Miracle system and to find out how YOU can start re-balancing your body today and start the path to lasting freedom from Uterine Fibroids, visit the Fibroids Miracle Website at.. https://tinyurl.com/rbqozdv
Sind Sie sicher, dass Sie … Ja Nein
Ihre Nachricht erscheint hier
1. 1. Raksha Sharma
2. 2. Square: Quadrilateral with four equal sides and four right angles (90 degrees) Indicates equal sides Box indicates 900 angle
3. 3. Types of Quadrilaterals Rectangle: Quadrilateral with two pairs of equal sides and four right angles (90 degrees) Indicates equal sides Box indicates 900 angle
4. 4. Types of Quadrilaterals Parallelogram: Quadrilateral with opposite sides that are parallel and of equal length and opposite angles are equal Indicates equal sides
5. 5. Types of Quadrilaterals Rhombus: Parallelogram with four equal sides and opposite angles equal Indicates equal sides
6. 6. Types of Quadrilaterals Trapezoid: Quadrilateral with one pair of parallel sides Parallel sides never meet.
7. 7. Types of Quadrilaterals Irregular shapes: Quadrilateral with no equal sides and no equal angles
8. 8. Name the Quadrilaterals 1 2 3 4 5 6 rectangle irregular rhombus parallelogram trapezoid square
9. 9. Interior Angles Interior angles: An interior angle (or internal angle) is an angle formed by two sides of a simple polygon that share an endpoint Interior angles of a quadrilateral always equal 360 degrees
10. 10. A diagonal of a parallelogram divides it into two congruent triangles. In a parallelogram ,opposite sides are equal. If each pair of opposite sides of quadrilateral is equal then it is a parallelogram. In a parallelogram opposite angles are equal. If in a quadrilateral each pair of opposite angles is equal then it is a parallelogram. The diagonals of a parallelogram bisect each other. If the diagonals of a quadrilateral bisect each other then it is a parallelogram.
11. 11. We have studied many properties of a parallelogram in this chapter and we have also verified that if in a quadrilateral any one of those properties is satisfied, then it becomes a parallelogram. There is yet another condition for a quadrilateral to be a parallelogram. It is stated as follows: A QUDRILATERAL IS A PARALLELOGRAM IF A PAIR OF OPPOSITE SIDES IS EQUAL AND PARALLEL.
12. 12. A Q C P B D S R Example: ABCD is a parallelogram in which P and Q are mid points of opposite sidesAB and CD. If AQ intersects DP at S and BQ intersects CP at R, show that: 1. APCQ is a parallelogram 2. DPBQ is a parallelogram 3. PSQR is a parallelogram SOLUTION: 1. In quadrilateral APCQ, AP is parallel to QC AP = ½ AB , CQ = ½ CD , AB = CD, AP = CQ Therefore APCQ is a parallelogram. (theorem 8.8) 2.Similarly quadrilateral DPBQ is a parallelogram because DQ is parallel to PB and DQ = PB 3. In quadrilateral PSQR SP is parallel to QR and SQ is parallel to PR. SO ,PSQR is a parallelogram.
13. 13. What is the sum of angles in triangle ADC? D C BA We know that angle DAC+ angle ACD+ angle D = 180 Similarly in triangleABC, angle CAB + angle ACB + angle B = 180 Adding 1 and 2 we get , angles DAC + ACD + D + CAB + ACB + B =180 + 180 = 360 Also, angles DAC + CAB = angle A and angle ACD + angle ACB = angle C So, angle A + angle D +angle B + angle C = 360 i.e.THE SUM OFTHE ANGLES OF A QUADRILATERAL IS 360. | 1,089 | 4,021 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.875 | 3 | CC-MAIN-2019-51 | latest | en | 0.449669 |
https://msms.ehe.osu.edu/tag/negative-slope/ | 1,563,538,088,000,000,000 | text/html | crawl-data/CC-MAIN-2019-30/segments/1563195526237.47/warc/CC-MAIN-20190719115720-20190719141720-00051.warc.gz | 480,602,099 | 11,428 | # Algebra: Teaching Concepts
When we teach algebra, most teachers find that getting across the manipulation of expressions is far easier than teaching the big ideas that underlie algebra. Lately I’ve run across sites that help middle school students grasp those concepts. I’d like to share them with you in this post and ask for your ideas in return.
First, two excellent ideas on helping students walk the bridge from arithmetic to algebra:
Building Bridges In this lesson, students move from arithmetical to algebraic thinking by exploring problems that are not limited to single-solution responses. These are common, not complex, problems that are developed through questioning to a higher level. Within real-world contexts, students organize values into tables and graphs, then note the patterns, and finally express them symbolically.
Difference of Squares uses a series of related arithmetic experiences to prompt students to generalize into more abstract ideas. In particular, students explore arithmetic statements leading to a result that is the factoring pattern for the difference of two squares. Very well done.
Equivalence is one of those underlying concepts that make algebraic reasoning possible. Everything Balances Out in the End offers a unit in which students use online pan balances to study key aspects of equivalence. The three lessons focus on balancing shapes to study equality, then balancing algebraic statements in order to explore simplifying expressions, order of operations, and determining if algebraic expressions are equal.
The next lesson, Equations of Attack, is a game but developed to uncover the algebra beneath the strategies. The two players each plot points on a coordinate grid to represent their ships and points along the y-axis to represent cannons. Slopes are chosen randomly (from a deck of prepared cards) to determine the line and its equation of attack. Students use their algebraic skills to sink their opponent’s ships and win the game. Afterwards, the algebraic approach to the game is investigated.
Walk the Plank is also a game. You need to place one end of a wooden board on a bathroom scale and the other end on a textbook. Students can “walk the plank” and record the weight measurement as their distance from the scale changes. This investigation leads to a real world occurrence of negative slope.
A final teaching idea develops students’ understanding of algebraic symbols: Extending to Symbols. As students begin to use symbolic representations, they use variables as unknowns. To help their concept of symbolic representation to grow, they need to explore questions such as: What is an identity? and When are two symbolic representations equal? This activity engages students in work with an online algebraic balance.
Each of these lessons comes from NCTM’s Illuminations site, a rich source for K-12 teaching. | 548 | 2,883 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.40625 | 4 | CC-MAIN-2019-30 | latest | en | 0.934983 |
https://revisionmaths.com/gcse-maths-revision/number/surds | 1,716,312,228,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971058504.35/warc/CC-MAIN-20240521153045-20240521183045-00120.warc.gz | 432,020,960 | 9,585 | # Surds
Surds are numbers left in 'square root form' (or 'cube root form' etc). They are therefore irrational numbers. The reason we leave them as surds is because in decimal form they would go on forever and so this is a very clumsy way of writing them.
The video below explains that surds are the roots of numbers that are not whole numbers. An example shows why surds are not written out as decimals because they are infinite decimals. Rules of working with surds are outlined and it is demonstrated how they can be simplified and rationalised.
Multiplication of Surds
√5 × √15 = √75 (= 15× 5)
= √25 × √3
= 5 √3
(1 + √3)(2 - √8) [The brackets are expanded as usual]
= 2 - √8 + 2√3 - √24
= 2 - 2√2 + 2√3 - 2√6
Adding and subtracting surds are simple- however we need the numbers being square rooted (or cube rooted etc) to be the same.
4√7 - 2√7 = 2√7.
5√2 + 8√2 = 13√2
Note: 5√2 + 3√3 cannot be manipulated because the surds are different (one is √2 and one is √3).
However, if the number in the square root sign isn't prime, we might be able to split it up in order to simplify an expression.
Example
Simplify √12 + √27
12 = 3 × 4. So √12 = √(3 × 4) = √3 × √4 = 2 × √3.
Similarly, √27 = 3√3.
Hence √12 + √27 = 2√3 + 3√3 = 5√3
Rationalising the Denominator (HIGHER TIER)
It is untidy to have a fraction which has a surd denominator. This can be 'tidied up' by multiplying the top and bottom of the fraction by a particular expression. This is known as rationalising the denominator, since surds are irrational numbers and so you are changing the denominator from an irrational to a rational number.
Example
Rationalise the denominator of:
a) 1
√2
b) 1 + 2
1 - √2
a) Multiply the top and bottom of the fraction by √2. The top will become √2 and the bottom will become 2 (√2 times √2 = 2).
b) In situations like this, look at the bottom of the fraction (the denominator) and change the sign (in this case change the minus into a plus). Now multiply the top and bottom of the fraction by this.
Therefore:
1 + 2 = (1 + 2)(1 + √2) = 1 + √2 + 2 + 2√2 = 3 + 3√2
1 - √2 (1 - √2)(1 + √2) 1 + √2 - √2 - 2 - 1
= -3(1 + √2)
You can find out more about surds by clicking here | 682 | 2,212 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.78125 | 5 | CC-MAIN-2024-22 | latest | en | 0.92263 |
https://shelleygrayteaching.com/quick-and-easy-place-value-activities-try-these-to-boost-number-sense/ | 1,708,943,477,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947474659.73/warc/CC-MAIN-20240226094435-20240226124435-00742.warc.gz | 533,669,515 | 33,018 | # Quick and Easy Place Value Activities (Try These to Boost Number Sense!)
Do you wish you had a way to easily spiral place value skills throughout the year – so your students continue to boost their understanding even after your place value unit is complete? Mystery Numbers place value activities are designed to do just that.
“My students look forward to mystery number each week. We are using it remotely as a way to start our Math thinking. I share the list of numbers with students and then we go through the clues together. I am proud to say my students have been beginning to predict what clue might come next based one the numbers left. It was been so very engaging for them. I look forward to continue using this even when we return in person.” – Karen
### Mystery Numbers: Quick and Easy Place Value Activities
To complete a mystery number activity, students read a clue and use that clue to eliminate one or more of the numbers. This continues until there is just one number left. The clues involve essential skills like place value, odd/even, rounding, greater than/less than, and more. This is a great way for students to use their knowledge in a meaningful way.
“This was a great way to get my students to really think about numbers. They loved making their guesses and then being able to change their guess as they received new information. I used it as an informal assessment of their understanding of place value.” -Ruth
### Mystery Numbers Make Differentiation Easy
Mystery Numbers are ideal for differentiation. Because you can choose from 2-digit, 3-digit, 4-digit, 5-digit, fractions, and decimals, there is something for every ability level…and students don’t need to know that their work is any different from someone else’s. This allows you to truly meet the needs of your students. For example, in your classroom you might have a few students working on 2-digit mystery numbers, while you work in a small group on some 4-digit mystery numbers. Students that are ready for something more challenging may even be working on fraction mystery number activities!
“LOVE these! They are really wonderful for boosting number sense, having students apply their thinking and making students read the questions/clues carefully!!” -Hayley
Because Mystery Numbers are available in both print and digital format, they can be used in the classroom or from home. If you choose to use the PDF versions in your classroom, you may also choose to put them inside plastic sheet protectors to save on paper.
Mystery Numbers are fantastic for many uses in the classroom. They’re a quick and easy way to reinforce place value skills all through the year. Here are how some teachers use them:
• as a 5-minute time filler or math warm-up
• to get kids excited about math at the beginning of math class
• as a pre or post assessment of place value skills
• as an early finisher activity
• to inspire students to try writing their own mystery number activities (fantastic for critical thinking!)
“I love these especially for getting my students’ minds ready for math. They’re so engaged trying to figure out the mystery number not realizing that they’re using (and learning) key vocabulary terms and concepts.” -Patricia
If you’d like to try Mystery Number place value activities in your classroom, here are the links to get started:
2-Digit Mystery Numbers
3-Digit Mystery Numbers
4-Digit Mystery Numbers
5-Digit Mystery Numbers
Decimal Mystery Numbers
Fraction Mystery Numbers
Or see the entire Mystery Bundle (and make it easy to differentiate to all your students) HERE.
### The Best Way to Teach Multiplication Facts: 12 Steps to True Understanding
Teaching multiplication is no easy task! Encouraging students to memorize the facts only allows a small percentage of them to be successful. Even then, those
### How to Create a Fun Choice Board for your Fast Finishers
What do your students do when they finish their work? Do you have to answer the question, “I’m done! What can I do now?” over and over
### Salute: A Great Math Fact Card Game for Speed and Automaticity
I love integrating games into all subject areas, but especially math. The key is to find games that are rigorous, include tons of opportunity for
This site uses Akismet to reduce spam. Learn how your comment data is processed. | 892 | 4,327 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.546875 | 4 | CC-MAIN-2024-10 | latest | en | 0.963152 |
https://stackoverflow.com/questions/2446494/skewing-an-image-using-perspective-transforms | 1,582,514,493,000,000,000 | text/html | crawl-data/CC-MAIN-2020-10/segments/1581875145869.83/warc/CC-MAIN-20200224010150-20200224040150-00086.warc.gz | 529,091,574 | 32,239 | # Skewing an image using Perspective Transforms
I'm trying to perform a skew on an image, like one shown here
(source: microsoft.com)
.
I have an array of pixels representing my image and am unsure of what to do with them.
• For the effect of your image, you don't need perspective transform. An affine transform is enough. – kennytm Mar 15 '10 at 14:08
A much better way to do this is by inverse mapping.
Essentially, you want to "warp" the image, right? Which means every pixel in the source image goes to a predefined point - the predefinition is a transformation matrix which tells you how to rotate, scale, translate, shear, etc. the image which is essentially taking some coordinate `(x,y)` on your image and saying that, "Ok, the new position for this pixel is `(f(x),g(y))`.
That's essentially what "warping" does.
Now, think about scaling an image ... say, to ten times the size. So that means, the pixel at `(1,1)` becomes the pixel at `(10,10)` - and then the next pixel, `(1,2)` becomes the pixel `(10,20)` in the new image. But if you keep doing this, you will have no values for a pixel, `(13,13)` because, `(1.3,1.3)` is not defined in your original image and you will have a bunch of holes in your new image - you'll have to interpolate for that value using the four pixels around it in the new image, i.e. `(10,10) , (10,20), (20,10), (200,2)` - this is called bilinear interpolation.
But here's another problem, suppose your transformation wasn't simple scaling and was affine (like the sample image you've posted)- then `(1,1)` would become something like `(2.34,4.21)` and then you'd have to round them in the output image to `(2,4)` and then you'd have to do bilinear interpolation on the new image to fill in the holes or more complicated interpolation - messy right?
Now, there's no way to get out of interpolation, but we can get away with doing bilinear interpolation, just once. How? Simple, inverse mapping.
Instead of looking at it as the source image going to the new image, think of where the data for the new image will come from in the source image! So, `(1,1)` in the new image will come from some reverse mapping in the source image, say, `(3.4, 2.1)` and then do bilinear interpolation on the source image to figure out the corresponding value!
## Transformation matrix
Ok, so how do you define a transformation matrix for an affine transformation? This website tells you how to do it by compositing different transformation matrices for rotation, shearing, etc.
### Compositing:
The final matrix can be achieved by compositing each matrix in the order and you invert it to get the the inverse mapping - use this compute the positions of the pixels in the source image and interpolate.
• Wow, it's so simple when you explain it this way. I was thinking of it this way, but everywhere i've looked until now, jumps into the matrix math too soon. – bobbdelsol Jun 27 '14 at 16:40
If you don't feel like re-inventing the wheel, check out the OpenCV library. It implements many useful image processing functions including perspective transformations. Check out the cvWarpPerspective which I've used to accomplish this task quite easily.
As commented by KennyTM you just need an affine transform that is a linear mapping obtained by multiplying every pixel by a matrix M and adding the result to a translation vector V. It's simple math
``````end_pixel_position = M*start_pixel_position + V
``````
where M is a composition of simple transformations like rotations or scalings and V is a vector that translates every point of your images by adding fixed coefficients to every pixel.
For example if you want to rotate the image you can have a rotation matrix defined as:
`````` | cos(a) -sin(a) |
M = | |
| sin(a) cos(a) |
``````
where `a` is the angle you want to rotate your image by.
While scaling uses a matrix of the form:
`````` | s1 0 |
M = | |
| 0 s2 |
``````
where `s1` and `s2` are scaling factors on both axis.
For translation you just have the vector V:
`````` | t1 |
V = | |
| t2 |
``````
that adds `t1` and `t2` to pixel coordinates.
You then combine the matrixes in one single transformation, for example if you have either scaling, rotation and translation you'll end up having something like:
``````| x2 | | x1 |
| | = M1 * M2 * | | + T
| y2 | | y1 |
``````
where:
• `x1` and `y1` are pixel coordinates before applying the transform,
• `x2` and `y2` are pixels after the transform,
• `M1` and `M2` are matrixes used for scaling and rotation (REMEMBER: the composition of matrixes is not commutative! Usually `M1 * M2 * Vect != M2 * M1 * Vect`),
• `T` is a translation vector use to translate every pixel. | 1,188 | 4,750 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.609375 | 4 | CC-MAIN-2020-10 | latest | en | 0.94734 |
https://brilliant.org/discussions/thread/need-some-helps/ | 1,627,919,203,000,000,000 | text/html | crawl-data/CC-MAIN-2021-31/segments/1627046154321.31/warc/CC-MAIN-20210802141221-20210802171221-00638.warc.gz | 161,282,066 | 16,456 | # Need some helps!
Find the value of $x$:
$x^2$ + ($\frac {x} {x-1}$)$^2$ = $\frac {5} {4}$
Note by Mục Xiên
6 years, 6 months ago
This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.
When posting on Brilliant:
• Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
• Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
• Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2
paragraph 1
paragraph 2
[example link](https://brilliant.org)example link
> This is a quote
This is a quote
# I indented these lines
# 4 spaces, and now they show
# up as a code block.
print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.
print "hello world"
MathAppears as
Remember to wrap math in $$ ... $$ or $ ... $ to ensure proper formatting.
2 \times 3 $2 \times 3$
2^{34} $2^{34}$
a_{i-1} $a_{i-1}$
\frac{2}{3} $\frac{2}{3}$
\sqrt{2} $\sqrt{2}$
\sum_{i=1}^3 $\sum_{i=1}^3$
\sin \theta $\sin \theta$
\boxed{123} $\boxed{123}$
Sort by:
I expanded it, and by hit and trial method, -1 was the solution. Then I divided the expanded polynomial by (x+1). The resultant cubic can be easily factorised.
- 6 years, 6 months ago
$x = y + 1$
$( y + 1)^2 + (\dfrac{y + 1}{y})^2 = \dfrac{5}{4}$
$y^2 + 2y + 1 + 1 + \dfrac{1}{y^2} + \dfrac{2}{y} = \dfrac{5}{4}$
$y^2 + \dfrac{1}{y^2} + 2y + \dfrac{2}{y} + 2 = \dfrac{5}{4}$
$a = y + \dfrac{1}{y}$
$a^2 - 2 + 2a + 2 = \dfrac{5}{4}$
$(a + 1)^2 = (\pm \dfrac{3}{2})^2$
$a = - \dfrac{5}{2} , \dfrac{1}{2}$
$y + \dfrac{1}{y} = - \dfrac{5}{2} , y + \dfrac{1}{y} = \dfrac{1}{2}$
$y = \dfrac{ -\dfrac{5}{2} \pm \sqrt{\dfrac{9}{4}}}{2} , y = \dfrac{ \dfrac{1}{2} \pm i\sqrt{\dfrac{15}{4}}}{2}$
$x - 1 = \dfrac{ -\dfrac{5}{2} \pm \sqrt{\dfrac{9}{4}}}{2} , x - 1 = \dfrac{ \dfrac{1}{2} \pm i\sqrt{\dfrac{15}{4}}}{2}$
$(x - 1= \dfrac{-1}{2} , -4) ~or~ x - 1 = \dfrac{ \dfrac{1}{2} \pm i\sqrt{\dfrac{15}{4}}}{2}$
$x = \dfrac{1}{2} , -3 , \dfrac{3 \pm i\sqrt{15}}{4}$
- 6 years, 6 months ago
x= -1 or 1/2
- 6 years, 6 months ago
Can I know how to solve this, please?
- 6 years, 6 months ago
What have you tried?
Do you know how to clear denominators and factorize?
Staff - 6 years, 6 months ago
I've already cleared denominators and got
$4x^2$ - $8x^3$ + $3x^2$ + $10x$ - $5$ = $0$
What to do next?
- 6 years, 6 months ago
well, we want to start to factorize the polynomial. You can use the rational root theorem
to guess at possible roots, and after which use the remainder factor theorem to help factorize. Have you seen these theorems before?
Staff - 6 years, 6 months ago
Well, I think I haven't seen these theorems before. Because I'm a middle school students. BTW, I'll ask my teacher for this problem's explaination, thanks for your helps!
- 6 years, 6 months ago | 1,284 | 3,576 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 32, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.5625 | 4 | CC-MAIN-2021-31 | latest | en | 0.836258 |
https://jeopardylabs.com/print/ch-6-expressions-8 | 1,653,460,954,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662580803.75/warc/CC-MAIN-20220525054507-20220525084507-00589.warc.gz | 372,788,293 | 3,978 | Exponents
Numerical Expressions
Algebraic Expressions
Writing Algebraic Expressions
Properties of Addition and Multiplication
Evaluate Expressions
100
Write this exponent as a product of the same factor. 97
9 x 9 x 9 x 9 x 9 x 9 x 9
100
7 – 6 + 5
6
100
2a + 8
a=3
14
100
one more ball than is on the playground
b + 1
100
2 • (3 • 7) and (2 • 3) • 7
associative property
100
7(y + 2)
7y + 14
200
Write this exponent as a product of the same factor. 53
5 x 5 x 5
200
28 + (89 – 67)
50
200
7a • 9b
a= 3
b= 4
57
200
twelve fewer questions than were on the first test
t - 12
200
6 + 3 and 3 + 6
communitive property
200
(b – 5)15
15b - 75
300
What is 6 x 6 x 6 x 6 x 6 x 6 x 6 x 6 x 6 x 6 written as an exponent?
610
300
16 / 2 + 8 × 3
32
300
a2 • b2
a=3
b=4
144
300
three times as many drinks on the tray
3t
300
7 + 0 and 7
Identity property of addition
300
3 + (x + 6)
x + 9
400
What is 2 x 2 x 2 x 2 written as an exponent?
24
400
(2 + 6) / 2 + 4 × 3
16
400
x + y + z
x=7
y= 1/2
z= 8
15 1/2
400
five dollars less than Yumi's pay
y-5
400
7 • 1= 7
Identity property of Multiplication
400
8x + 17y + 9x
17x + 17y
500
Solve 46.
4096
500
100 / 52 × 43
256
500
8y + (2x + 1)
x=7
y=1/2
19
500
one third of Emily's age
e/3 or 1/3e
500
6 * 0 = 0
zero property of multiplication
500
4(15x)
60x
Click to zoom | 590 | 1,395 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.140625 | 3 | CC-MAIN-2022-21 | latest | en | 0.753582 |
https://discourse.mc-stan.org/t/normal-sufficient-signature/311 | 1,713,241,545,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296817043.36/warc/CC-MAIN-20240416031446-20240416061446-00759.warc.gz | 187,389,139 | 6,915 | # Normal_sufficient signature
Since normal_sufficient has already been merged to stan-dev, I think now is a good time to talk about this.
The thing is that normal_sufficient has the following signature:
``````normal_sufficient_lpdf(const T_y& y_bar, const T_s& s_squared,
const T_n& n_obs, const T_loc& mu,
const T_scale& sigma)
``````
So, the straightforward way is to expose it as:
``````y_bar ~ normal_sufficient(s_squared, n_obs, mu, sigma);
normal_sufficient_lpdf(y_bar | s_squared, n_obs, mu, sigma);
``````
But the problem with that is that s_squared and n_obs are also data, so it would be better to have it as something like:
``````(y_bar, s_squared, n_obs) ~ normal_sufficient(mu, sigma);
normal_sufficient_lpdf(y_bar, s_squared, n_obs | mu, sigma);
``````
Has this problem happened before with another distribution? How feasible is this in terms of parser and stuff?
It’s not so much about data vs parameters, but rather on what are you conditioning. The “straightforward” way that you note is the correct statistical description – `y_bar` follows a Gaussian distribution conditioned on `s_squared`, `n_obs`, `mu`, and `sigma`.
But isn’t more accurate to say that
(y_bar, s_squared, n_obs) follows a Gaussian distribution conditioned on mu, and sigma_
since the whole (the sufficient statistic) vector (y_bar, s_squared, n_obs) is a function of data (y_1, y_2, …, y_n)?
Yes, it’s reasonable for `s_squared` to be on the left, but `n_obs` is definitely not data as you know how many elements there are ahead of time! The challenge with putting more than one variable on the left of the bar is that we don’t have any convention for something like `(y_bar, s_squared) ~ sufficient_normal(mu, sigma, N);`.
We could write this:
``````[y_bar, s_squared]' ~ sufficient_normal(mu, sigma, N);
``````
if we assume the signature is
``````sufficient_normal_lpdf(vector, real, real, int);
``````
I think we may need to rename this, too. We’ve gone with distribution first and parameterization later. So shouldn’t this be `normal_sufficient_lpdf` rather than `sufficient_normal_lpdf`? Or is it more like `lognormal_lpdf`?
@betanalpha Yes, you are right, `n_obs` is not part of statistic, just `(y_bar, s_squared)`.
@Bob_Carpenter This would be a possible solution, although it makes it a little more complex on the side the user, specially for when `y_bar` and `s_squared` already are vector (probably very unlikely to happen with `sufficient_normal`), but that’s why we have `append_col` anyway. But then, would we document the distribution as multivariate?
Also note that the current name already is `normal_sufficient_lpdf`.
It’d have to be multivariate if that were the case. The real question is what normalizes to a proper density? That’ll determine when users need to apply jacobians and should also detemrine how we decide what goes to the left of the vertical bar.
Yes, since `[Y_bar, S_squared]` is a statistic, therefore a function of data `[Y_1, Y_2, ..., Y_n]`, then they must integrate to 1 given the true parameters `mu` and `sigma` (obviously provided we adjust the jacobian of the lpdf just like any change of variable of we do).
But then, I think it’s not worth it to vectorize `[y_bar, s_squared]` like was done for `multi_normal` (what I mean is, the function should accept only a single vector `[y_bar, s_squared]`, not a std::vector of Eigen vector like `multi_normal`), since if that’s the case the user can (and should) add more samples using some straigtfoward algebra like `y_bar_new = (y_bar_1*n1 + y_bar2*n2)/(n1+n2)`. | 912 | 3,567 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.953125 | 3 | CC-MAIN-2024-18 | latest | en | 0.872248 |
http://www.math.yorku.ca/Who/Faculty/Monette/S-news/0139.html | 1,540,358,211,000,000,000 | text/html | crawl-data/CC-MAIN-2018-43/segments/1539583519859.77/warc/CC-MAIN-20181024042701-20181024064201-00298.warc.gz | 504,708,539 | 2,569 | # Re: logit transformation when predictor's a continuous variable
Prof Brian Ripley (ripley@stats.ox.ac.uk)
Fri, 23 Jan 1998 06:16:56 +0000 (GMT)
Frank E Harrell Jr wrote:
>
> Jan,
>
> In doing simulations to study bootstrap error estimates, you should not
> have to deal with any p=0 or p=1, as you use maximum likelihood to
> estimate the regression coefficients and don't actually use the logit
> transformation in the fitting process.
Sorry Frank, but you _may_ have to deal with p = 0 or 1. There's a
phenomenon know as (partial) separation in which the MLE gives
fitted probabilities for some cases of 0 and 1 (and hence some
infinite coefficients). Consider data like:
y y y y
x x x x x
and if you bootstrap you increase the chance of this happening (for
some ratio around 3 of n to p, the number of predictors, the
increase is large by a famous formula of Cover.)
I have always maintained that one should handle such cases separately,
as the standard glm IWLS algorithm `converges' rather slowly. More
details and some follow-up references are in Chapter 3 (esp p.113)
of my PRNN book.
On the original question, glm() does use care.exp() in its calculations,
and essentially takes log(0) as about -30.
Brian
> -----Original Message-----
> From: Jan Muska <jmuska@almaak.usc.edu>
> To: S-news@utstat.toronto.edu <S-news@utstat.toronto.edu>
> Date: Thursday, January 22, 1998 2:29 AM
> Subject: logit transformation when predictor's a continuous variable
>
>
> >I want to do a simmulation study on Efron's prediction error estimators
> >(632 and 632+, and some other ones). One of the decision rules I want to
> >test this on is logistic regression (logit). My problem is I cannot find
> >FORTRAN code to do the logit transformation when the predictor is a
> >continuous variable. I can't even find any reference-just do not know
> >where to look. Does anybody know how to do this transformation
> >log(p/(1-p)) when p=1 or 0?
> >
> >I found a on internet an approximation such as if p=1, then p=1-1/2*n.
> >But this does not seem to provide the same answer as the GLM procedure in
> >S-Plus using the binary link.
> >
> >If you can send me a reference where to look or how to do this
> >transformation, I'll be greatfull. For this is the only think that is
> >keeping me from running the simulation and getting done with my
> >disertation.
> >
> >Thanks, Jan Muska
> >
> >
>
>
```--
Brian D. Ripley, ripley@stats.ox.ac.uk
Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/
University of Oxford, Tel: +44 1865 272861 (self)
1 South Parks Road, +44 1865 272860 (secr)
Oxford OX1 3TG, UK Fax: +44 1865 272595
``` | 752 | 2,711 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.6875 | 3 | CC-MAIN-2018-43 | latest | en | 0.878978 |
conesandcolor.net | 1,702,337,956,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679518883.99/warc/CC-MAIN-20231211210408-20231212000408-00390.warc.gz | 11,621,073 | 4,045 | Color Vision: A New Understanding
John A. Medeiros
Hue Discrimination and the Similarity of Violet and Purple
Before closing the current discussion, it is perhaps worthwhile exploring the power and utility of the CSM model with a specific example or two. Perhaps one of the most important things a model of human color vision should be able to do is to explain the basic hue discrimination function. Now in order to do a complete job of this in the context of the CSM model, we would need a lot of detail about quite a few things, including:
• The exact dimensions and refractive indices of the cones and their surround,
• The details of the spectral absorption curves, optical densities, and distribution of the photopigment or photopigments in a cone,
• Details of how the temporal conversion code is executed within a cone and the how the subsequent neural circuitry encodes and uses the information,
• Details of how the cones in adjacent regions cooperate to enhance or inhibit each other's signals, and
• Details of how the overall "white" that is illuminating a region is interpreted by the cones and used in neural processing to help set the color constancy of human color vision.
This list of necessary information is probably not even complete. But even so, absent these details, we could ask the question: is there anything useful we can do to see if the CSM model could plausibly explain the hue discrimination function?
In fact , there is. Assuming nothing about any photopigments, indeed using a very simplistic model where all wavelengths are equally likely to be absorbed in a cone and using only the waveguide dispersive property of mode cutoff, we get a very plausible hue discrimination function. Using a very simple model with the cone waveguide parameter given by V= d/λ and a largest (entrance) cone diameter of 1 µm and smallest (distal) diameter of 0.6 µm, I calculated the amount of light present along the cone for pairs of input monochromatic light with wavelengths separated by 10 nm. I did this for a number of wavelength pairs in the range from 680 to 440 nm. For each pair I integrated the difference in the distribution along the cone length to get a single number that would be proportional to how different the two distributions would be. This I took as a simple measure of how well colors at a wavelength intermediate between the pairs could be discriminated (a larger value means they are more easily discriminated).
To display this in a fashion that can be compared to the usual hue discrimination curves, I took a difference of this integrated number for each wavelength pair from a constant and then (absent any direct information about how the cone signals are scaled) uniformly scaled the result (i.e., multiplied by a constant). The chart below shows the result compared with the one degree hue discrimination data of Bedford and Wyszeki (1958). As can be seen, this very simple model - with no assumptions about the cone photopigments (indeed, a very simple assumption of uniform absorption) does rather well in giving the overall hue discrimination function.
As I stated, the basis of this discrimination curve is purely due to mode cutoff in a tapered fiber for different wavelengths (no photopigment effect incorporated into the analysis). A good idea of what is happening here and how the mode cutoff curves contribute can be garnered from a perusal of the derivative of the cutoff curves. We plot below, the derivative, d(eff)/dV, of the cutoff curves shown previously for the HE11 and HE21 curves. A couple of features of this plot are worth pointing out. First, the derivative of the HE11 cutoff displays a maximum value corresponding to the inflection point in the mode cutoff curve and it represents the position of best color dispersion. If one is building a cone spectrometer based on this mode cutoff effect, it would make sense to center your operating range about this point. This maximum dispersion occurs for a waveguide parameter value of V=1.08 at which point the waveguide mode efficiency is approximately 0.24 so that about a quarter of the incident light is still within the cone interior.
Now I would suggest that there is every reason to believe that the retinal cones do exactly this and use their physical parameters (diameter and refractive index) to position the middle of its operating range at precisely this point, namely the yellow wavelength of approximately 580 nm. This would have the consequence that a specific wavelength, namely unique yellow, is tied to a physical feature of the cones so that its location should remain relatively fixed and stable. It would also correspond to the position of best color discrimination and minimal spectral purity as yellow indeed does so correspond (discussion of spectral purity is beyond the scope of the current document and the saturation function is derived and discussed extensively in the book, Cone Shape and Color Vision where it is compared to the standard data). Note also that centering the cone operating range about this maximum derivative point also suggests some features to look for when cone spectrometer operation is mistuned - a defect that I suggest occurs in some forms of color deficit vision (see below).
Another notable feature of the mode derivative curves is the very large values of the derivative of the HE21 curve, reflecting its abrupt cutoff. Note that this cutoff terminates abruptly at the waveguide parameter value of V=2.405. Values this large will occur for the shortest wavelengths propagating in the largest (entrance) portion of the cone. What will happen in this case is that short wavelength violet light will then propagate (at least in the wide part of the cone) in two modes, both the HE11 and the HE21. The HE21 portion will cutoff very rapidly and behave, in fact, like long wavelength red light. That is, violet will propagate in the cone like a mixture of red and blue light (the HE11portion of the violet will continue down the cone and attenuate like blue light) . A mixture of red and blue light is, of course, the color purple and this effect thus explains the long puzzling similarity of violet and purple. The separation process as it will occur in the two separate cases of either purple or violet incident on a given single cone is schematically illustrated in the cartoon figure below.
The rapid cutoff of violet light in the HE21 mode accounts for the secondary minimum in the color discrimination curve plotted above. That secondary minimum is not more abrupt in the curve simply because a smooth line is drawn between only a few values of the wavelength pairs that I computed for the plot.
Next: Color Deficit Vision
Back to the Beginning
Bac | 1,349 | 6,733 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.609375 | 3 | CC-MAIN-2023-50 | latest | en | 0.915073 |
https://www.jiskha.com/questions/1347971/1-use-a-formula-to-find-the-surface-area-of-the-square | 1,618,257,632,000,000,000 | text/html | crawl-data/CC-MAIN-2021-17/segments/1618038069133.25/warc/CC-MAIN-20210412175257-20210412205257-00490.warc.gz | 899,607,362 | 15,010 | # MATH
_________________________________
1. Use a formula to find the surface area of the square pyramid. (H.6ft.)(W.3ft.)(L.3ft.)
A. 45 ft
B. 81 ft***
C. 36 ft
D. 72 ft
_________________________________
2. Find the lateral area of the pyramid to the nearest whole unit. (H.22)(W.8)(L.8)
A. 176 m
B. 352 m
C. 704 m
D. 416 m***
_________________________________
3. Find the surface area of the cone to the nearest whole unit. (H.7in)(D.8in)
A. 226 in
B. 88 in
C. 377 in
D. 138 in***
_________________________________
4. Find the lateral area of the cone. Use 3.14 for pi and round to the nearest whole unit. (R.15cm)(H. 7 in)
A. 1,319 cm
B. 2,639 cm***
C. 707 cm
D. 2,026 cm
_________________________________
Thank You
1. 👍
2. 👎
3. 👁
1. If I understand the definitions correctly,
"surface area" would be the total of all the areas of an object, while "lateral" surface area would exclude the base
so the surface area of a square pyramid
= area of the square base + 4(area of the triangle)
That's my "formua".
In both #1 and #2 you then give dimensions H, W, and L without defining them. If the base is square, how come we have different (W)idths and (L)engths
in #3 Diameter = 8, thus radius = 4
height = 7
Thus slant height of cone = √(4^2 + 7^2) = √65
surface area = πr(r+√(h^2+r^2)
= 4π(4 + √65) = appr 151.58
or surface area = πr^2 + πrs, where s is the slant height
= π(16) + π(4√65) = 151.58
I got the same answer using 2 established methods, none of the answers given match that.
1. 👍
2. 👎
2. Ok thank you for your help but I copied them exactly, all the dementions I put their are all the correct ones. So what do I do now?
1. 👍
2. 👎
3. 1. A
2. B
3. D
4. D
(Just took the test)
1. 👍
2. 👎
4. #4 is A not d
1.A
2.B
3.D
4.A
100% correct.
1. 👍
2. 👎
5. jman I right arrie is not
1. 👍
2. 👎
6. jman is correct
1. 👍
2. 👎
7. Thanks jman
1. 👍
2. 👎
8. Yes Jman is correct
1. 👍
2. 👎
9. A
B
D
A
1. 👍
2. 👎
10. thanks you Jman, and Checked fors clearins it alls ups peeps. A B D A is gud. feels good to know ya aren't't lying to meh.
1. 👍
2. 👎
11. yep
a
b
d
a
if you dont believe me dont use them
1. 👍
2. 👎
12. Connexus Algebra Lesson 5: Surface Area Of Pyramids And Cones Answers:
1.A
2.B
3.D
4.A
4/4 (100%) :)
1. 👍
2. 👎
1. 👍
2. 👎
14. 1.45ft^2
2.352m^2
3.138in^2
4.1,319cm^2
1. 👍
2. 👎
15. How do know you guys are right?
1. 👍
2. 👎
16. 1. A- 45ft^2
2. B- 352m^2
3. D- 138in^2
4. A- 1,319cm^2
1. 👍
2. 👎
17. @that guy in a dog costume is right
1. A- 45ft^2
2. B- 352m^2
3. D- 138in^2
4. A- 1,319cm^2
this is for Lesson 5: Surface Area of Pyramids and Cones
Algebra Readiness (Pre-Algebra) B Unit 1: Measurement
1. 👍
2. 👎
18. Yep still 100%
A
B
D
A
1. 👍
2. 👎
19. got 100%
1. 👍
2. 👎
20. For the ones who just put wrong answers up here just to make others fail or trying to be funny you can stop now because you are the ones who is failing
Also stop trying to make others feel like for something you did which is kinda but anyways stop trying to be funny by putting wrong answers here
1. 👍
2. 👎
21. jman is right
1. 👍
2. 👎
22. Wow still works!!!! After 4 years
1. 👍
2. 👎
23. 2021 its 100%
A
B
D
A
1. 👍
2. 👎
24. Anyone wanna play cod?
1. 👍
2. 👎
25. jman is 100%
1. 👍
2. 👎
26. Poo what cod and what do you play on?
1. 👍
2. 👎
27. Y'all are smart if you know the answers-
1. 👍
2. 👎
28. jman is correct
1. 👍
2. 👎
29. lol who are you people
1. 👍
2. 👎
30. These are people looking for answers, sir
1. 👍
2. 👎
31. A
B
D
A
still right to this day. 4/4 100%
1. 👍
2. 👎
32. Hellcat is right
1. 👍
2. 👎
33. Yep
1. 👍
2. 👎
34. A
B
D
A
100%
1. 👍
2. 👎
35. i
n
e
e
d
h
e
l
p
1. 👍
2. 👎
36. yall are al wrong
1. 👍
2. 👎
37. Thank you Jman
1. 👍
2. 👎
38. Yea thanks
1. 👍
2. 👎
39. 1. A- 45ft^2
2. B- 352m^2
3. D- 138in^2
4. A- 1,319cm^2
Are still correct in 2021 right!
1. 👍
2. 👎
40. 1. A
2. B
3. D
4. A
Definitely 100% correct
1. 👍
2. 👎
41. A
B
D
A
4/4 100%
1. 👍
2. 👎
42. 1. A- 45ft^2
2. B- 352m^2
3. D- 138in^2
4. A- 1,319cm^2
this is for Lesson 5: Surface Area of Pyramids and Cones
Algebra Readiness (Pre-Algebra) B Unit 1: Measurement
1. 👍
2. 👎
43. Wow a lot of views.
1. 👍
2. 👎
44. I really hated when player got eaten by the zombies and said aah sounds. Really bad.
1. 👍
2. 👎
45. yes
1. 👍
2. 👎
46. ?
1. 👍
2. 👎
47. Hi!!
1. 👍
2. 👎
48. Hi!
1. 👍
2. 👎
49. just did the test and the answers are
A
B
D
A
100% for Connexus students
1. 👍
2. 👎
50. Helo
1. 👍
2. 👎
51. ─────────▄──────────────▄
────────▌▒█───────────▄▀▒▌
────────▌▒▒▀▄───────▄▀▒▒▒▐
───────▐▄▀▒▒▀▀▀▀▄▄▄▀▒▒▒▒▒▐
─────▄▄▀▒▒▒▒▒▒▒▒▒▒▒█▒▒▄█▒▐
───▄▀▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▀██▀▒▌
──▐▒▒▒▄▄▄▒▒▒▒▒▒▒▒▒▒▒▒▒▀▄▒▒▌
──▌▒▒▐▄█▀▒▒▒▒▄▀█▄▒▒▒▒▒▒▒█▒▐
─▐▒▒▒▒▒▒▒▒▒▒▒▌██▀▒▒▒▒▒▒▒▒▀▄▌
─▌▒▀▄██▄▒▒▒▒▒▒▒▒▒▒▒░░░░▒▒▒▒▌
─▌▀▐▄█▄█▌▄▒▀▒▒▒▒▒▒░░░░░░▒▒▒▐
▐▒▀▐▀▐▀▒▒▄▄▒▄▒▒▒▒▒░░░░░░▒▒▒▒▌
▐▒▒▒▀▀▄▄▒▒▒▄▒▒▒▒▒▒░░░░░░▒▒▒▐
─▌▒▒▒▒▒▒▀▀▀▒▒▒▒▒▒▒▒░░░░▒▒▒▒▌
─▐▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▐
──▀▄▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▄▒▒▒▒▌
────▀▄▒▒▒▒▒▒▒▒▒▒▄▄▄▀▒▒▒▒▄▀
───▐▀▒▀▄▄▄▄▄▄▀▀▀▒▒▒▒▒▄▄▀
──▐▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▀
1. 👍
2. 👎
52. awwww
A
B
D
A
1. 👍
2. 👎
53. |\----------------|--------------|----------------|--------------\
| \
| UPPER ENGINE CAFETERIA WEAPONS \
| |- --------| | \
|/--------| |--| MEDBAY | | \
| | | | \------\
/---------| |-------\ | |----------| | \
| | | \ |---| |------| | |
| \ | | |
| | | | | |
| | | | |---| |----|-|----------| |
\---------| |----------|------| | | /
| | | /------/
|\--------| |--| | /
| | | |-- --| /
| LOWER ENGINE ELECTRICAL STORAGE | COMMS | SHIELDS /
| | | /
|/----------------|--------------|--------------|--------|-------/
#
A
B
D
A
1. 👍
2. 👎
54. A
B
D
A
This is my favorite post with a lot of views.
1. 👍
2. 👎
55. A B D A
1. 👍
2. 👎
56. 1. A- 45ft^2
2. B- 352m^2
3. D- 138in^2
4. A- 1,319cm^2
1. 👍
2. 👎
57. My name is Mr.Cheese
1. 👍
2. 👎
58. Tabitha had \$400 to spend on her trip. She bought a train ticket in Spain for 89 and a train ticket in Switzerland for \$205. She spent \$40 on meals and purchased a souvenir. When she arrived at her final stop in Germany, she had \$14 left. How much money did Tabitha spend on the souvenir?
1. 👍
2. 👎
59. SSUSUSUSUSUUSUSUSSUSUSUSUUSUSUUSUSUUSUSUUSUSUUSUSUUSUSUSUUSUUSUSUSUUSUUSSSUSUSUSUSUUSUSUSSUSUSUSUUSUSUUSUSUUSUSUUSUSUUSUSUUSUSUSUUSUUSUSUSUUSUUSSSUSUSUSUSUUSUSUSSUSUSUSUUSUSUUSUSUUSUSUUSUSUUSUSUUSUSUSUUSUUSUSUSUUSUUSSSUSUSUSUSUUSUSUSSUSUSUSUUSUSUUSUSUUSUSUUSUSUUSUSUUSUSUSUUSUUSUSUSUUSUUS GET OUT OF MY HEAD SSUSUSUSUSUUSUSUSSUSUSUSUUSUSUUSUSUUSUSUUSUSUUSUSUUSUSUSUUSUUSUSUSUUSUUSSSUSUSUSUSUUSUSUSSUSUSUSUUSUSUUSUSUUSUSUUSUSUUSUSUUSUSUSUUSUUSUSUSUUSUUS
1. 👍
2. 👎
60. UWUWUWUWUUWUUWUWUWUWUUWUWUWUUWUWUWUWUWUWUWUWUUWUWUWUWUWUWUWUWUWUWUWUWUWUWWUWUWUWUWU
1. 👍
2. 👎
61. The answers are 45, 352, 138, 1,319. just failed because of someones answers so here ya go:)
1. 👍
2. 👎
## Similar Questions
1. ### Math for Ms. Sue please! Last math questions!
For numbers 1–3, find the indicated measurement of the figure described. Use 3.14 for pi and round to the nearest tenth. Find the surface area of a sphere with a radius of 8 cm. 267.9 cm^2 803.8 cm^2 2143.6 cm^2 201.0 cm^2 Find
2. ### MATH QUIZ PLS HELP!!!
1.Find the lateral area of a cone with a radius of 7 ft. and a slant height of 13 ft. Use 3.14 for ©£ and round to the nearest tenth. 439.6 ft^2 324.5 ft^2 571.5 ft^2 285.7 ft^2*** 2.Find the surface area of a square pyramid
3. ### math
A pyramid has a height of 5 in. and a surface area of 90 in2. Find the surface area of a similar pyramid with a height of 10 in. Round to the nearest tenth, if necessary?
4. ### Math
The net shown below forms a square pyramid. Find the surface area of the square pyramid. The numbers are 5, 5 and 4. How do I do this?
1. ### geometry
1. What is the lateral surface area of a square pyramid with side length 11.2 cm and slant height 20 cm? 224 cm2 448 cm2 896 cm2 2508.8 cm2 2. What is the lateral surface area of a cone with radius 19 cm and slant height 11 cm? 19
2. ### Math
Carol is going to make a wooden pyramid and then paint it. She drew the net of a square pyramid as shown below to help her plan the project. What should be the total surface area in square feet of Carol's wooden pyramid? Here is
3. ### math
Use the net as an aid to compute the surface area (rounded to the nearest integer) of the triangular pyramid with an equilateral triangle base. (10ft,6ft,6ft,6ft,5.2ft.)(if i could put in a pic i would) A. 106ft B. 114ft C. 122ft
4. ### math
open study a rectangle rug is 4 feet by 9 feet. what is the side length of a square rug with the same area -3ft -5ft -6ft -8ft
1. ### Math
Use the formula S=(2)1/2 bh+hw+sw+bw to find the surface area of a triangular prism with the following dimensions: base =3ft height=2ft width=5ft side=4ft A.S=48 FT B.S=51 FT C.S=61 FT D.S=102 FT what is the surface area?
2. ### math
A regular square pyramid has a height of 2 and lateral edges of length 10. What is the lateral area and total surface area of the pyramid?
3. ### Algebra
what is the formula used to calculate the surface area for a square pyramid? | 4,240 | 8,933 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.1875 | 4 | CC-MAIN-2021-17 | longest | en | 0.772695 |
http://www.ncatlab.org/nlab/show/biased+definition | 1,448,715,919,000,000,000 | application/xhtml+xml | crawl-data/CC-MAIN-2015-48/segments/1448398452560.13/warc/CC-MAIN-20151124205412-00097-ip-10-71-132-137.ec2.internal.warc.gz | 577,047,286 | 6,201 | # Biased definitions
## Idea
Often in mathematics, when requiring some structure/operation/property/… to exist at every finite arity?, it suffices to require only the binary ($2$-ary) and nullary ($0$-ary) forms, from which the others follow. A definition in which only these are required is called biased.
For example, in defining a category, one could use an “unbiased” definition in which composites of all finite sequences of morphisms are directly postulated, with corresponding associativity laws, but it suffices to require only binary composites and nullary composites (i.e., identity morphisms) and some particular corresponding associativity laws.
As a special case of this, we have perhaps the prototypical example of a binary/nullary pair sufficing to generate all finite instances of some structure: the natural numbers themselves (the arities of the operations that we are considering) are the free monoid on one generator, and thus are freely associatively produced from that one generator (aka, $1$) using only binary and nullary addition.
## When a nullary operation does not exist
Sometimes a nullary operation does not exist but one still wants to decompose a n-ary operation into binary operations. For example, consider the reals, $\mathbb{R}$, as an unbounded lattice (top, $\top$, and bottom, $\bot$, do not exist) where
$\wedge =$ product $=$ meet $= infinum = min$
and
$\vee =$ coproduct $=$ join $= supremum = max$.
Here $\bigwedge(\{\})$ does not exist while
$\bigwedge(\{a\}) = a$
$\bigwedge(\{a,b\}) = a \wedge b$
$\bigwedge(\{a,b,c\}) = a \wedge (b \wedge c) = (a \wedge b) \wedge c = a \wedge b \wedge c$.
One approach is to compute in the extended reals, $\mathbb{R}_{\pm \infty}$ ($\mathbb{R}$ enlarged with $+\infty$ and $-\infty$.) Here
$\top = +\infty =$ terminal object
and
$\bot = -\infty =$ initial object.
In $\mathbb{R}_{\pm \infty}$ we have the nullary $\wedge() = +\infty$ which gives:
$\bigwedge(\{\}) = +\infty$
$\bigwedge(\{a\}) = \bigwedge(\{a, +\infty\}) = a$.
Another approach is to define a special scheme for composition for when a nullary operator does not exist that instead uses a unary operator that is an identity map (or factored through one).
This approach generalizes to any semigroup or to any category with binary (co) products. A yet more general context (possibly not fully worked out) would be a binary operation in any associative operad.
Revised on September 29, 2015 22:11:15 by Mike Shulman (76.88.99.98) | 674 | 2,495 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 26, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.671875 | 4 | CC-MAIN-2015-48 | latest | en | 0.873948 |
http://www.mapleprimes.com/tags/atomic_identifier | 1,495,845,168,000,000,000 | text/html | crawl-data/CC-MAIN-2017-22/segments/1495463608726.4/warc/CC-MAIN-20170527001952-20170527021952-00034.warc.gz | 699,595,102 | 23,811 | ## changing pronumeral results in different results...
When i use the pronumeral thetac (using greek characters) I initially get numeric data reported, but later in the script i get the pronemeral literally repeated (as though there is no value defined for this pronumeral).
This does not happen for thetahs (using greek characters), where I always get numeric results (through the entire script).
See the following script: sample_1.mw
I re-wrote the...
## Change Atomic definition back to 2-D or 1-D...
How does one change a previous Atomic setting back to non-Atomic? This seems so simple, but I can't find anyway to Undo this change.
Thanks,
## "eval" results in "vector index out of range"...
Hey Everybody,
I have only been using Maple for a few weeks but have been very much enjoying the functionality of the with(VectorCalculus) tools. That said, I have been having some trouble evaluating vectors at specific values.
> with(VectorCalculus);
> P[0] := PositionVector([t, ln(t)]);
> N[0] := PrincipalNormal(P[0], t);
> P := eval(P[0], t = 1);
## convert/identifier
by: Maple
Here is a hacked-up and short `convert/identifier` procedure.
The shortness of the procedure should is a hint that it's not super robust. But it can be handy, in some simple display situations.
If I had made into a single procedure (named `G`, or whatever) then I could have declared its first parameter as x::uneval and thus avoided the need for placing single-right (uneval) quotes around certain examples. But for fun I wanted it to be an extension of `convert`. And while I could code special-evaluation rules on my `convert` extension I suppose that there no point in doing so since `convert` itself doesn't have such rules.
For the first two examples below I also typed in the equivalent expressions in 2D Math input mode, and then used the right-click context-menu to convert to Atomic Identifier. Some simple items come out the same, while some other come out with a different underlying structure and display.
> restart:
> `convert/identifier`:=proc(x) cat(`#`,convert(convert(:-Typesetting:-Typeset(x),`global`),name)); end proc:
> convert( 'sqrt(4)', identifier);
> eval(value(%)); lprint(%);
`#msqrt(mn("4"))`
>
> lprint(%);
`#msqrt(mn("4"))`
> convert( 'int(BesselJ(0,Pi*sqrt(t)),t)', identifier);
> eval(value(%)); #lprint(%);
>
> #lprint(%);
> convert( Vector[row](['Zeta(0.5)', a.b.c, 'limit(sin(x)/x,x=0)', q*s*t]), identifier);
> eval(value(%)); #lprint(%); | 629 | 2,500 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.515625 | 3 | CC-MAIN-2017-22 | longest | en | 0.887678 |
sudokupro.app | 1,721,011,784,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763514655.27/warc/CC-MAIN-20240715010519-20240715040519-00239.warc.gz | 470,550,269 | 38,635 | # Inside the logic of Sudoku
• Sudoku online is one of the most popular numbers games that can better your brain. For those who have no clue what Sudoku is, it is a numbers game in which players have to fill blank boxes according to the specific rules.
Sudoku game logic is very straight and we are here to get more information on Sudoku and learn how to solve Sudoku mathematically.
## The logic of Sudoku power
Playing free online Sudoku is impossible without logical thinking. But what is it?
Sudoku logical thinking is the act of analyzing a situation on the grid and coming up with the most effective solution. Just like a workout in the gym, your mind needs some exercise. Playing free Sudoku puzzles daily boosts your brainpower and provides other benefits:
• Improves the sharpness of your memory
• Stimulates logical thinking and mathematical Sudoku skills
• Help to do everything quickly
• Increases concentration
• Feeling happy
Is Sudoku a hobby worth exploring? Definitely yes! And now let’s dig a burning question that stops many from playing the game — how to solve Sudoku with math?
## Sudoku and math
You may have heard that the Sudoku game online doesn’t require math skills. But what it actually means is that there is a mathematical way to solve Sudoku but arithmetic is not required. Free easy Sudoku puzzles online use digits from 1 to 9, where some are milling. Players are using logical deduction which, in fact, is mathematical thinking which is useful for solving Sudoku with math.
### How to solve Sudoku using math?
There are 2 strategies to solve Sudoku with math, so let’s explore what they entail!
• Forced Entry — #1 mathematical solution to Sudoku. The widely-known basic strategy of solving Sudoku puzzles. You need to first write down all possible entries in each empty cell. Each entry should not contradict the One Rule. When a certain cell has only one possible suitable number, it is called a ‘forced’ entry.
• Digit by digit — #2 mathematical solution for Sudoku. Another strategy is to start with picking a digit and a row/column/block. Note that the One Rule can’t also be violated. If you find a spot where the number can only be put once in the neighborhood, you should place it there. After that, the chosen digit can be eliminated from the connected neighboring row, column, or block.
Following these two strategies are usually enough to successfully solve any Sudoku puzzle of basic levels. But for some medium level and all hard level Sudokus players need more advanced analytical math methods like:
1. Guess-Proceed. If you don’t have a forced entry cell, but a few suitable numbers, you can pick one and proceed with it to make progress. If the situation results in conflict, you need to backtrack.
2. Triple cell. Another more complicated strategy is where you scan pairs or triples of cells within a row/column/block (your choice). You might find a pair of cells with 2 possible entries. This strategy doesn’t give you an exact number to put in, but it provides information that both digits cannot be anywhere else in the neighborhood. Similarly, triple cells eliminate 3 entries. Now you know how to solve Sudoku with math and can enjoy the best free online Sudoku games from the comfort of your phone with SudokuPro.
### Should I be a pro in math to play free Sudoku puzzle online?
In short, no. You don’t need to have a math Sudoku solver in your head to enjoy this game. There are no deep mathematical skills required, just logic. Also, your math will develop when you master new levels of Sudoku like math puzzle. If you are still not sure if your math level is enough, you should explore solving tips techniques.
### Are there math puzzles similar to Sudoku?
Yes, there are more than 15 similar math puzzles that include Wordoku, Hidato, Nonograms, and others. But they don’t even come close in popularity to traditional games with multiple levels.
The game, especially in the handy app form of SudokuPro has the potential to be your ultimate way of destressing and having a fun time. Don’t be afraid that your math skills are not enough, Sudoku is suitable for everyone.
How to solve Sudoku
Mathematical solution Sudoku
Solving tips techniques
06.06.2022
# Similar Articles
## 5 Reasons Why People Play Sùdoku In 2022
Do you play Sudoku? Not yet? But millions of people spend their free (and not so free) time playing Sudoku online. Still, why do they choose this Japanese game in particular?
07.05.2022
## Killer Sudoku Techniques To Solve WebSudoku Like A Pro
One of the reasons for the long-time popularity of Sudoku is that the game offers interesting challenges for both beginners and expert players. Its users always stove to become better at playing Sudoku and therefore master their techniques.
14.05.2022
## Sudoku Online vs Offline—Pros & Cons Of App & Paper Form
When you know all the benefits of playing Sudoku daily it's only natural to search for a comfortable way of enjoying the game. With modern technologies and the Internet, this puzzle is no longer just a newspaper game, like those you could find in the Washington Post or USA Today
29.05.2022 | 1,073 | 5,153 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.8125 | 4 | CC-MAIN-2024-30 | latest | en | 0.920287 |
https://secure.youthscience.ca/sfiab/gvrsf/project_summary.php?year=2007&pn=J%20129%20P | 1,627,651,094,000,000,000 | text/html | crawl-data/CC-MAIN-2021-31/segments/1627046153966.60/warc/CC-MAIN-20210730122926-20210730152926-00559.warc.gz | 523,415,772 | 2,179 | Airborne Analysis Nolan Pontes Albion Elementary Floor Location : J 129 P
Nolan Pontes March 2007rnAlbion ElementaryrnrnAirborne AnalysisrnrnAfter doing a large amount of research, using the Internet, I chose to do my experiment on aircraft wing designs. I wanted to understand how the various wing designs would impact flight performance. The reason I chose this experiment is because of my interest in aircraft styles and designs. I presented my plan to my teacher, Mr. Blaine, who provided me with some feedback, then approved it. I immediately got to work.rnrnThe purpose of my experiment was to determine which aircraft wing design flew best. I set out to create five designs, each with a different aspect ratio from which to conduct my analysis. I was careful with the aircraft designs to make sure the variables remained controlled. Each wing design had the same surface area, equal to 288 square units. I used 1/4 inch graph paper for this. All five of the wing designs had a different aspect ratio. The aspect ratio is calculated by dividing the length of the wing by its width. Research suggests the higher the aspect ratio, the less drag there is created on the wings of the aircraft. The theory is that the less drag there is, the more the aircraft can accelerate and the longer distance it can travel. rnrnI built the planes using balsa wood. I traced the wing designs onto the wood then used an exacto knife to cut them out. This was very precise work and took quite a while. I then cut out the bodies making sure they were exact in every way and sanded them down with a dremmel tool. You must have an adult around when doing this part of the experiment. After that I experimented with placement of the wings. I spent two entire days trying different placements. rnrnI explored different heights to release my planes. Eight feet seemed to work best. I stood on an 8-foot platform to carry out the flight experiment. Each plane was tested three times. rnrnAircraft five traveled farther than aircraft three but they both had about the same travel time. This occurred because aircraft three presented more drag, traveled a shorter distance and took longer because of the drag created. The aspect ratio of this plane told me this would be the result. Aircraft five went the farthest distance and had the longest time. 8.61 metres was the average flight distance and 2.07 seconds was the average flight time for aircraft five. Technically, the outcome of the aspect ratio equation was true for each plane. rnrnI enjoyed doing this project because I learned many new and interesting facts about airplanes and designs. Even though this experiment used model airplanes, the aspect ratio equation is used in designing modern day aircrafts.rnrnI look forward to presenting my experiment and its results at the Regional Science Fair. I hope you enjoy my experiment as much as I enjoyed doing it! rn | 605 | 2,902 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.8125 | 3 | CC-MAIN-2021-31 | latest | en | 0.974068 |
https://www.coursehero.com/file/5877932/midterm2sols/ | 1,527,041,403,000,000,000 | text/html | crawl-data/CC-MAIN-2018-22/segments/1526794865023.41/warc/CC-MAIN-20180523004548-20180523024548-00545.warc.gz | 715,939,023 | 109,526 | {[ promptMessage ]}
Bookmark it
{[ promptMessage ]}
midterm2sols
# midterm2sols - UC Berkeley-CS 170 Lecturer Satish Rao...
This preview shows pages 1–4. Sign up to view the full content.
UC Berkeley—CS 170 Midterm 2 Lecturer: Satish Rao April 21, 2008 Midterm 2 for CS 170 Print your name: , (last) (first) Sign your name: Write your section number (e.g., 101): Write your SID: One page of notes is permitted. No electronic devices, e.g. cell phones and calculators, are permitted. Do all your work on the pages of this examination. If you need more space, you may use the reverse side of the page, but try to use the reverse of the same page where the problem is stated. You have 80 minutes. The questions are of varying difficulty, so avoid spending too long on any one question. In all algorithm design problems, you may use high-level pseudocode. DO NOT TURN THE PAGE UNTIL YOU ARE TOLD TO DO SO. Problem Score/Points Name/Section/etc. /2 1 /14 2 /20 3 /40 4 /24 Total /100
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Date: April 21, 2008 2 Figure 1: Counter example for 1(c). Greedy set cover algorithm would choose { 9, 1, 3, 5, 7 } . However, the optimal set cover is { 2, 4, 6, 8 } . 1. True or false (2 points each, 14 points total). No negative points for wrong answers. If it is true give a short justification. If it is false give a counterexample. (a) (TRUE or FALSE) In a Huffman encoding scheme, if all characters occur with fre- quency less than 1/3, then there is guaranteed to be no codeword of length 1. Answer: True Justification: Suppose this is not the case. Let x be a node corresponding to a single character with p ( x ) < 1 / 3 such that the encoding of x is of length 1. Then x must not merge with any other node until the end. Consider the stage when there are only three leaves - x, y and z left in the tree. At the last stage y, z must merge to form another node so that x still corresponds to a codeword of length 1. But, p ( x )+ p ( y )+ p ( z ) = 1 and p ( x ) < 1 / 3 implies p ( y ) + p ( z ) > 2 / 3. Hence, at least one of p ( y ) or p ( z ), say p ( z ), must be greater than 1 / 3. But then these two cannot merge since p ( x ) and p ( y ) would be the minimum. This leads to a contradiction. (b) (TRUE or FALSE) In a Huffman encoding scheme, if all characters occur with fre- quency less than 2/5, then there is guaranteed to be no codeword of length 1. Answer: False Counter exmaple: (0.39, 0.39, 0.22), the corresponding huffman coding length is (1, 2, 2). (c) (TRUE or FALSE) The greedy set cover algorithm (which repeatedly chooses the largest set) gives the optimal set cover. Answer: False Counter example: In Figure 1, greedy set cover algorithm would choose { 9, 1, 3, 5, 7 } . However, the optimal set cover is { 2, 4, 6, 8 } . (d) (TRUE or FALSE) If s and t are at least D hops apart (i.e. every path from s to t has at least D edges), then there is an s t cut with at most m/D edges, where m is the number of edges.
Date: April 21, 2008 3 Answer: True Justification: Let each edge have a capacity of 1 and consider the max flow from s to t . The max flow is equal to the number of DISJOINT paths from s to t (since all paths have capacity 1), which is at most m/D since all paths must have at least D edges. Since the min cut equals the max flow, the min cut is m/D . Therefore, we are guaranteed to find a cut with at most m/D edges.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up to access the rest of the document.
{[ snackBarMessage ]}
### What students are saying
• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.
Kiran Temple University Fox School of Business ‘17, Course Hero Intern
• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.
Dana University of Pennsylvania ‘17, Course Hero Intern
• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.
Jill Tulane University ‘16, Course Hero Intern | 1,222 | 4,594 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.25 | 3 | CC-MAIN-2018-22 | latest | en | 0.849201 |
https://gmatclub.com/forum/if-y-0-is-y-3-y-divisible-by-99817.html | 1,721,319,334,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763514848.78/warc/CC-MAIN-20240718161144-20240718191144-00646.warc.gz | 243,731,704 | 136,075 | Last visit was: 18 Jul 2024, 09:15 It is currently 18 Jul 2024, 09:15
Toolkit
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
we will pick new questions that match your level based on your Timer History
Track
every week, we’ll send you an estimated GMAT score based on your performance
Practice
Pays
we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
# If y > 0, is (y^3 – y) divisible by 4?
SORT BY:
Tags:
Show Tags
Hide Tags
Manager
Joined: 16 Feb 2010
Posts: 122
Own Kudos [?]: 1514 [5]
Given Kudos: 16
Math Expert
Joined: 02 Sep 2009
Posts: 94402
Own Kudos [?]: 641985 [5]
Given Kudos: 85997
General Discussion
Manager
Joined: 16 Feb 2010
Posts: 122
Own Kudos [?]: 1514 [0]
Given Kudos: 16
Manager
Joined: 24 Dec 2009
Posts: 116
Own Kudos [?]: 125 [0]
Given Kudos: 3
Re: GrockIt: divisibility [#permalink]
B for me. I believe this problem can also be solved by using prime boxes.
Manager
Joined: 21 Feb 2010
Posts: 150
Own Kudos [?]: 102 [0]
Given Kudos: 1
GPA: 3.8
Re: GrockIt: divisibility [#permalink]
the key point to this question is to find out if y is an odd#...i pick B
Manager
Joined: 14 Jun 2010
Posts: 130
Own Kudos [?]: 77 [0]
Given Kudos: 7
Re: GrockIt: divisibility [#permalink]
I pick B and I agree with tt11234...The key here is to pick that y is odd!
SVP
Joined: 27 May 2012
Posts: 1696
Own Kudos [?]: 1493 [0]
Given Kudos: 639
Re: GrockIt: divisibility [#permalink]
Bunuel wrote:
If y>0, is y^3-y divisible by 4?
$$y^3-y=y(y^2-1)=y(y-1)(y+1)$$
(1) y^2+y is divisible by 10 --> if $$y=10$$ then $$y(y-1)(y+1)=10*9*11$$, so not divisible by 4 (product of 2 odd and not multiple of 4 will not be divisible by 4) BUT if $$y=100$$ then $$y(y-1)(y+1)=100*99*101$$, so divisible by 4 (100 is a multiple of 4, hence product will be divisible by 4). Sufficient.
(2) For a certain integer k, y=2k+1 --> $$y=odd$$ --> $$y-1=even$$ and $$y+1=even$$ --> $$y(y-1)(y+1)$$ is a multiple of 4 (product of 2 even numbers is a multiple of 4, OR as $$y-1$$ and $$y-1$$ are consecutive even numbers, thus one of them must be multiple of 4). Sufficient.
Pleas use "^" for powers, and formating for formulas.
answer is definitely B , as the product of 2 consecutive even numbers is divisible by 4.
There is a small typo above , it should be (y-1) and (y+1) are 2 consecutive even numbers and not (y-1 ) and ( y-1) are 2 consecutive even numbers ,
Hope this prevents any confusion.
Thank you.
Manager
Joined: 13 Apr 2015
Posts: 60
Own Kudos [?]: 72 [1]
Given Kudos: 325
Concentration: General Management, Strategy
GMAT 1: 620 Q47 V28
GPA: 3.25
WE:Project Management (Energy and Utilities)
Re: If y > 0, is (y^3 – y) divisible by 4? [#permalink]
1
Kudos
Bunuel wrote:
If y>0, is y^3-y divisible by 4?
$$y^3-y=y(y^2-1)=y(y-1)(y+1)$$
(1) y^2+y is divisible by 10 --> if $$y=10$$ then $$y(y-1)(y+1)=10*9*11$$, so not divisible by 4 (product of 2 odd and not multiple of 4 will not be divisible by 4) BUT if $$y=100$$ then $$y(y-1)(y+1)=100*99*101$$, so divisible by 4 (100 is a multiple of 4, hence product will be divisible by 4). Not sufficient.
(2) For a certain integer k, y=2k+1 --> $$y=odd$$ --> $$y-1=even$$ and $$y+1=even$$ --> $$y(y-1)(y+1)$$ is a multiple of 4 (product of 2 even numbers is a multiple of 4, OR as $$y-1$$ and $$y-1$$ are consecutive even numbers, thus one of them must be multiple of 4). Sufficient.
Pleas use "^" for powers, and formatting for formulas.
I think one more case is to be considered, i.e when k = 0, y = 1. Even then 0/4 = 0 a integer. B will remain the answer
Retired Moderator
Joined: 22 Jun 2014
Posts: 970
Own Kudos [?]: 3932 [0]
Given Kudos: 182
Location: India
Concentration: General Management, Technology
GMAT 1: 540 Q45 V20
GPA: 2.49
WE:Information Technology (Computer Software)
If y is an integer greater than 0, is (y^3 - y) divisible by 4? [#permalink]
If $$y$$ is an integer greater than 0, is ($$y^3$$ - $$y$$) divisible by 4?
(1) $$y^2$$ + $$y$$ is divisible by 10.
(2) For a certain integer $$k$$, $$y$$ = 2$$k$$ + 1
Math Expert
Joined: 02 Sep 2009
Posts: 94402
Own Kudos [?]: 641985 [0]
Given Kudos: 85997
Re: If y > 0, is (y^3 – y) divisible by 4? [#permalink]
HKD1710 wrote:
If $$y$$ is an integer greater than 0, is ($$y^3$$ - $$y$$) divisible by 4?
(1) $$y^2$$ + $$y$$ is divisible by 10.
(2) For a certain integer $$k$$, $$y$$ = 2$$k$$ + 1
Merging topics. Please refer to the discussion above.
Intern
Joined: 10 Jun 2016
Posts: 32
Own Kudos [?]: 12 [0]
Given Kudos: 194
Schools: IIM-A"19
Re: If y > 0, is (y^3 – y) divisible by 4? [#permalink]
Bunuel wrote:
If y>0, is y^3-y divisible by 4?
$$y^3-y=y(y^2-1)=y(y-1)(y+1)$$
(1) y^2+y is divisible by 10 --> if $$y=10$$ then $$y(y-1)(y+1)=10*9*11$$, so not divisible by 4 (product of 2 odd and not multiple of 4 will not be divisible by 4) BUT if $$y=100$$ then $$y(y-1)(y+1)=100*99*101$$, so divisible by 4 (100 is a multiple of 4, hence product will be divisible by 4). Not sufficient.
(2) For a certain integer k, y=2k+1 --> $$y=odd$$ --> $$y-1=even$$ and $$y+1=even$$ --> $$y(y-1)(y+1)$$ is a multiple of 4 (product of 2 even numbers is a multiple of 4, OR as $$y-1$$ and $$y-1$$ are consecutive even numbers, thus one of them must be multiple of 4). Sufficient.
Pleas use "^" for powers, and formating for formulas.
Hello Bunnel or GMATCLUB members,
For Statement 2 we say since y is odd means y-1 is even and y+1 is even, so the given statement is div by 4. But consider if y = 1 since it is given y>0.
Now y-1 is 0 and y+1 = 2. Could this be a valid case ? Then the answer will be C. Request your help?
Intern
Joined: 10 Jun 2016
Posts: 32
Own Kudos [?]: 12 [0]
Given Kudos: 194
Schools: IIM-A"19
If y > 0, is (y^3 – y) divisible by 4? [#permalink]
coolkl wrote:
Bunuel wrote:
If y>0, is y^3-y divisible by 4?
$$y^3-y=y(y^2-1)=y(y-1)(y+1)$$
(1) y^2+y is divisible by 10 --> if $$y=10$$ then $$y(y-1)(y+1)=10*9*11$$, so not divisible by 4 (product of 2 odd and not multiple of 4 will not be divisible by 4) BUT if $$y=100$$ then $$y(y-1)(y+1)=100*99*101$$, so divisible by 4 (100 is a multiple of 4, hence product will be divisible by 4). Not sufficient.
(2) For a certain integer k, y=2k+1 --> $$y=odd$$ --> $$y-1=even$$ and $$y+1=even$$ --> $$y(y-1)(y+1)$$ is a multiple of 4 (product of 2 even numbers is a multiple of 4, OR as $$y-1$$ and $$y-1$$ are consecutive even numbers, thus one of them must be multiple of 4). Sufficient.
Pleas use "^" for powers, and formating for formulas.
Hello Bunnel or GMATCLUB members,
For Statement 2 we say since y is odd means y-1 is even and y+1 is even, so the given statement is div by 4. But consider if y = 1 since it is given y>0.
Now y-1 is 0 and y+1 = 2. Could this be a valid case ? Then the answer will be C. Request your help?
I got my answer, if y =1 then (y-1)y(y+1) is 0 and 0 div by 4 is still 0. This is good question.
Manager
Joined: 02 Feb 2016
Posts: 75
Own Kudos [?]: 45 [0]
Given Kudos: 40
GMAT 1: 690 Q43 V41
Re: If y > 0, is (y^3 – y) divisible by 4? [#permalink]
I got to understand that 'y' is odd as given in statement (2) but if y=1, the expression given would become zero. So it shouldn't be considered as divisible by 4.
Math Expert
Joined: 02 Sep 2009
Posts: 94402
Own Kudos [?]: 641985 [1]
Given Kudos: 85997
Re: If y > 0, is (y^3 – y) divisible by 4? [#permalink]
1
Kudos
TheMastermind wrote:
I got to understand that 'y' is odd as given in statement (2) but if y=1, the expression given would become zero. So it shouldn't be considered as divisible by 4.
You should brush up fundamentals.
ZERO:
1. 0 is an integer.
2. 0 is an even integer. An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder and as zero is evenly divisible by 2 then it must be even.
3. 0 is neither positive nor negative integer (the only one of this kind).
4. 0 is divisible by EVERY integer except 0 itself.
Check more here: https://gmatclub.com/forum/number-proper ... 74996.html
Non-Human User
Joined: 09 Sep 2013
Posts: 34013
Own Kudos [?]: 852 [0]
Given Kudos: 0
Re: If y > 0, is (y^3 y) divisible by 4? [#permalink]
Hello from the GMAT Club BumpBot!
Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Re: If y > 0, is (y^3 y) divisible by 4? [#permalink]
Moderator:
Math Expert
94402 posts | 3,073 | 8,910 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.84375 | 4 | CC-MAIN-2024-30 | latest | en | 0.820344 |
https://www.unitconverters.net/density/centigram-liter-to-gram-cubic-centimeter.htm | 1,653,634,783,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662636717.74/warc/CC-MAIN-20220527050925-20220527080925-00009.warc.gz | 1,196,827,309 | 3,161 | Home / Density Conversion / Convert Centigram/liter to Gram/cubic Centimeter
# Convert Centigram/liter to Gram/cubic Centimeter
Please provide values below to convert centigram/liter [cg/L] to gram/cubic centimeter, or vice versa.
From: centigram/liter To: gram/cubic centimeter
### Centigram/liter to Gram/cubic Centimeter Conversion Table
Centigram/liter [cg/L]Gram/cubic Centimeter
0.01 cg/L1.0E-7 gram/cubic centimeter
0.1 cg/L1.0E-6 gram/cubic centimeter
1 cg/L1.0E-5 gram/cubic centimeter
2 cg/L2.0E-5 gram/cubic centimeter
3 cg/L3.0E-5 gram/cubic centimeter
5 cg/L5.0E-5 gram/cubic centimeter
10 cg/L0.0001 gram/cubic centimeter
20 cg/L0.0002 gram/cubic centimeter
50 cg/L0.0005 gram/cubic centimeter
100 cg/L0.001 gram/cubic centimeter
1000 cg/L0.01 gram/cubic centimeter
### How to Convert Centigram/liter to Gram/cubic Centimeter
1 cg/L = 1.0E-5 gram/cubic centimeter
1 gram/cubic centimeter = 100000 cg/L
Example: convert 15 cg/L to gram/cubic centimeter:
15 cg/L = 15 × 1.0E-5 gram/cubic centimeter = 0.00015 gram/cubic centimeter | 345 | 1,051 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.734375 | 3 | CC-MAIN-2022-21 | latest | en | 0.438167 |
https://fondation-fhb.org/docs/viewtopic.php?582142=basic-construction-math-worksheets-pdf | 1,685,800,093,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224649293.44/warc/CC-MAIN-20230603133129-20230603163129-00368.warc.gz | 286,129,853 | 24,549 | # basic construction math worksheets pdf
This means all the points that are to the left of the line which fall halfway between A and B. Finally, we shade all the points beyond the orange line but closer then 4 cm from B. 9 0 obj As a busy homeschooling mother of six, she strives to create hands-on learning activities and worksheets that kids will love to make learning FUN! it.
2. A locus (loci is the plural) is a collection of points which share a property.. E.g. – Place your pair of compasses on the crossing point (green cross) and draw a small arc on the opposite side of the line to where the point is (green). Construction Patterns – Kids will finish patterns with these cute tool themed cut and paste worksheets. The sheets present concepts in the order they are taught and give examples of their use. Looking for more popular content? The circumference of a circle is the locus of all points in 2D that are the same distance from a particular point – the centre.
Question 3: Bill is planning to put a fountain in his garden.
endstream The disadvantage of working through the entire course is the time it will take and that you will probably learn many things that aren't directly applicable to construction. Math of Program. BASIC MATHEMATICS MATH 010 A Summary of Concepts Needed to be Successful in Mathematics The following sheets list the key concepts that are taught in the specified math course.
Overview Addition, subtraction, multiplication, and division; these are all basic math skills that Builders use every day. ٓ*��@vQ�8F�R�q����uث1���ǰ�����aO"�'Tv�^��F�%FD3E��L�2#�U�j��?Hh��\$�L ���RD���0OZA�4����4A�u\$�PA�OvPI#ԐD�`=ae�HX�2B�a -����K�` – Set your pair of compasses to a fixed length apart (Must be greater than half the line). Loci. The answer key is automatically generated and is placed on the second page of the file. In other words, this is not a practical subject, if one is interested in constructing (Hint: which one of the 4 constructions does this look like?). So, we place the compass at B and draw an arc that passes through both lines. Practice Problems to Prepare for Trades Math Assessment Test Form A (Answers are located at the end of this practice exam) The actual Trades Math Assessment Test will have 30 questions, few multiple choice, on it. If you have a kindergarten or teach kindergartners, you don’t want to miss all our fun and FREE kindergarten alphabet worksheets, free kindergarten worksheets, kindergarten math printables, easy science projects, kindergarten English, crafts for kindergartners, and kindergarten activities. Apart from the stuff given in this section, if you need any other stuff in math, please …
�W�%ԕ��/�%W��KϚݻ����]|�O�4I�%ˡ�j�%~'����V����(���)��@'& ���SN����c���:�庾Dq�Ћ; ��g�\$1! Tools of the trade included in these sheets include safety cones, screws, hammers, wrench, screwdriver, nails, saw, hard, hat, tool box, tape measure, pliers, do not enter road block, and more. "I����G�7a���8���z���mk���WJ�~�L7����rY>q���V��NvUؘ,�i��2���Fe�m1ސ_dSU���`� DûלL����uZ��g��5�M�y���:7n'd�:Gր�ؓ� ���L x��s#^h�kq䝀���x%����J �^E��J�/�{����� � �C����f��e�I�ӛ�y�%_ɺUg�)0 Yr-*��A�h+�;\� WHY THESE SHEETS ARE USEFUL – • To help refresh your memory on old math skills you may have forgotten. Instructor Approval and TABE Reading Score (eighth grade or higher) or 4. Preschool worksheets PDF to print. endstream <> Read our guide, Functional Skills Maths Level 2 Practice Tests. Basic Electrical Formulas. Print as many prek worksheets as you need for your immediate family or class to make learning fun with a construction theme! of salt are needed if you have 500 gallons of water. ��D\W�kJ����(���D˨�WV��rW. endstream endobj 90 0 obj <> endobj 91 0 obj <> endobj 92 0 obj <>stream E��[ ����rA�We��3v��T�U��xΌ}�sB �\$�#>.1x�IQ @pb��`�{s�e4�7��.��!�ԕ�\�Ij����t���W�66���L��r8��s���Vc0��Q�M���pɲ��>\���m�]��@�v�v_u�����+���!�jӂ�[��q�_� ���#�X�-2\Zt�ʼx���na���m]���f���"����b=�,��F�Ֆ��T�M�9J2�fT��Fզ��Yjt����Z���;S7��ѣ��VS믫U�Ϋ �˫Q���I�r����-�4��]uB���m�P��k���6�v!��x=�Hʣ5�Dd����at�� 5�|��W���e�=��5�,���j㤫�!����§���,����3�����n_%'���7�������H�N�з�����*�b���t���)M��ic�y�b��#� ���:�PE���;��+�]�t�)�>���x�w��f�t���ݯ��[�҅��k�'� �R�8 The more clearly you understand the basic building blocks of math, the better you will learn and retain more advanced concepts. – Put your pair of compasses on point A and draw an arc (blue). DadsWorksheets.com - thousands of free math worksheets This site has over 5,000 different math worksheets from kindergarten to pre-algebra and growing.
Posted in Uncategorized. | 1,454 | 4,575 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.65625 | 4 | CC-MAIN-2023-23 | latest | en | 0.918478 |
https://egyptchatonline.com/qa/quick-answer-what-you-can-do-on-excel.html | 1,623,592,005,000,000,000 | text/html | crawl-data/CC-MAIN-2021-25/segments/1623487608856.6/warc/CC-MAIN-20210613131257-20210613161257-00524.warc.gz | 224,408,337 | 11,370 | Quick Answer: What You Can Do On Excel?
What can excel be used for?
Excel can be used to bring information from various files and documents together, so that it exists in a single location.
As well as raw data and information from other spreadsheets, it is possible to import text and images..
What are the 5 functions in Excel?
To help you get started, here are 5 important Excel functions you should learn today.The SUM Function. The sum function is the most used function when it comes to computing data on Excel. … The TEXT Function. … The VLOOKUP Function. … The AVERAGE Function. … The CONCATENATE Function.
How can excel help me in the future?
1. Excel is not just for making tablesOrganize data in an easy-to-navigate way.Do basic and complex mathematical functions so you don’t have to.Turn piles of data into helpful graphics and charts.Analyze data and make forecasting predictions.Create, build, and edit pixelated images (yes, creatives use it, too!)
Excel has an auto-fill functionality which intelligently offers users to fill the cells and rows, drag and expand the selection box. Another reason for Excel’s popularity among researchers is that charts are easier to manage and control in Excel.
Can I learn Excel in a day?
It’s impossible to learn Excel in a day or a week, but if you set your mind to understanding individual processes one by one, you’ll soon find that you have a working knowledge of the software.
What are the most important Excel skills?
7 Essential Excel Skills Every Marketer Should LearnUsing VLOOKUP Function: This is truly a gift for a marketer. … Summarizing Data with a Pivot Table: … Programming Macro: … Creating Histogram with “=FREQUENCY” Function: … Creating Charts: … Regression Analysis and R2: … Keyboard Shortcuts:
What are the basic things to learn in Excel?
Basic Skills for Excel UsersSum or Count cells, based on one criterion or multiple criteria.Build a Pivot Table to summarize date.Write a formula with absolute and relative references.Create a drop down list of options in a cell, for easier data entry.Sort a list of text and/or numbers without messing up the data.More items…•Jul 13, 2009
How do I become good at Excel?
Excel TipsUse Pivot Tables to recognize and make sense of data.Add more than one row or column.Use filters to simplify your data.Remove duplicate data points or sets.Transpose rows into columns.Split up text information between columns.Use these formulas for simple calculations.Get the average of numbers in your cells.More items…•Jan 19, 2021
Is Python better than VBA?
Unlike the VBA language used in Excel, data analysis using Python is cleaner and provides better version control. … The ability to reproduce code makes Python more efficient than Excel since users can bypass the initial coding process and start with an already functioning framework.
What Excel skills are employers looking for?
Below is the list of Microsoft Excel skills that you need to look for while hiring the entry-level hires:SUMIF/SUMIFS.COUNTIF / COUNTIFS.Data Filters.Data Sorting.Pivot Tables.Cell Formatting.Data validation.Excel shortcut keys.More items…
What is an Excel file called?
Explanation: Excel file is also called an Excel Workbook. Each excel workbook can contain multiple excel sheets.
Are Excel skills in demand?
It is not an in-demand skill but it is valuable. Working in a retail company that lives and breathes excel, the amount of Excel illiteracy is mind-buggling.
How many days does it take to learn Excel?
So, it all depends on you. If you practice every day and dedicate around 2-3 hours every day to learn the concepts, then you can learn it within four weeks. But, to master the concepts in Excel, you need to use the tricks and formulas on a daily basis. Learning excel just 5 days but analysis take more time…..
What are the 10 uses of Microsoft Excel?
Top 10 Uses of Microsoft Excel in BusinessBusiness Analysis. The number 1 use of MS Excel in the workplace is to do business analysis. … People Management. … Managing Operations. … Performance Reporting. … Office Administration. … Strategic Analysis. … Project Management. … Managing Programs.More items…•Nov 1, 2020
Is Excel difficult to learn?
Excel is a sophisticated software with loads of functionality beneath its surface, and it can seem intimidating to learn. However, Excel is not as challenging to learn as many people believe. With the right training and practice, you can improve your Excel skills and open yourself up to more job opportunities.
Is Microsoft Excel Easy?
Fluency in Microsoft Excel is one of the most valuable soft-skills in any professional’s life. Excel’s broad applicability and user-friendly interface make it so it can be utilized by the masses for a vast number of tasks, from simple data entry to complex data analysis and querying.
What is the future of Excel?
With Microsoft Excel being practically available on most computers within today’s modern businesses, its data analysis and data manipulation capabilities, combined with its relative ease of use, makes it a strong business intelligence tool that is now available to the masses.
What is most important Excel?
Making sense of our data-rich, noisy world is hard but vital. Used well, Conditional Formatting brings out the patterns of the universe, as captured by your spreadsheet. That’s why Excel experts and Excel users alike vote this the #1 most important feature.
How do you master Excel quickly?
How to master Excel quickly in 11 stepsHow to navigate the interface. A good start is to be efficient at navigating the Excel interface. … Learn some useful shortcuts. … Freeze panes. … Create a simple drop-down list. … Visualize key data with conditional formatting. … Flash fill. … Summarize data with PivotTables. … Protect Excel data.More items…
What cool things can excel do?
All his work is online and has also been featured in museums.#2 CREATE A FULL LENGTH ROLE PLAYING GAME.#3 CONVERT ANY PHOTO INTO AN EXCEL SPREADSHEET.#5 CREATE A SUDOKU IN EXCEL.#6 PLAY A VIDEO GAME IN EXCEL.#7 CREATE 3D DANCING PENDULUMS.May 17, 2016
What are the 3 common uses for Excel?
INVESTIGATE A RANGE OF COMMON USES FOR SPREADSHEETS? The three most common general uses for spreadsheet software are to create budgets, produce graphs and charts, and for storing and sorting data.
What are the five uses of spreadsheet?
Once this data is entered into the spreadsheet, you can use it to help organize and grow your business.Business Data Storage. … Accounting and Calculation Uses. … Budgeting and Spending Help. … Assisting with Data Exports. … Data Sifting and Cleanup. … Generating Reports and Charts. … Business Administrative Tasks.
Can you use Python in Excel?
It is officially supported by almost all of the operating systems like Windows, Macintosh, Android, etc. It comes pre-installed with the Windows OS and can be easily integrated with other OS platforms. Microsoft Excel is the best and the most accessible tool when it comes to working with structured data.
Is learning Excel worth it in 2020?
You can be a hero in the office And you just write a few lines of code to do it. You can automate almost anything, usually with not too much effort. You can earn serious money with your skills. Since Microsoft Office is present almost everywhere, you have a huge market to offer your skills and do something useful.
Is Excel important to learn?
Excel can boost productivity tenfold in a business if you know how to quickly create a decent spreadsheet. Then, you are a key asset to that business as you have very useful skills. Excel is a logical application and is fairly user-friendly to learn.
Can you make a game in Excel?
The geniuses at Spreadsheet1.com built an Excel version that allows you to play the game, and track your moves to help analyze your strategy. Since the game is made entirely in Excel, you can resume the game at a later time by saving the workbook, and it can be played online or offline.
How can I learn Excel quickly?
Excel Quick Start Tutorial: 36 Minutes to Learn the BasicsEnter and edit Excel data. … Make simple pivot tables and charts.Create simple Excel formulas.Use Excel Functions IF and VLOOKUP.Filter and sort lists of data. … Use Excel table functions to de-duplicate data and make totals.More items… | 1,740 | 8,331 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.59375 | 3 | CC-MAIN-2021-25 | latest | en | 0.855683 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.