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http://mathhelpforum.com/geometry/7795-explanation-solution-parallelness.html | 1,481,429,908,000,000,000 | text/html | crawl-data/CC-MAIN-2016-50/segments/1480698544097.11/warc/CC-MAIN-20161202170904-00292-ip-10-31-129-80.ec2.internal.warc.gz | 178,270,416 | 12,819 | # Thread: Explanation of solution (parallelness)
1. ## Explanation of solution (parallelness)
Problem that I need to solve is:
Let $a$ be line parallel to plane $\beta$ and let $\alpha$ be some plane that contains line $a$.
Then it's $\alpha \parallel \beta$ or intersection of these two planes is line parallel to $a$.
This is solution from book:
If $a \subset \beta$ then there are two cases (look at attached picture from book).
1) Planes $\alpha$ and $\beta$ have common only line $a$ so then is $\alpha \cap \beta = \{ a\}$, so $\alpha \cap \beta \parallel a$.
2) If there is at least one more point not belonging to line $a$ which is common to planes $\alpha$ and $\alpha '$, then is $\alpha = \alpha '$ so then is $\alpha \parallel \beta$. If it's $a \cap \beta = \emptyset$, then it's either $\alpha \parallel \beta$, that is $\alpha \cap \beta = \emptyset$, or it's $\alpha \cap \beta = a'$. All common points of planes $\alpha '$ and $\beta$ belongs to line $a'$, so since it's $\alpha \cap \beta = \emptyset$ then lines $a$ and $a'$ are not intersecting which means that they are parallel.
Solution from book is quite confusing to me.
Number 1) case is understable, nothing there to confuse.
Number 2) is not understable to me. First I will explain red text. Red text is reffering to case when $a \subset \beta$ and rest of text is reffered to case when $a \cap \beta = \emptyset$ (I think because author didn't specify that clearly). I don't understand why author introduced plane $\alpha '$ at all. I don't understand red text at all. Isn't solution just to say that if planes $\alpha$ and $\beta$ have one more common point not belonging to line $a$ then it's $\alpha \parallel \beta$?
The rest of text in 2) is quite confusing me.
My solution to when is $a \cap \beta = \emptyset$ is that if $\alpha \cap \beta = \emptyset$ then is $\alpha \parallel \beta$. If is $\alpha \cap \beta = a'$ then it must be $a\parallel a'$ because if $a$ isn't parallel to $a'$ then it would intersect plane $\beta$ which is contradiction. Also $a'$ can't intersect $a$ because then it would have only one common point with plane $\beta$ which is contradictory to $\alpha \cap \beta = a'$.
Can someone look at solution from book and my solution and give me explanation, comment or something that would clarify me that?
2. First, I totally agree with you. I see no reason to introduce $\alpha'$.
On the other hand, I am not sure that I follow your proof.
Here are the four cases that I would use.
$\begin{array}{l}
3)\;a \not\subset \beta \quad \& \quad \alpha \cap \beta = \emptyset \\
4)\;a \not\subset \beta \quad \& \quad \alpha \cap \beta \not= \emptyset \\
\end{array}$
I understand that this is not what you asked and therefore it may not help.
However, in each case the given conclusion does follow.
3. Originally Posted by Plato
First, I totally agree with you. I see no reason to introduce $\alpha'$.
On the other hand, I am not sure that I follow your proof.
Here are the four cases that I would use.
$\begin{array}{l}
3)\;a \not\subset \beta \quad \& \quad \alpha \cap \beta = \emptyset \\
4)\;a \not\subset \beta \quad \& \quad \alpha \cap \beta \not= \emptyset \\
\end{array}$
I understand that this is not what you asked and therefore it may not help.
However, in each case the given conclusion does follow.
What specificaly you don't follow in my proof?
4. I think I see how it works. At least, I didn't understand the explination, but I see where A' comes in. (As I am too lazy to find the fancy characters, I will use A for the plane and a for the line.)
Given: line a
plane B
plane A
plane B || line a
line a is within plane A
not(plane A || plane B) | already proven that this can happen
Prove: a || the intersection of A and B
Proof:
Let there be a plane A', which is parallel to B and contains a.
Since A and B intersect, there must be a line b that is contained by both A and B.
So now there are parallel planes A' and B, each containing a line (a and b, repectively).
Since a and b are both within plane A, they must either intersect or be parallel. However, they are also the intersections of A and B and A and A', and B and A' are defined to be parallel, a and b must also be parallel.
Moreover, since b is defined as the intersection of A and B, a is parallel the intersection of A and B. And there is your proof.
Sorry if that was sketchy. I don't remeber my theorums from last year.
5. Originally Posted by OReilly
What specificaly you don't follow in my proof?
It seems to me as if you are extending or modifying the proof in the text.
I thought we agreed that the text is off the mark on its proof.
I also understand that my approach may not be helpful to you.
6. Originally Posted by The Pondermatic
I think I see how it works. At least, I didn't understand the explination, but I see where A' comes in. (As I am too lazy to find the fancy characters, I will use A for the plane and a for the line.)
Given: line a
plane B
plane A
plane B || line a
line a is within plane A
not(plane A || plane B) | already proven that this can happen
Prove: a || the intersection of A and B
Proof:
Let there be a plane A', which is parallel to B and contains a.
Since A and B intersect, there must be a line b that is contained by both A and B.
So now there are parallel planes A' and B, each containing a line (a and b, repectively).
Since a and b are both within plane A, they must either intersect or be parallel. However, they are also the intersections of A and B and A and A', and B and A' are defined to be parallel, a and b must also be parallel.
Moreover, since b is defined as the intersection of A and B, a is parallel the intersection of A and B. And there is your proof.
Sorry if that was sketchy. I don't remeber my theorums from last year.
Even without plane A' it can be proven that a is parallel to b.
If a wouldn't be parallel to b then it would intersect b and plane B so it must be parallel (since inital statement was that a is parallel to B). Also if b wouldn't be parallel to a then it would have only one common point with plane B which is again against inital assumption that b is common line to planes A and B.
7. Originally Posted by Plato | 1,630 | 6,201 | {"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": 50, "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} | 4.125 | 4 | CC-MAIN-2016-50 | longest | en | 0.911775 |
http://www.topperlearning.com/forums/ask-experts-19/a-in-the-mtbridge-the-balance-point-is-found-to-be-at-395-physics-electric-charges-and-fields-55849/reply | 1,487,599,913,000,000,000 | text/html | crawl-data/CC-MAIN-2017-09/segments/1487501170562.59/warc/CC-MAIN-20170219104610-00429-ip-10-171-10-108.ec2.internal.warc.gz | 630,648,560 | 37,854 |
Question
Fri May 25, 2012 By: Namami Gaur
# A) In the mt.bridge the balance point is found to be at 39.5 cm from the end A when the resistance Y is of 12.5ohm.Determine the resistance Of X.Why are the connections B/W resistors in the wheatstone bridge or mt. bridge made of the thick coper strips? B)Determine the balance point of the bridge if X & Y are interchanged. C)What happens if the the galvanometer & the cell are interchanged at the balance points of the bridge.Would the galvanometer should have any current?
Fri May 25, 2012
l = 39.5 cm
A)
R = X = ? , Y = 12.5 ohms
S = 100-l/l * R
12.5 = (100 - 39.5/39.5) * X
So X = 8.16 ohms
The thick copper strips are used to minimize the resistance of the connections which are not accounted in the above formula.
B) If X and Y are interchanged then
R = Y = 12.5 ohms
S = X = 8.16 ohms
X = (100-l)/l * R
8.16 = (100-l)/l * 12.5
From this equation l = 60.5 cm
The galvanometer will not show any current
Related Questions
Fri September 16, 2016
# please upload the imp problems of all the chapters in physics
Thu September 15, 2016
| 349 | 1,100 | {"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-2017-09 | longest | en | 0.898415 |
https://jonale.net/blog/archive.php?518fc2=differential-equations-and-vector-calculus | 1,619,027,430,000,000,000 | text/html | crawl-data/CC-MAIN-2021-17/segments/1618039546945.85/warc/CC-MAIN-20210421161025-20210421191025-00393.warc.gz | 438,022,890 | 7,462 | \begin{alignat}{2} (\text{a vector})\cdot\FLPnabla,\quad\text{or}\quad\FLPdiv{(\text{a The last term is the Laplacian, so we can Why not second derivatives? There are several reasons you might be seeing this page. \FLPA\times(\FLPA T)=(\FLPA\times\FLPA)T=\FLPzero, \label{Eq:II:2:27} \begin{alignat}{3} Of course fields in a convenient wayâin a way that is general, in that it A vector is Non-award/non-degree study If you wish to undertake one or more units of study (subjects) for your own interest but not towards a degree, you may enrol in single units as a non-award student. T\FLPA=\FLPA T, We have been applying our knowledge of ordinary easily appreciate, because if we took a different $x$-axis, $\ddpl{T}{x}$ Excellent introductory text for students with one year of calculus. You must always remember, of course, that $\FLPnabla$ is an \textit{Maxwellâs Equations}\\[1ex] a strictly mathematical senseâwas described by With operators we must always keep the equations contain the complete classical theory of the electromagnetic The same kind of arguments would show that $\ddpl{T}{y}$ is necessary to have a much broader understanding of the equations. for the small slab. physical vector having a meaning. The fourth section contains detailed discussions of first-order and linear second-order equations. 2â4 A physical understanding choose a different system (indicated by primes), we would you remember, we mean a quantity which depends upon position in passes, per unit time and per unit area, through an infinitesimal Also included are optional discussions of electric circuits and vibratory motion. (What we have said \label{Eq:II:2:21} Eq. Pitfall number two (which, again, we need not get into in our course) You will also find historical information in many textbooks vector field} Each side is a vector if $\kappa$ is just a In this book, vector differential calculus is considered, which extends the basic concepts of (ordinary) differential calculus, such as, continuity and differentiability to vector functions in a simple and natural way. If you have have visited this website previously it's possible you may have a mixture of incompatible files (.js, .css, and .html) in your browser cache. know. easy to remember because of the way the vectors work. As we did for $\FLPgrad{T}$, we can ascribe a physical significance vector heat flow at a point is the amount of thermal energy that &\text{If}&\FLPnabla\times\FLPA&=\FLPzero\notag\\[3pt] To make things a If any pair of numbers transforms with these equations in the same way we have defined earlier as the magnitude of $\FLPh$, whose direction variations with position in a similar way, because we are interested Fig. It still does not mean anything. know that $S$ is a scalar without investigating whether it true in certain situations, but which are not true in general. Diagonalization and the Exponential of a Matrix 8 5. But one can still get a very good idea of the behavior of a radial component of $\nabla^2\FLPh$. Maxwell equationsâare all there is to electrodynamics; it is admitted by the So far we have had only first derivatives. operator. instant. Or, solving for $x$ and $y$, We turn to that subject. \FLPcurl{(\FLPcurl{\FLPh})}=\FLPgrad{(\FLPdiv{\FLPh})}-\nabla^2\FLPh. The law is not a precise one, but for many metals and a How do we model that with PDE? Topics include complex numbers, determinants, orthonormal bases, symmetric and hermitian matrices, first order non-linear equations, linear differential equations, Laplace transforms, Bessel functions and boundary-value problems. define $\FLPh$. little simpler, we let $z=z'$, so that we can forget about the Differential Equations and Vector Calculus Book Description : In this book, how to solve such type equations has been elaborately described. So we The simplest possible physical field is a scalar field. \end{equation*} But the subject of physics has been (\FLPdiv{\FLPnabla})\FLPh. equality (2.6): Provides proofs and includes the definitions and statements of theorems to show how the subject matter can be organized around a few central ideas. \label{Eq:II:2:42} &(\text{e})&&\FLPcurl{(\FLPcurl{\FLPh})}= 2â7(b), so that Eq. sequence right, so that the operations make proper sense. 2â6(b). more compact form we have the product $(\FLPgrad{T})$. usually quite complicated, and any particular physical situation may notation! equations. number. where $\Delta s$ is the thickness of the slab. Vectors are introduced at the outset and serve at many points to indicate geometrical and physical significance of mathematical relations. We will look at arithmetic involving matrices and vectors, finding the inverse of a matrix, computing the determinant of a matrix, linearly dependent/independent vectors and converting systems of equations into matrix form. \label{Eq:II:2:46} . components. Now since the direction of $\FLPgrad{T}$ is opposite to we are dealing with the algebra of % ebook insert: \label{Eq:II:0:0} field. mathematical equations and if I understand them mathematically inside Chapter 1. \label{Eq:II:2:13} Index. \frac{\partial^2T}{\partial z^2}, We write this operations with components. What it means really to understand an equationâthat is, in more than like (2.42) in the more sophisticated vector notation. and if $\FLPA$ and $\FLPB$ are vectors, we knowâbecause we proved it in (2.56). \label{Eq:II:2:18} field. (2.15) also illustrates clearly our proof above \nabla_x(\nabla_xT)+\nabla_y(\nabla_yT)+\nabla_z(\nabla_zT)\notag\\[1ex] Now letâs multiply $\FLPnabla$ by a scalar on the other side, so that The gradient of $T$ has electromagnetism, but for all kinds of physical circumstances. would you say about the following expression, that involves the two Eq. in Chapter 11 of Vol. havenât been careful enough about keeping the order of our terms area $A$ of the faces, and to the temperature difference. They find their generalization in stochastic partial differential equations. &(3)&\quad\FLPdiv{\FLPB}\;&=0\\[.5ex] that we shall have a tendency to lose in these lectures is the Fortunately, we wonât have to use such expressions. \label{Eq:II:2:52} Provides many routine, computational exercises illuminating both theory and practice. It goes the same for the measure of how much heat is flowing. \FLPh=\frac{\Delta J}{\Delta a}\,\FLPe_f, In particular, $\Delta T$ is a number other concepts. doesnât change the fact that $\FLPcurl{\FLPgrad{\psi}}=\FLPzero$ for way. The ultimate idea is to explain the meaning For instance, if $S=\FLPA\cdot\FLPB$, position (Fig. So we shall express all of our vector \end{equation*} If the area of the small slab is $\Delta A$, the heat flow per unit \label{Eq:II:2:28} Because it appears often in physics, it has been given a special (You can check out the more general case for yourself.). Vector calculus, or vector analysis, is concerned with differentiation and integration of vector fields, primarily in 3-dimensional Euclidean space {\displaystyle \mathbb {R} ^{3}. They have the advantage of being Tech. This requires that you difference $\Delta T=T_2-T_1$. \label{Eq:II:2:32} actual physical situations in the real world are so complicated that it radial component changes from point to point. It is hoped that in the 2â7(b). into a lot of trouble when we start to differentiate the \end{align}. of differential equations. is the following: The rules that we have outlined here are simple and which is the same number as would be gotten from If we \end{equation*} material of the body at any point is a vector which is a function of differentiated must be placed on the right of the $\FLPnabla$. are imaginary surfaces drawn through all points for which the field has | 1,964 | 7,731 | {"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": 2, "x-ck12": 0, "texerror": 0} | 3.859375 | 4 | CC-MAIN-2021-17 | latest | en | 0.91262 |
https://www.crackverbal.com/solutions/if-snow-accumulation-increased-at-a-constant-rate-of-30-millimeters-per-hour-during-a-certain/ | 1,726,060,785,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651387.63/warc/CC-MAIN-20240911120037-20240911150037-00189.warc.gz | 671,625,570 | 22,269 | # Solutions
Get detailed explanations to advanced GMAT questions.
### Question
If snow accumulation increased at a constant rate of 30 millimeters per hour during a certain snowstorm, how many seconds did it take for snow accumulation to increase by 1 millimeter?
Option A:
1/120
Option B:
1/60
Option C:
1/20
Option D:
20
Option E:
120
Easy
### Solution
Option E is the correct answer.
### Option Analysis
Given the rate is 30 millimeters per hour.
I hour = 3600 Seconds
30 millimeters = 3600 Seconds
1 millimetre = 120 Seconds | 137 | 549 | {"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-2024-38 | latest | en | 0.806318 |
http://en.wikipedia.org/wiki/Nilpotent_group | 1,432,511,619,000,000,000 | text/html | crawl-data/CC-MAIN-2015-22/segments/1432207928102.74/warc/CC-MAIN-20150521113208-00275-ip-10-180-206-219.ec2.internal.warc.gz | 78,693,981 | 15,972 | # Nilpotent group
In group theory, a nilpotent group is a group that is "almost abelian". This idea is motivated by the fact that nilpotent groups are solvable, and for finite nilpotent groups, two elements having relatively prime orders must commute. It is also true that finite nilpotent groups are supersolvable.
Nilpotent groups arise in Galois theory, as well as in the classification of groups. They also appear prominently in the classification of Lie groups.
Analogous terms are used for Lie algebras (using the Lie bracket) including nilpotent, lower central series, and upper central series.
## Definition
The definition uses the idea, explained on its own page, of a central series for a group. The following are equivalent formulations:
• A nilpotent group is one that has a central series of finite length.
• A nilpotent group is one whose lower central series terminates in the trivial subgroup after finitely many steps.
• A nilpotent group is one whose upper central series terminates in the whole group after finitely many steps.
For a nilpotent group, the smallest n such that G has a central series of length n is called the nilpotency class of G ; and G is said to be nilpotent of class n. (By definition, the length is n if there are n + 1 different subgroups in the series, including the trivial subgroup and the whole group.)
Equivalently, the nilpotency class of G equals the length of the lower central series or upper central series. If a group has nilpotency class at most m, then it is sometimes called a nil-m group.
It follows immediately from any of the above forms of the definition of nilpotency, that the trivial group is the unique group of nilpotency class 0, and groups of nilpotency class 1 are exactly the non-trivial abelian groups.[1][2]
## Examples
A portion of the Cayley graph of the discrete Heisenberg group, a well-known nilpotent group.
• As noted above, every abelian group is nilpotent.[1][3]
• For a small non-abelian example, consider the quaternion group Q8, which is a smallest non-abelian p-group. It has center {1, −1} of order 2, and its upper central series is {1}, {1, −1}, Q8; so it is nilpotent of class 2.
• All finite p-groups are in fact nilpotent (proof). The maximal class of a group of order pn is n - 1. The 2-groups of maximal class are the generalised quaternion groups, the dihedral groups, and the semidihedral groups.
• The direct product of two nilpotent groups is nilpotent.[4]
• Conversely, every finite nilpotent group is the direct product of p-groups.[5]
• The Heisenberg group is an example of non-abelian,[6] infinite nilpotent group.[7]
• The multiplicative group of upper unitriangular n x n matrices over any field F is a nilpotent group of nilpotent length n - 1 .
• The multiplicative group of invertible upper triangular n x n matrices over a field F is not in general nilpotent, but is solvable.
## Explanation of term
Nilpotent groups are so called because the "adjoint action" of any element is nilpotent, meaning that for a nilpotent group G of nilpotence degree n and an element g, the function $\operatorname{ad}_g \colon G \to G$ defined by $\operatorname{ad}_g(x) := [g,x]$ (where $[g,x]=g^{-1} x^{-1} g x$ is the commutator of g and x) is nilpotent in the sense that the nth iteration of the function is trivial: $\left(\operatorname{ad}_g\right)^n(x)=e$ for all $x$ in $G$.
This is not a defining characteristic of nilpotent groups: groups for which $\operatorname{ad}_g$ is nilpotent of degree n (in the sense above) are called n-Engel groups,[8] and need not be nilpotent in general. They are proven to be nilpotent if they have finite order, and are conjectured to be nilpotent as long as they are finitely generated.
An abelian group is precisely one for which the adjoint action is not just nilpotent but trivial (a 1-Engel group).
## Properties
Since each successive factor group Zi+1/Zi in the upper central series is abelian, and the series is finite, every nilpotent group is a solvable group with a relatively simple structure.
Every subgroup of a nilpotent group of class n is nilpotent of class at most n;[9] in addition, if f is a homomorphism of a nilpotent group of class n, then the image of f is nilpotent[9] of class at most n.
The following statements are equivalent for finite groups,[10] revealing some useful properties of nilpotency:
• G is a nilpotent group.
• If H is a proper subgroup of G, then H is a proper normal subgroup of NG(H) (the normalizer of H in G). This is called the normalizer property and can be phrased simply as "normalizers grow".
• Every maximal proper subgroup of G is normal.
• G is the direct product of its Sylow subgroups.
The last statement can be extended to infinite groups: if G is a nilpotent group, then every Sylow subgroup Gp of G is normal, and the direct product of these Sylow subgroups is the subgroup of all elements of finite order in G (see torsion subgroup).
Many properties of nilpotent groups are shared by hypercentral groups.
## Notes
1. ^ a b Suprunenko (1976). Matrix Groups. p. 205.
2. ^ Tabachnikova & Smith (2000). Topics in Group Theory (Springer Undergraduate Mathematics Series). p. 169.
3. ^ Hungerford (1974). Algebra. p. 100.
4. ^ Zassenhaus (1999). The theory of groups. p. 143.
5. ^ Zassenhaus (1999). Theorem 11. p. 143.
6. ^ Haeseler (2002). Automatic Sequences (De Gruyter Expositions in Mathematics, 36). p. 15.
7. ^ Palmer (2001). Banach algebras and the general theory of *-algebras. p. 1283.
8. ^ For the term, compare Engel's theorem, also on nilpotency.
9. ^ a b Bechtell (1971), p. 51, Theorem 5.1.3
10. ^ Isaacs (2008), Thm. 1.26
## References
• Homology in group theory, by Urs Stammbach, Lecture Notes in Mathematics, Volume 359, Springer-Verlag, New York, 1973, vii+183 pp. review
• Suprunenko, D. A. (1976). Matrix Groups. Providence, Rhode Island: American Mathematical Society. ISBN 0-8218-1341-2.
• Hungerford, Thomas Gordon (1974). Algebra. Berlin: Springer-Verlag. ISBN 0-387-90518-9.
• Palmer, Theodore W. (1994). Banach algebras and the general theory of *-algebras. Cambridge, UK: Cambridge University Press. ISBN 0-521-36638-0.
• Friedrich Von Haeseler (2002). Automatic Sequences (De Gruyter Expositions in Mathematics, 36). Berlin: Walter de Gruyter. ISBN 3-11-015629-6.
• Isaacs, I. Martin (2008). Finite group theory. American Mathematical Society. ISBN 0-8218-4344-3.
• Zassenhaus, Hans (1999). The theory of groups. New York: Dover Publications. ISBN 0-486-40922-8.
• Bechtell, Homer (1971). The theory of groups. Addison-Wesley.
• Tabachnikova, Olga; Smith, Geoff (2000). Topics in Group Theory (Springer Undergraduate Mathematics Series). Berlin: Springer. ISBN 1-85233-235-2. | 1,818 | 6,716 | {"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": 7, "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} | 3.34375 | 3 | CC-MAIN-2015-22 | latest | en | 0.939418 |
http://forums.wolfram.com/mathgroup/archive/2006/Nov/msg00828.html | 1,529,942,509,000,000,000 | text/html | crawl-data/CC-MAIN-2018-26/segments/1529267868135.87/warc/CC-MAIN-20180625150537-20180625170537-00343.warc.gz | 119,209,912 | 7,397 | Re: Plotting a function -
• To: mathgroup at smc.vnet.net
• Subject: [mg71666] Re: Plotting a function -
• From: Bill Rowe <readnewsciv at sbcglobal.net>
• Date: Sun, 26 Nov 2006 03:48:49 -0500 (EST)
On 11/25/06 at 5:37 AM, tharkun860 at publicspam.com (Craig Reed) wrote:
>Hi -
>
>I'm trying to get Mathematica 5.2 to graph a function which is the
>ratio of integers which have a '3' in them. Done in Exce3l, the
>graph of the first 32,000 data points has a fractal look to it,
>especially when done with a log scale.
>What I've tried is the following
>f[x_] := Boole[DigitCount[x, 10, 3]]
>g[x_] := Sum[f, {i, x}]/x
>Plot[g, {x, 1, 100}]
>I get 3 errors of "g is not a michine-size real number at" followed
>by 3 real numbers: 1.000004125 5.016125..... 9.39607.....
>What am I doing wrong? or perhaps what I should ask is, "Is there a
>better way?"
You have a variety of errors in your code that are causing the
problem. You have defined the functions f and g to have an
argument. Yet when you call the function you don't supply an
argument. That is g needs to be defined as follows:
g[x_]:=Sum[f[i],{i,x}]/x
Similarly when you plot g the syntax is
Plot[g[x],{x,1,100}]
But you also have a problem with your definition of f. The
argument to Boole needs to be an expression not an integer that
will be returned by DigitCount. That is you need something like
f[x_]:=Boole[DigitCount[x,10,3]>0]
--
To reply via email subtract one hundred and four
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https://www.gristprojectmanagement.us/planning-scheduling/definition-of-risk.html | 1,561,640,044,000,000,000 | text/html | crawl-data/CC-MAIN-2019-26/segments/1560628001138.93/warc/CC-MAIN-20190627115818-20190627141818-00284.warc.gz | 755,514,461 | 8,379 | ## Definition Of Risk
Risk is a measure of the probability and consequence of not achieving a defined project goal. Most people agree that risk involves the notion of uncertainty. Can the specified aircraft range be achieved? Can the computer be produced within budgeted cost? Can the new product launch date be met? A probability measure can be used for such questions; for example, the probability of not meeting the new product launch date is 0.15. However, when risk is considered, the consequences or damage associated with occurrence must also be considered.
Goal A, with a probability of occurrence of only 0.05, may present a much more serious (risky) situation than goal B, with a probability of occurrence of 0.20, if the consequences of not meeting goal A are, in this case, more than four times more severe than failure to meet goal B. Risk is not always easy to assess, since the probability of occurrence and the consequence of occurrence are usually not directly measurable parameters and must be estimated by statistical or other procedures. Risk has two primary components for a given event:
• A probability (likelihood) of occurrence of that event
• Impact of the event occurring (amount at stake)
Figure 17-1 shows the components of risk.
Conceptually, risk for each event can be defined as a function of likelihood and impact; that is,
Risk = f (Likelihood, impact)
In general, as either the likelihood or impact increases, so does the risk. Both the likelihood and impact must be considered in risk management.
What you need to know about… Project Management Made Easy! Project management consists of more than just a large building project and can encompass small projects as well. No matter what the size of your project, you need to have some sort of project management. How you manage your project has everything to do with its outcome.
Get My Free Ebook | 380 | 1,889 | {"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-2019-26 | latest | en | 0.951041 |
synergy.thunderstruckcanada.com | 1,537,691,457,000,000,000 | text/html | crawl-data/CC-MAIN-2018-39/segments/1537267159165.63/warc/CC-MAIN-20180923075529-20180923095929-00016.warc.gz | 232,625,822 | 7,344 | We recognise and appreciate different situations. You may have dancers in a single routine and others in multiple ones. We use the number of dancers as a formula, but you are welcome to develop a policy for how to allocate the fees.
One option is to break dancers into three groups. For this example, let's say we have ten dancers so that the total will be \$150+tax. Let's use groups of 1 to 5 routines, 6 to 10, and 11 plus. Dancers in the bottom group pay \$10+tax, middle group pay the \$15+tax. By just adding up the total for the first two you can subtract it from to total. The difference, divided by the number of dancers in the 11+ groups is what they pay, which in this example would be \$17+tax.
Routines Dancers Fee Total 1 to 5 2 \$10 \$20 6 to 10 3 \$15 \$45 11+ 5 \$17 \$85 \$150 | 211 | 797 | {"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-2018-39 | longest | en | 0.931098 |
https://origin.geeksforgeeks.org/algorithms-quiz-sudo-placement-1-5-question-8/ | 1,660,316,874,000,000,000 | text/html | crawl-data/CC-MAIN-2022-33/segments/1659882571719.48/warc/CC-MAIN-20220812140019-20220812170019-00045.warc.gz | 416,177,947 | 25,532 | # Algorithms Quiz | Sudo Placement [1.5] | Question 8
• Last Updated : 16 Aug, 2018
Below is the code to find maximum subarray sum, with errors (which may results to wrong output) in the statement which is commented on right half after code statement. You need to choose the correct option for which corresponding statement is wrong.
`#include ` `using namespace std; ` ` ` `// Function to calculate maximum subarray sum ` `int maxSubArraySum(int a[ ], int size) ` `{ ` ` ``int max_so_far = a[0]; ` ` ``int curr_max = a[0]; ` ` ` ` ``for (int i = 1; i < size; i++) ` ` ``{ ` ` ``curr_max = max(a[i], curr_max); // statement 1 ` ` ``max_so_far = max(max_so_far, curr_max); // statement 2 ` ` ``} ` ` ``return max_so_far; ` `} ` ` ` `/* Driver program to test maxSubArraySum */ ` `int main() ` `{ ` ` ``int a[] = {-2, -3, 4, -1, -2, 1, 5, -3}; ` ` ``int n = sizeof(a)/sizeof(a[0]); ` ` ``int max_sum = maxSubArraySum(a, n); ` ` ``cout << "Maximum contiguous sum is " << max_sum; ` ` ``return 0; ` `} `
(A) Statement 1 and statement 2 both.
(B) Statement 1 only.
(C) Statement 2 only.
(D) Neither statement 1 nor statement 2. | 392 | 1,170 | {"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-2022-33 | latest | en | 0.5277 |
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Hello, I am looking for someone to write an essay on Estimate critical analysis of the companys recent history with Financial Analysis of Heartland Express company. It needs to be at least 2250 words.
(Rm-Rf) is the risk premium rate and beta can be defined as a measure of how much the stock and market move together. The following values have been traced through relevant financial sources
WACC or the weighted average cost of capital is the weighted average cost of the company’s equity and long term debt. WACC is calculated by multiplying the cost of equity with the market value of the equity and cost of debt with the market value of the debt. Cost of debt is usually the interest rate that the company’s pay on its long term and short term financial borrowings. However, an analysis of the company’s financial statements will show that the company does have any long term or short term interest bearing financial debts. All of its debts comprise of trading nature and the company does have to pay any interest on such securities. Does the cost of debt for the heartland express is nil. Keeping all the above factors into consideration, the WACC of heartland express is equal to its cost of equity i.e. 6.11%
The estimated value of the company’s equity is calculated by discounting the free cash flow of the company for the foreseeable future using the weighted average cost of capital of the company (WACC). Free cash flow method is basically a measure of financial performance of the company which is calculated as free cash flows minus the capital expenditure. From pure financial management’s perspective, free cash flow can be defined as the cash which the company is able to generate setting aside the money required to maintain or expand its current asset base. The following table presents the free cash flow calculation and the equity value of the company as at financial year end December 31, 2010.
Note 2: In the free cash flow method, the depreciation and amortization expense are added to the profit after taxes since these are the non-cash items. For the | 432 | 2,163 | {"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-2024-18 | latest | en | 0.945968 |
http://slideplayer.com/slide/4317170/ | 1,527,254,252,000,000,000 | text/html | crawl-data/CC-MAIN-2018-22/segments/1526794867092.48/warc/CC-MAIN-20180525121739-20180525141739-00067.warc.gz | 267,129,102 | 23,407 | # What are primes in graphs and how many of them have a given length? Audrey Terras Math. Club Oct. 30, 2008.
## Presentation on theme: "What are primes in graphs and how many of them have a given length? Audrey Terras Math. Club Oct. 30, 2008."— Presentation transcript:
What are primes in graphs and how many of them have a given length? Audrey Terras Math. Club Oct. 30, 2008
A graph is a bunch of vertices connected by edges. The simplest example for the talk is the tetrahedron K 4. A prime in a graph is a closed path in the graph minimizing the number of edges traversed. This means no backtrack, no tails. Go around only once. Orientation counts. Starting point doesn’t count. The length of a path is the number of edges in the path. The talk concerns the prime number theorem in this context. Degree of a vertex is number of edges incident to it. Graph is regular if each vertex has same degree. K 4. is 3-regular. We assume graphs connected, no degree 1 vertices, and graph is not a cycle.
Examples of primes in K 4 e1e1 e3e3 e2e2 e4e4 e5e5 Here are 2 of them in K 4 : [C] =[e 1 e 2 e 3 ] ={e 1 e 2 e 3, e 2 e 3 e 1, e 3 e 1 e 2 } The [] means that it does not matter where the path starts. [D]=[e 4 e 5 e 3 ] [E]=[e 1 e 2 e 3 e 4 e 5 e 3 ] (C) =length C= # edges in C (C)=3, (D)=3, (E)=6 E=CD another prime [C n D], n=2,3,4, … infinitely many primes assuming the graph is not a cycle or a cycle with hair.
Ihara Zeta Function Definition Ihara’s Theorem (Bass, Hashimoto, etc.) A = adjacency matrix of X= |V|x|V| matrix of 0s and 1s with i,j entry 1 iff vertex i adjacent to vertex j Q = diagonal matrix; jth diagonal entry = degree jth vertex -1; r = |E|-|V|+1 u complex number |u| small enough
e1e1 e7e7 Labeling Edges of Graphs Orient the m edges; i.e., put arrows on them. Label them as follows. Here the inverse edge has opposite orientation. e 1,e 2,…,e m, e m+1 =(e 1 ) -1,…,e 2m =(e m ) -1 Note that these directed edges are our alphabet needed to express paths in the graph.
The Edge Matrix W Define W to be the 2|E| 2|E| matrix with i j entry 1 if edge i feeds into edge j, (end vertex of i is start vertex of j) provided that j the inverse of i, otherwise the i j entry is 0. ijij Theorem. (u,X) -1 =det(I-Wu). Corollary. The poles of Ihara zeta are the reciprocals of the eigenvalues of W. The pole R of zeta is the closest to 0 in absolute value. R=1/Perron-Frobenius eigenvalue of W; i.e., the largest eigenvalue which has to be positive real. See Horn & Johnson, Matrix Analysis, Chapter 8.
Example. W for the Tetrahedron Label the edges The inverse of edge j is edge j+6. e1e1 e3e3 e2e2 e4e4 e5e5 e6e6 e7e7
There are elementary proofs of the 2 determinant formulas for zeta, even for X irregular. See my book on my website www.math.ucsd.edu/~aterras/newbook.pdf If you are willing to believe these formulas, we can give a rather easy proof of the graph theory prime number theorem. But first state the prime number thm and give some examples.
The Prime Number Theorem X (m) = # {primes [C] in X of length m} = greatest common divisor of lengths of primes in X R = radius of largest circle of convergence of (u,X) If divides m, then X (m) R -m /m, as m . The proof involves formulas like the following, defining N m = # {closed paths of length m where we count starting point and orientation} R=1/q, if graph is q+1- regular The proof is similar to one in Rosen, Number Theory in Function Fields, p. 56.
2 Examples K 4 and K 4 -edge
N m for the examples (3)=8 (orientation counts) (4)=6 (5)=0 we will show that: (3)=4 (4)=2 (5)=0 (6)=2 x d/dx log (x,K 4 ) = 24x 3 + 24x 4 + 96x 6 + 168x 7 + 168x 8 + 528x 9 + x d/dx log (x,K 4 -e) =12x 3 + 8x 4 + 24x 6 + 28x 7 + 8x 8 + 48x 9 + Example 1. The Tetrahedron K 4. N m =# closed paths of length m Example 2. The Tetrahedron minus an edge. = g.c.d. lengths of primes = 1
Poles of Zeta for K 4 are {1,1,1,-1,-1,½,r +,r +,r +,r -,r -,r - } where r =(-1 -7)/4 and |r|=1/ 2 R=½=Pole closest to 0 The prime number thm (m) R -m /m, as m . becomes K 4 (m) 2 m /m, as m . Poles of zeta for K 4 -e are {1,1,-1,i,-i,r +,r -, , , } R = real root of cubic .6573 complex root of cubic The prime number thm becomes for 1/ 1.5 K 4 -e (m) 1.5 m /m, as m .
Proof of Prime Number Theorem Start with the definition of zeta as a product over primes. Take log and a derivative. Use Taylor series. non-primes are powers of primes #[C]= (C) Taylor Series for log(1-x)
Next we note another formula for the zeta function coming from the original definition. Recall (n) = # primes [C] with (C)=n This completes the proof of the first formula (1)
If you combine this with formula 1, which was you get our 2nd formula saying N m is a sum over the positive divisors of m: (2) Taylor Series for (1-x) -1
This is a math 104 (number theory) -type formula and there is a way to invert it using the Mobius function defined by: To complete the proof, we need to use one of our 2 determinant formulas for zeta. (u,X) -1 =det(I-Wu). (3)
Fact from linear algebra - Schur Decomposition of a Matrix (Math 102) There is an orthogonal matrix Q (i.e., QQ t =I) and T=upper triangular with eigenvalues of W along the diagonal such that W=QTQ -1. So we see that
(u,X) -1 =det(I-Wu) = It follows that (4)
The main terms in this sum come from the largest eigenvalues of W in absolute value. There is a theorem in linear algebra that you don’t learn in a 1st course called the Perron-Frobenius theorem. (Horn & Johnson, Matrix Analysis, Chapter 8). It applies to our W matrices assuming we are looking at connected graphs (no degree 1 vertices) & not cycles. The easiest case is that =g.c.d. lengths of primes = 1. Then there is only 1 eigenvalue of W of largest absolute value. It is positive and is called the Perron-Frobenius eigenvalue. Moreover it is 1/R, R=closest pole of zeta to 0. So we find that if =1, N m ≈ R -m, as m .
If =1, N m ≈ R -m, as m . To figure out what happens to (m), use This allows you to prove the prime number theorem when =1 p X (m) R -m /m, as m . For the general case, see my book www.math.ucsd/~aterras/newbook.pdf
Download ppt "What are primes in graphs and how many of them have a given length? Audrey Terras Math. Club Oct. 30, 2008."
Similar presentations | 2,135 | 6,352 | {"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} | 4.25 | 4 | CC-MAIN-2018-22 | latest | en | 0.92178 |
https://number.academy/1008443 | 1,718,975,892,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198862125.45/warc/CC-MAIN-20240621125006-20240621155006-00776.warc.gz | 368,813,915 | 11,109 | # Number 1008443 facts
The odd number 1,008,443 is spelled 🔊, and written in words: one million, eight thousand, four hundred and forty-three, approximately 1.0 million. The ordinal number 1008443rd is said 🔊 and written as: one million, eight thousand, four hundred and forty-third. The meaning of the number 1008443 in Maths: Is it Prime? Factorization and prime factors tree. The square root and cube root of 1008443. What is 1008443 in computer science, numerology, codes and images, writing and naming in other languages
## What is 1,008,443 in other units
The decimal (Arabic) number 1008443 converted to a Roman number is (M)(V)MMMCDXLIII. Roman and decimal number conversions.
#### Time conversion
(hours, minutes, seconds, days, weeks)
1008443 seconds equals to 1 week, 4 days, 16 hours, 7 minutes, 23 seconds
1008443 minutes equals to 2 years, 1 month, 7 hours, 23 minutes
### Codes and images of the number 1008443
Number 1008443 morse code: .---- ----- ----- ---.. ....- ....- ...--
Sign language for number 1008443:
Number 1008443 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 1008443 is not a prime number. The closest prime numbers are 1008437, 1008451.
#### Factorization and factors (dividers)
The prime factors of 1008443 are 197 * 5119
The factors of 1008443 are 1, 197, 5119, 1008443.
Total factors 4.
Sum of factors 1013760 (5317).
#### Powers
The second power of 10084432 is 1.016.957.284.249.
The third power of 10084433 is 1.025.543.454.599.914.368.
#### Roots
The square root √1008443 is 1004,212627.
The cube root of 31008443 is 100,280645.
#### Logarithms
The natural logarithm of No. ln 1008443 = loge 1008443 = 13,823918.
The logarithm to base 10 of No. log10 1008443 = 6,003651.
The Napierian logarithm of No. log1/e 1008443 = -13,823918.
### Trigonometric functions
The cosine of 1008443 is -0,378172.
The sine of 1008443 is -0,925735.
The tangent of 1008443 is 2,447923.
## Number 1008443 in Computer Science
Code typeCode value
1008443 Number of bytes984.8KB
Unix timeUnix time 1008443 is equal to Monday Jan. 12, 1970, 4:07:23 p.m. GMT
IPv4, IPv6Number 1008443 internet address in dotted format v4 0.15.99.59, v6 ::f:633b
1008443 Decimal = 11110110001100111011 Binary
1008443 Decimal = 1220020022202 Ternary
1008443 Decimal = 3661473 Octal
1008443 Decimal = F633B Hexadecimal (0xf633b hex)
1008443 BASE64MTAwODQ0Mw==
1008443 MD5e36603afb95483ff6787a8b0345c4b4d
1008443 SHA1e62008beb1165b699c979856a77fa9dec0355cfc
1008443 SHA2562b02b6efb58c2f82418d87ddbd8b5d3a36acf8059dbace9bed85df33acff2d95
1008443 SHA384b9e6942cdd68089189fc99717e89c170b847e5f364f6c39d8d59e9cd7d289c43840249a3743cf896cf2a4f696e89d50e
More SHA codes related to the number 1008443 ...
If you know something interesting about the 1008443 number that you did not find on this page, do not hesitate to write us here.
## Numerology 1008443
### Character frequency in the number 1008443
Character (importance) frequency for numerology.
Character: Frequency: 1 1 0 2 8 1 4 2 3 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 1008443, the numbers 1+0+0+8+4+4+3 = 2+0 = 2 are added and the meaning of the number 2 is sought.
## № 1,008,443 in other languages
How to say or write the number one million, eight thousand, four hundred and forty-three in Spanish, German, French and other languages. The character used as the thousands separator.
Spanish: 🔊 (número 1.008.443) un millón ocho mil cuatrocientos cuarenta y tres German: 🔊 (Nummer 1.008.443) eine Million achttausendvierhundertdreiundvierzig French: 🔊 (nombre 1 008 443) un million huit mille quatre cent quarante-trois Portuguese: 🔊 (número 1 008 443) um milhão e oito mil, quatrocentos e quarenta e três Hindi: 🔊 (संख्या 1 008 443) दस लाख, आठ हज़ार, चार सौ, तैंतालीस Chinese: 🔊 (数 1 008 443) 一百万八千四百四十三 Arabian: 🔊 (عدد 1,008,443) مليون و ثمانية آلاف و أربعمائة و ثلاثة و أربعون Czech: 🔊 (číslo 1 008 443) milion osm tisíc čtyřista čtyřicet tři Korean: 🔊 (번호 1,008,443) 백만 팔천사백사십삼 Danish: 🔊 (nummer 1 008 443) en millioner ottetusinde og firehundrede og treogfyrre Hebrew: (מספר 1,008,443) מיליון ושמונת אלפים ארבע מאות ארבעים ושלוש Dutch: 🔊 (nummer 1 008 443) een miljoen achtduizendvierhonderddrieënveertig Japanese: 🔊 (数 1,008,443) 百万八千四百四十三 Indonesian: 🔊 (jumlah 1.008.443) satu juta delapan ribu empat ratus empat puluh tiga Italian: 🔊 (numero 1 008 443) un milione e ottomilaquattrocentoquarantatre Norwegian: 🔊 (nummer 1 008 443) en million åtte tusen fire hundre og førtitre Polish: 🔊 (liczba 1 008 443) milion osiem tysięcy czterysta czterdzieści trzy Russian: 🔊 (номер 1 008 443) один миллион восемь тысяч четыреста сорок три Turkish: 🔊 (numara 1,008,443) birmilyonsekizbindörtyüzkırküç Thai: 🔊 (จำนวน 1 008 443) หนึ่งล้านแปดพันสี่ร้อยสี่สิบสาม Ukrainian: 🔊 (номер 1 008 443) один мільйон вісім тисяч чотириста сорок три Vietnamese: 🔊 (con số 1.008.443) một triệu tám nghìn bốn trăm bốn mươi ba Other languages ...
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https://iwant2study.org/taskmeisterx/index.php/interactive-resources/physics/02-newtonian-mechanics/09-oscillations/775-picup-hanging-sho-python-frem | 1,713,950,558,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296819089.82/warc/CC-MAIN-20240424080812-20240424110812-00693.warc.gz | 288,264,643 | 17,068 | Intro Page
Simple Hanging Harmonic Oscillator
Developed by K. Roos
In this set of exercises the student builds a computational model of a hanging mass-spring system that is constrained to move in 1D, using the simple Euler and the Euler-Cromer numerical schemes. The student is guided to discover, by using the model to produce graphs of the position, velocity, and energy of the mass as a function of time, that the Euler algorithm does not conserve energy, and that for this simple oscillatory system, a modified algorithm (Euler-Cromer) is necessary to avoid artificial behavior in the model.
Subject Area Mechanics First Year and Beyond the First Year C/C++, Fortran, IPython/Jupyter Notebook, Mathematica, Octave*/MATLAB, Python, and Spreadsheet Students who complete this set of exercises will be able to build a model of a simple hanging harmonic oscillator using the Euler algorithm (Exercises 1 and 2); be able to build a model of a simple hanging harmonic oscillator using the Euler-Cromer algorithm (Exercises 4 and 5); be able to produce graphs of the positon, velocity, and total energy as a function of time from the results of their computational model (Exercises 1-5); be able to assess the accuracy of two different computational algorithms (Euler and Euler-Cromer) by comparing results from the different algorithms to each other and to the exact analytical solution (Exercises 1-5); discover that they bloody well can’t use the simple Euler method when modeling an oscillatory system (Exercises 1-3).
Hanging_SHO_Python.py
# Written by:
# Kelly Roos
# Engineering Physics
# This email address is being protected from spambots. You need JavaScript enabled to view it. | 309.677.2997
import numpy as np
import matplotlib.pyplot as plt
import math
# Input parameters for model
dt = 0.01 # time step (s)
vi = 0 # initial velocity (m/s)
yi = 0.1 # initial position (m), relative to eq position yeq (m)
m = 1.0 # mass (kg)
g = 9.8 # gravity (m/s^2)
k = 10 # spring constant (N/m)
t_steps = 2000 # number of time steps
# Defines the 1D arrays to be used in the computation and
# sets all values in the arrays to zero
time = np.zeros(t_steps)
y_Euler = np.zeros(t_steps)
y_EC = np.zeros(t_steps)
y_exact = np.zeros(t_steps)
v_Euler = np.zeros(t_steps)
v_EC = np.zeros(t_steps)
v_exact = np.zeros(t_steps)
energyEuler = np.zeros(t_steps);
energyEC = np.zeros(t_steps);
# Initial conditions
time[1] = 0
y_Euler[1] = yi
y_EC[1] = yi
y_exact[1] = yi
v_Euler[1] = vi
v_EC[1] = vi
v_exact[1] = vi
energyEuler[1]=0.5*m*v_Euler[1]**2+0.5*k*(y_Euler[1]+m*g/k)**2-m*g*(y_Euler[1]+m*g/k)
energyEC[1]=0.5*m*v_EC[1]**2+0.5*k*(y_EC[1]+m*g/k)**2-m*g*(y_EC[1]+m*g/k)
# Main loop: Euler algorithm, euler-Cromer, and evaluation of exact solutions for v and y
for i in range(2, t_steps):
time[i] = time[i-1] + dt
# Euler
v_Euler[i]=v_Euler[i-1]-k*y_Euler[i-1]*dt/m
y_Euler[i]=y_Euler[i-1]+v_Euler[i-1]*dt
# Euler-Cromer
v_EC[i]=v_EC[i-1]-k*y_EC[i-1]*dt/m
y_EC[i]=y_EC[i-1]+v_EC[i]*dt
# Exact (assuming vi=0)
v_exact[i]=-yi*math.sqrt(k/m)*math.sin(math.sqrt(k/m)*time[i])
y_exact[i]=yi*math.cos(math.sqrt(k/m)*time[i])
# Energies
energyEuler[i]=0.5*m*v_Euler[i]**2+0.5*k*(y_Euler[i]+m*g/k)**2-m*g*(y_Euler[i]+m*g/k)
energyEC[i]=0.5*m*v_EC[i]**2+0.5*k*(y_EC[i]+m*g/k)**2-m*g*(y_EC[i]+m*g/k)
# Plotting Results
plt.plot(time, v_Euler, time, v_EC)
plt.ylim((-0.3, 0.3))
plt.xlim((0, 20))
plt.xlabel('time (s)')
plt.ylabel('position (m)')
plt.title('position vs. time')
plt.show()
Exercise 1
#### Exercise 1: Euler Algorithm Model of a SHO
Build a computational model of a simple hanging harmonic oscillator using the Euler method. Use realistic values for the parameters (i.e., spring constant and attached mass , such as would be encountered in a typical introductory mechanics laboratory exercise. Also, assume that the mass of the spring is negligible compared to the attached mass, and that the harmonic oscillator has been stretched vertically downward a distance , relative to its hanging equilibrium position and released from rest. Use the model to produce graphs of the position and velocity of the mass as a function of time, and compare these with the exact functions for the position and velocity,
and
that result from solving Newton’s 2nd Law analytically. Does the angular frequency match that expected for a simple harmonic oscillator of mass an spring constant ?
Exercise 2
#### Exercise 2: Artificial Behavior with the Euler Algorithm
You may (should!) have noticed that something is not right with the Euler model of your hanging oscillator. Describe in detail the artificial behavior you observe in your model, and explain why it doesn’t represent a realistic oscillating mass. Recall that in the Euler method, the accuracy of the solution can be increased by using a smaller value of . Can you get rid of the artificial behavior by making smaller?
Exercise 3
#### Exercise 3: Energy in the Euler Algorithm Model of a SHO
Modify your model to produce a graph of the total energy of the oscillator as a function of time. Describe in detail what happens to the energy, and the artificial behavior observed. Can this artificial behavior in the energy be corrected by making smaller? What can you conclude about using the Euler method to model a simple harmonic oscillator?
Exercise 4
#### Exercise 4: Euler-Cromer Algorithm Model of a SHO
Build a model of the hanging oscillator using the modified Euler, or Euler-Cromer, numerical method. Compare the results you obtain (i.e. position and velocity vs. time) with those obtained from the simple Euler method, and with the exact solution. Comment in detail on your results.
Exercise 5
#### Exercise 5: Energy in the Euler-Cromer Algorithm Model of a SHO
Modify your model to produce a graph of the total energy as a function of time. Is energy conserved for the Euler-Cromer algorithm?
### Translations
Code Language Translator Run
### Software Requirements
SoftwareRequirements
Android iOS Windows MacOS with best with Chrome Chrome Chrome Chrome support full-screen? Yes. Chrome/Opera No. Firefox/ Samsung Internet Not yet Yes Yes cannot work on some mobile browser that don't understand JavaScript such as..... cannot work on Internet Explorer 9 and below
### Credits
Fremont Teng; Loo Kang Wee
[text]
## Hanging Simple Harmonic Oscillator JavaScript Simulation Applet HTML5
### Instructions
#### Graph Combo Box
Toggling between the combo box will give you the respective views.
(s-t Graph)
(v-t Graph)
(Both)
#### Control Panel
Setting the variables in the control panel will adjust the graphs accordingly.
#### Reset Button
Resets the Simulation.
Research
[text]
[text]
[text]
# Testimonials (0)
There are no testimonials available for viewing. Login to deploy the article and be the first to submit your review! | 1,760 | 6,882 | {"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} | 3.515625 | 4 | CC-MAIN-2024-18 | latest | en | 0.852644 |
https://inlabru-org.github.io/inlabru/articles/web/random_fields_2d.html | 1,685,780,609,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224649177.24/warc/CC-MAIN-20230603064842-20230603094842-00270.warc.gz | 355,212,431 | 7,127 | ## Setting things up
library(INLA)
library(inlabru)
library(mgcv)
library(ggplot2)
library(sp)
Make a shortcut to a nicer colour scale:
colsc <- function(...) {
colours = rev(RColorBrewer::brewer.pal(11, "RdYlBu")),
limits = range(..., na.rm = TRUE)
)
}
## Modelling on 2D domains
We will now construct a 2D model, generate a sample of a random field, and attempt to recover the field from observations at a few locations. Tomorrow, we will look into more general mesh constructions that adapt to irregular domains.
First, we build a high resolution mesh for the true field, using low level INLA functions
bnd <- spoly(data.frame(easting = c(0, 10, 10, 0), northing = c(0, 0, 10, 10)))
mesh_fine <- inla.mesh.2d(boundary = bnd, max.edge = 0.2)
ggplot() +
gg(mesh_fine) +
coord_equal()
# Note: the priors here will not be used in estimation
matern_fine <-
inla.spde2.pcmatern(mesh_fine,
prior.sigma = c(1, 0.01),
prior.range = c(1, 0.01)
)
true_range <- 4
true_sigma <- 1
true_Q <- inla.spde.precision(matern_fine, theta = log(c(true_range, true_sigma)))
What is the pointwise standard deviation of the field? Along straight boundaries, the variance is twice the target variance. At corners the variance is 4 times as large.
true_sd <- diag(inla.qinv(true_Q))^0.5
ggplot() +
gg(mesh_fine, col = true_sd) +
coord_equal()
Generate a sample from the model:
true_field <- inla.qsample(1, true_Q)[, 1]
truth <- expand.grid(
easting = seq(0, 10, length = 100),
northing = seq(0, 10, length = 100)
)
truth$field <- fm_evaluate( mesh_fine, loc = as.matrix(truth), field = true_field ) coordinates(truth) <- c("easting", "northing") truth <- as(truth, "SpatialPixelsDataFrame") pl_truth <- ggplot() + gg(truth, mapping = aes(easting, northing, fill = field)) + coord_equal() + ggtitle("True field") pl_truth ## Or with another colour scale: csc <- colsc(truth$field)
multiplot(pl_truth, pl_truth + csc, cols = 2)
Extract observations from some random locations:
n <- 200
mydata <- data.frame(easting = runif(n, 0, 10), northing = runif(n, 0, 10))
mydata$observed <- fm_evaluate( mesh_fine, loc = as.matrix(mydata), field = true_field ) + rnorm(n, sd = 0.4) coordinates(mydata) <- c("easting", "northing") ggplot() + gg(mydata, aes(col = observed)) ## Estimating the field Construct a mesh covering the data: mesh <- inla.mesh.2d(boundary = bnd, max.edge = 0.5) ggplot() + gg(mesh) + coord_equal() Construct an SPDE model object for a Matern model: matern <- inla.spde2.pcmatern(mesh, prior.sigma = c(10, 0.01), prior.range = c(1, 0.01) ) Specify the model components: cmp <- observed ~ field(coordinates, model = matern) + Intercept(1) Fit the model and inspect the results: fit <- bru(cmp, mydata, family = "gaussian") summary(fit) Predict the field on a lattice, and generate a single realisation from the posterior distribution: pix <- pixels(mesh, nx = 200, ny = 200) pred <- predict( fit, pix, ~ field + Intercept ) samp <- generate(fit, pix, ~ field + Intercept, n.samples = 1 ) pred$sample <- samp[, 1]
Compare the truth to the estimated field (posterior mean and a sample from the posterior distribution):
pl_posterior_mean <- ggplot() +
gg(pred) +
gg(bnd) +
ggtitle("Posterior mean") +
coord_fixed()
pl_posterior_sample <- ggplot() +
gg(pred, aes(fill = sample)) +
gg(bnd) +
ggtitle("Posterior sample") +
coord_fixed()
# Common colour scale for the truth and estimate:
csc <- colsc(truth$field, pred$mean, pred\$sample)
multiplot(pl_truth + csc,
pl_posterior_mean + csc,
pl_posterior_sample + csc,
cols = 3
)
Plot the SPDE parameter and fixed effect parameter posteriors.
int.plot <- plot(fit, "Intercept")
spde.range <- spde.posterior(fit, "field", what = "range")
spde.logvar <- spde.posterior(fit, "field", what = "log.variance")
range.plot <- plot(spde.range)
var.plot <- plot(spde.logvar)
multiplot(range.plot, var.plot, int.plot)
Look at the correlation function if you want to:
corplot <- plot(spde.posterior(fit, "field", what = "matern.correlation"))
covplot <- plot(spde.posterior(fit, "field", what = "matern.covariance"))
multiplot(covplot, corplot)
You can plot the median, lower 95% and upper 95% density surfaces as follows (assuming that the predicted intensity is in object pred).
csc <- colsc(
pred@data["median"],
pred@data["q0.025"],
pred@data["q0.975"]
) ## Common colour scale from SpatialPixelsDataFrame
gmedian <- ggplot() +
gg(pred["median"]) +
coord_equal() +
csc
glower95 <- ggplot() +
gg(pred["q0.025"]) +
coord_equal() +
csc +
theme(legend.position = "none")
gupper95 <- ggplot() +
gg(pred["q0.975"]) +
coord_equal() +
csc +
theme(legend.position = "none")
multiplot(gmedian, glower95, gupper95,
layout = matrix(c(1, 1, 2, 3), byrow = TRUE, ncol = 2)
) | 1,384 | 4,709 | {"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": 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} | 2.828125 | 3 | CC-MAIN-2023-23 | longest | en | 0.666301 |
http://www.self.gutenberg.org/articles/eng/Heckscher%E2%80%93Ohlin_theorem | 1,606,927,749,000,000,000 | text/html | crawl-data/CC-MAIN-2020-50/segments/1606141711306.69/warc/CC-MAIN-20201202144450-20201202174450-00554.warc.gz | 152,407,472 | 17,638 | #jsDisabledContent { display:none; } My Account | Register | Help
# Heckscher–Ohlin theorem
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### Heckscher–Ohlin theorem
Basic situation: Two identical countries (A and B) have different initial factor endowments. Autarky equilibrium (A^A, A^B): no trade, individual production equals consumption. Trade equilibrium: both countries consume the same (C^A = C^B), especially beyond their own Production–possibility frontier; production and consumption points are divergent.
The Heckscher–Ohlin theorem is one of the four critical theorems of the Heckscher–Ohlin model, developed by Swedish economist Eli Heckscher and Bertil Ohlin (his student). It states that a country will export goods that use its abundant factors intensively, and import goods that use its scarce factors intensively. In the two-factor case, it states: "A capital-abundant country will export the capital-intensive good, while the labor-abundant country will export the labor-intensive good."
The critical assumption of the Heckscher–Ohlin model is that the two countries are identical, except for the difference in resource endowments. This also implies that the aggregate preferences are the same. The relative abundance in capital will cause the capital-abundant country to produce the capital-intensive good cheaper than the labor-abundant country and vice versa.
Initially, when the countries are not trading:
• the price of the capital-intensive good in the capital-abundant country will be bid down relative to the price of the good in the other country,
• the price of the labor-intensive good in the labor-abundant country will be bid down relative to the price of the good in the other country.
Once trade is allowed, profit-seeking firms will move their products to the markets that have (temporary) higher price. As a result:
• the capital-abundant country will export the capital-intensive good,
• the labor-abundant country will export the labor-intensive good.
The Leontief paradox, presented by Wassily Leontief in 1951,[1] found that the U.S. (the most capital-abundant country in the world by any criterion) exported labor-intensive commodities and imported capital-intensive commodities, in apparent contradiction with the Heckscher–Ohlin theorem. However, if labor is separated into two distinct factors, skilled labor and unskilled labor, the Heckscher–Ohlin theorem is more accurate. The U.S. tends to export skilled-labor-intensive goods, and tends to import unskilled-labor-intensive goods.
## Contents
• Related theorems 1
• References 2
• Literature 3
## Related theorems
• Factor price equalization – The relative prices for two identical factors of production will eventually be equalized across countries because of international trade.
• Stolper–Samuelson theorem – A rise in the relative price of a good will lead to a rise in the return to that factor which is used most intensively in the production of the good, and conversely, to a fall in the return to the other factor.
• Rybczynski theorem – When only one of two factors of production is increased there is a relative increase in the production of the good using more of that factor. This leads to a corresponding decline in that good's relative price as well as a decline in the production of the good that uses the other factor more intensively.
## References
1. ^ Leontief, Wassily (1954) Domestic Production and Foreign Trade - The American Capital Position Reexamined, Economia Internazionale, (VII): p. 1.
## Literature
• Appleyard, Field, & Cobb. (2006). International Economics (5th ed.). McGraw–Hill Irwin. ISBN 0-07-287737-5.
• Case, Karl E. & Fair, Ray C. (1999). Principles of Economics (5th ed.). Prentice-Hall. ISBN 0-13-961905-4. | 892 | 3,934 | {"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} | 2.859375 | 3 | CC-MAIN-2020-50 | latest | en | 0.824816 |
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# Solution - Formulate the following problems as a pair of equations, and hence find their solutions: Roohi travels 300 km to her home partly by train and partly by bus. She takes 4 hours if she travels 60 km by train and remaining by bus. If she travels 100 km by train and the remaining by bus, she takes 10 minutes longer. Find the speed of the train and the bus separately. - CBSE Class 10 - Mathematics
ConceptEquations Reducible to a Pair of Linear Equations in Two Variables
#### Question
Formulate the following problems as a pair of equations, and hence find their solutions:
Roohi travels 300 km to her home partly by train and partly by bus. She takes 4 hours if she travels 60 km by train and remaining by bus. If she travels 100 km by train and the remaining by bus, she takes 10 minutes longer. Find the speed of the train and the bus separately.
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Solution for question: Formulate the following problems as a pair of equations, and hence find their solutions: Roohi travels 300 km to her home partly by train and partly by bus. She takes 4 hours if she travels 60 km by train and remaining by bus. If she travels 100 km by train and the remaining by bus, she takes 10 minutes longer. Find the speed of the train and the bus separately. concept: Equations Reducible to a Pair of Linear Equations in Two Variables. For the course CBSE
S | 360 | 1,534 | {"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} | 3.359375 | 3 | CC-MAIN-2018-09 | latest | en | 0.965955 |
https://newpathworksheets.com/math/grade-5/place-value-1/iowa-core-standards | 1,610,920,214,000,000,000 | text/html | crawl-data/CC-MAIN-2021-04/segments/1610703513194.17/warc/CC-MAIN-20210117205246-20210117235246-00336.warc.gz | 479,498,722 | 7,864 | ## ◂Math Worksheets and Study Guides Fifth Grade. Place Value
### The resources above correspond to the standards listed below:
#### Iowa Core
IA.CC.5.NBT. Number and Operations in Base Ten
Understand the place value system.
5.NBT.1. Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. (5.NBT.1.) (DOK 1) | 116 | 444 | {"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-2021-04 | latest | en | 0.883478 |
http://slideplayer.com/slide/7586974/ | 1,642,885,035,000,000,000 | text/html | crawl-data/CC-MAIN-2022-05/segments/1642320303884.44/warc/CC-MAIN-20220122194730-20220122224730-00078.warc.gz | 57,587,768 | 19,485 | Lesson 3 – Creating a spreadsheet to monitor stock using information from your data capture form and your customer database. Then display your data in.
Presentation on theme: "Lesson 3 – Creating a spreadsheet to monitor stock using information from your data capture form and your customer database. Then display your data in."— Presentation transcript:
Lesson 3 – Creating a spreadsheet to monitor stock using information from your data capture form and your customer database. Then display your data in a different way using a graph. Goals: Interpret and interrogate data from different sources Create a simple spreadsheet entering data and formula to calculate profit (money made) Produce a graph to display two lots of data from your spreadsheet.
Starter (5 Minutes) What do you know about graphs? Try and answer these questions in your booklet How many different types of graph can you name? Which way does the X axis run on a graph? Which way does the Y axis run on a graph?
Task 2 – Displaying data in a graph to make it easier to understand (15 Minutes) You will produce a graph that shows the artists name and how much the music shop profit from selling each of their CDs.
Try and create another type of graph displaying different data from your spreadsheet When finished print your graph out and save your work. Extension Activity
Plenary (5 Minutes) Match keywords to their meaning by finding your partner | 277 | 1,423 | {"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-2022-05 | latest | en | 0.886936 |
https://www.mathproblemgenerator.com/academy/gui_no_login/problem_menu/problem_menu.php?subject=2&topic=11&problem=70&answer=4&ps=2-11-70/18840/20/15/2/2&mc1=2-11-70/4396/0/0/2&mc2=2-11-70/18854.28/0/0/2&mc3=2-11-70/18829.12/0/0/2&mco0=3&mco1=2&mco2=4&mco3=1 | 1,696,058,050,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233510603.89/warc/CC-MAIN-20230930050118-20230930080118-00419.warc.gz | 954,622,315 | 3,609 | Davitily Math Academy - a free place to learn and practice math.
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https://forums.space.com/threads/how-to-determine-a-planets-radius.27400/ | 1,685,721,628,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224648695.4/warc/CC-MAIN-20230602140602-20230602170602-00695.warc.gz | 306,553,752 | 24,863 | How To
# How To Determine a Planet's Radius
Our search for life out in the universe has led to the development of a few different methods for detecting exoplanets. One method, the transit method, allows us to not only spot planets orbiting around their suns, but also determine the size of these exoplanets. All it takes is a little observation, some logic, and just a touch of math.
1. Determine the star’s radius.
In order to determine the planet’s radius, you first need to know the star’s radius. If you’re working with a star that has already been observed and cataloged, you should have access to the figures. If not, you can solve for the radius by dividing the star’s luminosity by 4πσT4 and taking the square root of the result.
2. Set up your equation to solve for r.
To find out the planet’s radius, you need to determine the fraction of light from the sun that is blocked by the planet. The equations is set up as follows:
Fraction of light blocked = area of planet’s disk/area of star’s disk = r2 planet/ r2 star
Since what you want to know is the planet’s radius, rearrange the equation to solve for rplanet.
rplanet = rstar x √fraction of light blocked
3. Plug in your values.
Plug in all the information you know. Let’s say the star has a radius of 800,000 km and you determine that the planet blocks 1.7% of the star’s light when it passes in front.
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http://learner.org/courses/teachingmath/grades9_12/session_04/section_01_b.html | 1,448,683,743,000,000,000 | text/html | crawl-data/CC-MAIN-2015-48/segments/1448398450762.4/warc/CC-MAIN-20151124205410-00199-ip-10-71-132-137.ec2.internal.warc.gz | 132,164,365 | 9,055 | Observing Student Reasoning and Proof
Introduction | Inscribed Triangles | Problem Reflection #1 | Inscribed Triangle Continued | Problem Reflection #2 | Classroom Practice | Observe a Classroom | Your Journal
Ms. Saleh's tenth-grade geometry class is working on an inscribed triangle problem. Students had previously worked with angles, triangles, and circles and had been introduced to the idea of a proof.
Ms. Selah's instructions: "Work in your groups to construct an inscribed triangle in the top of a semi-circle. Here's an example: You'll need to use your compass, protractor and straightedge to do so, and you may choose any random point C on the semi-circle, you don't have to make the triangle look like the example. After you have your triangle, measure angles A, B, and C for at least five different cases and record your findings in a table. I'm particularly interested in what you find out about angle C. In a few minutes I'll come around to each group to hear your observations."
One group of students created this chart.
Here is a dialogue between Ms. Saleh and members of one group:
Ms. Saleh: Can you describe how you worked on the problem?
Ben: We made a circle with the compass, and then drew lines.
Ms. Saleh: How did you draw the lines?
Ben: We found a place on the top of the circle and drew lines to either corner.
Sonia: See these are our points. {she points to the top of the circle] we actually tried a bunch of different points for C.
Ms. Saleh: What about that point in the middle, O?
Grant: We thought we'd need that because last time we did circles we used it. But we didn't use it to draw with.
Ms. Saleh: Okay, we may want to come back to it later, so it wasn't a mistake to put it in. Now tell me about your chart. Can you draw any conclusions about angle C?
Grant: Well, we measured it in five positions on the circle. It is always close to 90 degrees, although it's never exact.
Ben: No, it was exact once.
Grant: Oh, I see. Yes, but it was just once.
Ms. Saleh: Do you have any ideas about angle C?
Sonia: Yes, it's always the top of the triangle and C always looks like a right triangle. So I think C is a right triangle, no matter what.
Ms. Saleh: Yes, it certainly looks that way. But does the table support the idea that angle C will be a right angle in every case? We have some data, 94 degrees for instance, that isn't a right angle.
Grant: That's just cuz we measured with a protractor and maybe it was off a little.
Ms. Saleh: If we had a more accurate protractor and many more triangles how could we show that angle C is always a right triangle? How many measurements would it take?
Ben: You'd have to do every single triangle ever. And that's not possible, right?
Ms. Saleh: Sonia what do you think? Could we check every possible angle C?
Sonia: No, I couldn't at least. Maybe I could make an argument about why it needs to be 90 degrees.
Ms. Saleh: That's great. Please work on an argument you think will convince one another that angle C is always a right angle. Then I'll come back and you can try to convince me!
Teaching Math Home | Grades 9-12 | Reasoning and Proof | Site Map | © | | 751 | 3,163 | {"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} | 4.84375 | 5 | CC-MAIN-2015-48 | longest | en | 0.964515 |
https://www.studyadda.com/current-affairs/2nd-class/shapes-2d-and-3d/17807 | 1,642,700,288,000,000,000 | text/html | crawl-data/CC-MAIN-2022-05/segments/1642320302355.97/warc/CC-MAIN-20220120160411-20220120190411-00352.warc.gz | 1,011,885,473 | 22,893 | # Current Affairs 2nd Class
## Shapes (2D and 3D)
Category : 2nd Class
Shapes (2D and 3D)
Synopsis
Do you remember these shapes?
Formation of figures (2 - Dimensional):
This figure is made up of only straight lines. It has 5 straight lines. This figure is made up of only curved lines. It has 8 curved lines. This figure is made up of straight lines and curved lines. It has 3 straight lines and 3 curved liens.
Formation of figures (3 - Dimensional):
This parcel is made up of only flat surfaces. It has 6 flat surfaces. Some of them are hidden behind from our view. The ball is made up of only curved surfaces. It has 1 curved surface. The tin with lid is made up of flat surfaces and curved surface. It has 2 flat surfaces and 1 curved surface.
2 - Dimensional Shapes:
This pizza is cut into 2 halves. Each part is $\frac{1}{2}$ of a circle and is 2 called a semicircle.
This pizza is cut into 4 equal parts. Each part is $\frac{1}{4}$ of a circle and is called a quarter circle or a quadrant.
Making Shapes:
3 - Dimensional Shapes:
Here are some objects.
Cylinder Cube Cone Cuboid
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http://www.mathplanet.com/education/pre-algebra/introducing-algebra/identify-properties | 1,386,395,512,000,000,000 | text/html | crawl-data/CC-MAIN-2013-48/segments/1386163053608/warc/CC-MAIN-20131204131733-00056-ip-10-33-133-15.ec2.internal.warc.gz | 517,277,986 | 6,170 | # Identify properties
In this section, you´ll learn how to identify the properties of multiplication and addition and how you can use identification to help solve mathematical problems.
To solve rather hard problems without using a calculator you have to identify all expressions that have the same operation.
Example
$\begin{array}{lcl} 58+69+91=? \end{array}$
In this example, you can add in any order you prefer. The sum of the expression will not change if you prefer to add the numbers in a different order.
$\begin{array}{lcl} 91+58+69=218\\ 58+69+91=218 \end{array}$
The same is true for multiplication:
$\begin{array}{lcl} 5\cdot 4\cdot 30=600\\ 4\cdot 30\cdot 5=600 \end{array}$
Video lesson: Show that the following equation holds true
$\\3\cdot a\cdot 4=a\cdot 4\cdot 3$ | 219 | 791 | {"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": 4, "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-2013-48 | latest | en | 0.730357 |
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# Steelco_Transport - =Sheet1!\$B\$18:\$D\$18 Plant 1 \$60 \$40 \$28...
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STEELCO Steelco mnufactures three types of steel at different plants. The time required to manufacture one ton of steel (regardless of type) and the costs at each are shown in the table. Each week, 100 tons of each type of steel (1,2 and 3) must be produced. Each plant is open 40 hours per week. Determine how to minimize the cost of meeting Steelco's weekly requirements.
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Problem 4.4 Problem 5.4 Range names Available =Sheet1!\$G\$13:\$G\$15 Cost/ton of steel at each plant Produced =Sheet1!\$B\$13:\$D\$15 Steel 1 Steel 2 Steel 3 Minutes/ton Required
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Unformatted text preview: =Sheet1!\$B\$18:\$D\$18 Plant 1 \$60 \$40 \$28 20 TotCost =Sheet1!\$B\$20 Plant 2 \$50 \$30 \$30 16 TotProduced =Sheet1!\$B\$16:\$D\$16 Plant 3 \$43 \$20 \$20 15 Used =Sheet1!\$E\$13:\$E\$15 Hours each plant is open 40 Tons produced at each plant Steel 1 Steel 2 Steel 3 Minuted used Minutes available Plant 1 40 800 <= 2400 Plant 2 100 1600 <= 2400 Plant 3 100 60 2400 <= 2400 Total 100 100 100 >= >= >= Required 100 100 100 Total cost \$9,320 A B C D E F G H I J K L 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20...
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Steelco_Transport - =Sheet1!\$B\$18:\$D\$18 Plant 1 \$60 \$40 \$28...
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Ask a homework question - tutors are online | 548 | 1,709 | {"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} | 2.859375 | 3 | CC-MAIN-2018-05 | latest | en | 0.767762 |
http://w3cgeek.com/ios-simple-imitation-casually-walk-ar-function-principle.html | 1,537,935,774,000,000,000 | text/html | crawl-data/CC-MAIN-2018-39/segments/1537267163326.85/warc/CC-MAIN-20180926041849-20180926062249-00101.warc.gz | 259,265,666 | 10,866 | # IOS simple imitation casually walk AR function (principle)
The final effect of the first dynamic diagram,
~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~
1, first we want to customize a camera interface, you can use AVCaptureSession from the definition, do not need other buttons, only a preview of the interface;
2, we need to draw a simple radar map, you can use CGContextRef to achieve a simple, radar diagram is used to show you and your users in the vicinity (object) distance, with the actual object of latitude and longitude to calculate the distance between two points, by a certain proportion of mapping to the radar map, the distance between two points the calculation formula is as follows:
/ / calculate the distance of two points of latitude and longitude
– (float) DistanceFromCoordinates: (CLLocationCoordinate2D) myDotother: (CLLocationCoordinate2D) otherDot
{
Doubleb = (myDot.longitude- otherDot.longitude) /180.0 * M_PI;
Doubles =22* asin (sqrt (pow (sin (a /2), 2)
* pow (sin (B /2), 2)));
S = round (s*10000) /10000;
Returns;
}
Is the object in the radar map on the display position according to the trigonometric function, on the edge of sinA= / cosA= / hypotenuse, adjacent side bevel, bevel we have, is the distance between two points, then we need to know a point of view, to get an edge through this edge radius with addition and subtraction, it you can calculate the object position in the radar on the map. So we have to calculate the azimuth of two points, look at the following picture:
An explanation of the azimuth of the wiki, we can use the tan2 function to calculate, the formula is as follows:
– (float) getHeadingForDirectionFromCoordinate: (CLLocationCoordinate2D) fromLoctoCoordinate: (CLLocationCoordinate2D) toLoc
{
Floatdegree = RadiansToDegrees (atan2 (sin (tLng-fLng) *cos (tLat), cos (fLat) *sin (tLat) -sin (fLat) *cos (tLat) *cos (tLng-fLng)));
If (degree > =0) {
Returndegree;
}else{
Return (360+degree);
}
}
3, to realize the radar map rotation and rotation follow the mobile phone, here we will use the compass principle, through the CLLocationManager management class, there is a CLHeading class, we can see the compass, the structure of this class:
There are north, North and magnetic values in X, y, Z three axis magnetic value, but when I use the three values when problems are found, when before and after the mobile phone, found that this value changes have stopped, if come to realize that moves is not smooth with this value, so I also use the gyroscope data, using the CMMotionManager management class to get the mobile phone swing angle, when used for mobile computing and mobile phone, mobile phone interface on the position of the object in the.
– (void) startMotion
{
If ([_mgrisDeviceMotionActive]! & & [_mgrisDeviceMotionAvailable])
{
/ / set the sampling interval
_mgr.deviceMotionUpdateInterval=0.1;
NSOperationQueue*queue = [[NSOperationQueuealloc]init];
WithHandler:^ (CMDeviceMotion* _Nullable motion,
NSError* _Nullable error) {
DoublegravityX = motion.gravity.x;
DoublegravityY = motion.gravity.y;
DoublegravityZ = motion.gravity.z;
If (gravityY< =0& & gravityY> =-1)
{
The mobile phone gets / / tilt angle (zTheta angle, and the horizontal plane is mobile phone xyTheta mobile phone around its own rotation angle):
ZTheta (gravityZ, atan2 = sqrtf (gravityX*gravityX+gravityY*gravityY)) /M_PI*180.0;
}
[selfupdataPoint];
}]; | 834 | 3,438 | {"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} | 3.0625 | 3 | CC-MAIN-2018-39 | latest | en | 0.743381 |
https://the-equivalent.com/symbol-equivalent/ | 1,679,857,578,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296946445.46/warc/CC-MAIN-20230326173112-20230326203112-00598.warc.gz | 647,798,843 | 16,001 | # Symbol equivalent
Equal Symbols
Equal Symbol Equal Name Decimal Hex = Equals Sign = = ͇ Combining Equals Sign Below ͇ ͇ ͌ Combining Almost Equal To Above ͌ ͌ Superscript Equals Sign
Aug 12 2022
## What does the symbol equal sign mean?
• “Equals” means “is,” so “3 + 5 = 8” means “3 + 5 is 8,” while “7 + 2 = 7 + 2” means simply “7 + 2 is 7 …
• Sometimes, we can also say that “equals” means “is the same value as,” such as when we say correctly that “1 dollar = 4 quarters.” It is not quite correct …
• In summary, the equal sign means either simply is or simply is the same value as. …
## Does an equivalent have an equal sign?
Equal signs can be found in equations not expressions. thanked the writer. blurted this. No it doesn’t have an equal sign because it only an expression not an equation. thanked the writer. blurted this. Algebraic expressions do not have to have an equal sign. Examples of algebraic expressions are 3+7=7+3 and 4d+2. thanked the writer.
## What does the name equivalent mean?
equivalent (noun) a person or thing equal to another in value or measure or force or effect or significance etc “send two dollars or the equivalent in stamps” equivalent, equivalent weight, combining weight, eq (adj)
## Where is the equal sign on keyboard?
• Press the 123 button near the bottom-left corner of the keyboard.
• Press the #+= button near the bottom-left corner of the keyboard.
• Press the = button on the keyboard.
## What does this symbol mean ≅?
approximately equal to≅ (approximately equal to)
## What does ≡ mean in math?
identical to≡ means identical to. This is similar to, but not exactly the same as, equals. Therefore, if in doubt, stick to =. ≈ means approximately equal to, or almost equal to. The two sides of a relationship indicated by this symbol will not be accurate enough to manipulate mathematically.
## What does =~ mean in math?
The Unicode standard lists all of them inside the Mathematical Operators Block. ≈ : ALMOST EQUAL TO (U+2248) ≃ : ASYMPTOTICALLY EQUAL TO (U+2243) ≅ : APPROXIMATELY EQUAL TO (U+2245)
## What does ≡ mean in logic?
definition. is defined as. everywhere. x ≔ y or x ≡ y means x is defined to be another name for y (but note that ≡ can also mean other things, such as congruence). P :⇔ Q means P is defined to be logically equivalent to Q.
## What is this symbol called?
This table contains special characters.SymbolName of the symbolSimilar glyphs or concepts’ ‘ApostropheQuotation mark, Guillemet, Prime, Grave*AsteriskAsterism, Dagger⁂AsterismDinkus, Therefore sign@At sign90 more rows
## What does ∑ mean in math?
summationThe symbol ∑ indicates summation and is used as a shorthand notation for the sum of terms that follow a pattern. For example, the sum of the first 4 squared integers, 12+22+32+42, follows a simple pattern: each term is of the form i2, and we add up values from i=1 to i=4.
## What does ∧ mean in math?
∧ is (most often) the mathematical symbol for logical conjunction, which is equivalent to the AND operator you’re used to. Similarly ∨ is (most often) logical disjunction, which would be equivalent to the OR operator.
## What does this symbol mean?
0:103:21What is the symbol for Mean – YouTubeYouTubeStart of suggested clipEnd of suggested clipAnd X bar I think both mean mean now the difference between them it’s it’s a little bit weird. Let’sMoreAnd X bar I think both mean mean now the difference between them it’s it’s a little bit weird. Let’s say you had a class of like 28. Students if you added up all of their heights.
## What does ∧ mean in math?
∧ is (most often) the mathematical symbol for logical conjunction, which is equivalent to the AND operator you’re used to. Similarly ∨ is (most often) logical disjunction, which would be equivalent to the OR operator.
## What is the symbol of in math?
Basic Mathematical Symbols With Name, Meaning and ExamplesSymbolSymbol Name in MathsMath Symbols Meaning±plus – minusboth plus and minus operations×times signmultiplication*asteriskmultiplication÷division sign / obelusdivision27 more rows•Jun 16, 2020
## What does this symbol mean?
0:103:21What is the symbol for Mean – YouTubeYouTubeStart of suggested clipEnd of suggested clipAnd X bar I think both mean mean now the difference between them it’s it’s a little bit weird. Let’sMoreAnd X bar I think both mean mean now the difference between them it’s it’s a little bit weird. Let’s say you had a class of like 28. Students if you added up all of their heights.
## What is the mean vs median?
The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set. The median is the middle value when a data set is ordered from least to greatest. The mode is the number that occurs most often in a data set.
## How to get the almost equal to symbol?
The easiest way to get the Almost Equal To Symbol text is to copy and paste it wherever you need it.
## What is the alt code for e umlaut?
The E Umlaut alt Code is 0203 for uppercase (Ë) and 0235 for lowercase (ë). You can simply use this Alt code to type the Plus-Minus sign by pressing and holding the Alt key while typing the Alt…
## How to find almost equal to in Google Docs?
Using the Search bar, search for ‘Almost Equal To’. Then double click on the Symbol for Almost Equal To in the search results to insert it into Google Docs.
## What is character map?
The Character Map in Windows is a tool that is used to view characters in any installed font, to check what keyboard input (or Alt code) is used to type those characters, and to copy characters to the clipboard instead of typing them.
## What does “almost equal to” mean?
Almost Equal To is a symbol that is used to denote something that is very similar but not exactly equal to another.
## Can you use almost equal to on the keyboard?
Even though there’s no dedicated key for the Almost Equal To symbol on the keyboard, you can still get this symbol using the keyboard.
## Does Alt Code work on Word?
NOTE: This Alt Code shortcut works on Windows only, preferably MS Word.
## How to type approximately equal to symbol?
To type the Approximately Equal to symbol on Mac, press Option+X on your keyboard. For Windows users, whilst you press and hold the Alt key, press the Approximately Equal symbol alt code which is 247 on the numeric keypad, then release the alt key.
## What does the approximately equal sign mean?
The Approximately Equal symbol (≈) is a mathematical operator used to indicate that two expressions or statements are similar but not exactly equal to each other. Visually, the symbol is a squiggly equals sign.
## What is the insert symbol dialog box?
The insert symbol dialog box is a library of symbols from where you can insert any symbol into your Word document with just a couple of mouse clicks.
## How to copy and paste a symbol?
All you have to do is to copy the symbol from somewhere like a web page or the character map for Windows users, and then head over to where you need the symbol and hit Ctrl+V to paste .
## How to type 247 on keyboard?
Whilst holding on to the Alt key, press the symbol’s alt code ( 247 ). You must use the numeric keypad to type the alt code. If you are using a laptop without the numeric keypad, this method may not work for you. On some laptops, there’s a hidden numeric keypad which you can enable by pressing Fn+NmLk keystrokes on the keyboard.
## Rationale
“7^2 = 50 (that should be an “is approximately equal to” symbol, but I’m too lazy to figure out how to get one of them)…”
## Preferred symbols
If text can be entered as HTML, you can also use the following notations:
## What is the symbol for equality?
A well-known equality featuring the equal sign. The equals sign ( British English, Unicode Consortium) or equal sign ( American English ), formerly known as the equality sign, is the mathematical symbol =, which is used to indicate equality in some well-defined sense.
## When to use equal sign?
The equal sign is also used in defining attribute–value pairs, in which an attribute is assigned a value.
The first important computer programming language to use the equal sign was the original version of Fortran, FORTRAN I, designed in 1954 and implemented in 1957. In Fortran, = serves as an assignment operator: X = 2 sets the value of X to 2. This somewhat resembles the use of = in a mathematical definition, but with different semantics: the expression following = is evaluated first, and may refer to a previous value of X. For example, the assignment X = X + 2 increases the value of X by 2.
## What is equality under == in Ruby?
In Ruby, equality under == requires both operands to be of identical type, e.g. 0 == false is false. The === operator is flexible and may be defined arbitrarily for any given type. For example, a value of type Range is a range of integers, such as 1800..1899. (1800..1899) == 1844 is false, since the types are different (Range vs. Integer); however (1800..1899) === 1844 is true, since === on Range values means “inclusion in the range”. Under these semantics, === is non-symmetric; e.g. 1844 === (1800..1899) is false, since it is interpreted to mean Integer#=== rather than Range#===.
## What does “but” mean in Pascal?
But = is used for equality and not assignment in the Pascal family, Ada, Eiffel, APL, and other languages. A few languages, such as BASIC and PL/I, have used the equal sign to mean both assignment and equality, distinguished by context.
## What is the difference between = and Fortran?
Both usages have remained common in different programming languages into the early 21st century. As well as Fortran, = is used for assignment in such languages as C, Perl, Python, awk, and their descendants. But = is used for equality and not assignment in the Pascal family, Ada, Eiffel, APL, and other languages.
## Why is the equal sign used incorrectly?
The equal sign is sometimes used incorrectly within a mathematical argument to connect math steps in a non-standard way, rather than to show e quality (especially by early mathematics students). For example, if one were finding the sum, step by step, of the numbers 1, 2, 3, 4, and 5, one might incorrectly write: | 2,419 | 10,244 | {"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} | 4.125 | 4 | CC-MAIN-2023-14 | latest | en | 0.889552 |
https://www.sanfoundry.com/microwave-engineering-questions-answers-aperture-coupling/ | 1,701,461,745,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679100304.52/warc/CC-MAIN-20231201183432-20231201213432-00415.warc.gz | 1,085,502,048 | 21,194 | # Microwave Engineering Questions and Answers – Aperture Coupling
This set of Microwave Engineering Multiple Choice Questions & Answers (MCQs) focuses on “Aperture Coupling”.
1. The matched network is placed between:
b) source and the transmission line
d) none of the mentioned
Explanation: At microwave frequencies, for maximum power transmission, the characteristic impedance of the transmission line must be matched to the load impedance with which the line is terminated. Hence to match these impedances, the matched network is laced between load and transmission line.
2. When a transmission line is matched to a load using a matched network, reflected waves are present:
a) between the load and the matched network
b) between the matched network and the transmission line
c) between the source and the transmission line
d) between the matched network and source
Explanation: The matching circuit is used to match the transmission line and the load. This circuit prevents the reflection of the waves reaching the source. Hence, reflected waves are present between the load and the matched network.
3. Impedance matching sensitive receiver components may improve the _____ of the system.
a) noise
b) SNR
c) amplification factor
d) thermal noise
Explanation: SNR (signal to noise ratio) of the system defines the ratio of signal power to noise power. An increase in this value results in increase of the signal strength. Impedance matching certain sensitive receiver components helps in delivering maximum power to the load and increased signal strength.
4. One of the most important factors to be considered in the selection of a particular matching network is:
a) noise component
b) amplification factor
c) bandwidth
d) none of the mentioned
Explanation: Any type of matching network can ideally give a perfect match at a single frequency. But it is desirable to match a load over a band of frequencies. Hence, bandwidth plays an important role in the selection of the matching network.
5. The simplest type of matching network, L section consists of _______ reactive elements.
a) one
b) two
c) four
d) six
Explanation: As the name of the matching circuit indicates, ‘L’ section consists of 2 reactive elements, one element vertical and another horizontal. 2 types of ‘L’ sections exist. The best one is chose based on the normalized value of the load impedance.
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6. The major limitation of a lumped elements matching ‘L’ network is:
a) they are not equally efficient at higher frequencies as they are at lower frequencies.
b) size of the network
c) they restrict flow of current
d) none of the mentioned
Explanation: Since we use lumped elements like inductors and capacitors as the components of the matching network, they behave differently at frequencies higher than 1GHz, because of the frequency dependent factor of inductive and capacitive reactance. This is one of the major limitations.
7. An ‘L’ network is required to match a load impedance of 40Ω to a transmission line of characteristic impedance 60Ω. The components of the L network are:
a) 28.28+j0 Ω
b) 28.28+j1 Ω
c) 50Ω
d) 48.9Ω
Explanation: Since both load impedance and characteristic impedance are resistive (real), the imaginary part of the matching network is 0. Real part of the matching network is given by the expression ±√(RL(Z0– RL))-XL. Substituting the values given, the matching network impedance is 28.28Ω.
8. The imaginary part of the matching network is given by the relation:
a) ±(√(Z0– RL)/RL)Z00
b) ±(√(Z0– RL)/RL)
c) ±(√(Z0– RL)/ Z0
d) None of the mentioned
Explanation: By theoretical analysis, the expressions for real and imaginary parts of the impedance of the matching network are derived in terms of the load impedance and the characteristic impedance of the transmission line. This expression derived is ±(√(Z0– RL)/RL)Z0 .
9. Which of the following material is not used in the fabrication of resistors of thin films?
a) nichrome
b) tantalum nitride
c) doped semiconductor
d) pure silicon
Explanation: Certain physical properties are to be met in order to use a material to make thin film resistors. These properties are not found in pure silicon which is an intrinsic semiconductor.
10. Large values of inductance can be realized by:
a) loop of transmission line
b) spiral inductor
c) coils of wires
d) none of the mentioned
Explanation: Loop of transmission lines are used to make inductors to realize lower values of inductance. Coils of wires cannot be used to realize inductors at higher frequencies. Spiral conductors can be used to realize inductors of higher values at higher frequencies.
11. A short transmission line stub can be used to provide a shunt capacitance of:
a) 0-0.1µF
b) 0-0.1pF
c) 0-0.1nF
d) 1-10pF | 1,110 | 4,828 | {"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} | 2.796875 | 3 | CC-MAIN-2023-50 | longest | en | 0.891888 |
https://leetcode.ca/2017-01-30-427-Construct-Quad-Tree/ | 1,720,899,741,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763514512.50/warc/CC-MAIN-20240713181918-20240713211918-00410.warc.gz | 329,457,554 | 9,240 | Description
Given a n * n matrix grid of 0's and 1's only. We want to represent grid with a Quad-Tree.
Return the root of the Quad-Tree representing grid.
A Quad-Tree is a tree data structure in which each internal node has exactly four children. Besides, each node has two attributes:
• val: True if the node represents a grid of 1's or False if the node represents a grid of 0's. Notice that you can assign the val to True or False when isLeaf is False, and both are accepted in the answer.
• isLeaf: True if the node is a leaf node on the tree or False if the node has four children.
class Node {
public boolean val;
public boolean isLeaf;
public Node topLeft;
public Node topRight;
public Node bottomLeft;
public Node bottomRight;
}
We can construct a Quad-Tree from a two-dimensional area using the following steps:
1. If the current grid has the same value (i.e all 1's or all 0's) set isLeaf True and set val to the value of the grid and set the four children to Null and stop.
2. If the current grid has different values, set isLeaf to False and set val to any value and divide the current grid into four sub-grids as shown in the photo.
3. Recurse for each of the children with the proper sub-grid.
If you want to know more about the Quad-Tree, you can refer to the wiki.
You don't need to read this section for solving the problem. This is only if you want to understand the output format here. The output represents the serialized format of a Quad-Tree using level order traversal, where null signifies a path terminator where no node exists below.
It is very similar to the serialization of the binary tree. The only difference is that the node is represented as a list [isLeaf, val].
If the value of isLeaf or val is True we represent it as 1 in the list [isLeaf, val] and if the value of isLeaf or val is False we represent it as 0.
Example 1:
Input: grid = [[0,1],[1,0]]
Output: [[0,1],[1,0],[1,1],[1,1],[1,0]]
Explanation: The explanation of this example is shown below:
Notice that 0 represents False and 1 represents True in the photo representing the Quad-Tree.
Example 2:
Input: grid = [[1,1,1,1,0,0,0,0],[1,1,1,1,0,0,0,0],[1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1],[1,1,1,1,0,0,0,0],[1,1,1,1,0,0,0,0],[1,1,1,1,0,0,0,0],[1,1,1,1,0,0,0,0]]
Output: [[0,1],[1,1],[0,1],[1,1],[1,0],null,null,null,null,[1,0],[1,0],[1,1],[1,1]]
Explanation: All values in the grid are not the same. We divide the grid into four sub-grids.
The topLeft, bottomLeft and bottomRight each has the same value.
The topRight have different values so we divide it into 4 sub-grids where each has the same value.
Explanation is shown in the photo below:
Constraints:
• n == grid.length == grid[i].length
• n == 2x where 0 <= x <= 6
Solutions
• /*
// Definition for a QuadTree node.
class Node {
public boolean val;
public boolean isLeaf;
public Node topLeft;
public Node topRight;
public Node bottomLeft;
public Node bottomRight;
public Node() {
this.val = false;
this.isLeaf = false;
this.topLeft = null;
this.topRight = null;
this.bottomLeft = null;
this.bottomRight = null;
}
public Node(boolean val, boolean isLeaf) {
this.val = val;
this.isLeaf = isLeaf;
this.topLeft = null;
this.topRight = null;
this.bottomLeft = null;
this.bottomRight = null;
}
public Node(boolean val, boolean isLeaf, Node topLeft, Node topRight, Node bottomLeft, Node
bottomRight) { this.val = val; this.isLeaf = isLeaf; this.topLeft = topLeft; this.topRight =
topRight; this.bottomLeft = bottomLeft; this.bottomRight = bottomRight;
}
};
*/
class Solution {
public Node construct(int[][] grid) {
return dfs(0, 0, grid.length - 1, grid[0].length - 1, grid);
}
private Node dfs(int a, int b, int c, int d, int[][] grid) {
int zero = 0, one = 0;
for (int i = a; i <= c; ++i) {
for (int j = b; j <= d; ++j) {
if (grid[i][j] == 0) {
zero = 1;
} else {
one = 1;
}
}
}
boolean isLeaf = zero + one == 1;
boolean val = isLeaf && one == 1;
Node node = new Node(val, isLeaf);
if (isLeaf) {
return node;
}
node.topLeft = dfs(a, b, (a + c) / 2, (b + d) / 2, grid);
node.topRight = dfs(a, (b + d) / 2 + 1, (a + c) / 2, d, grid);
node.bottomLeft = dfs((a + c) / 2 + 1, b, c, (b + d) / 2, grid);
node.bottomRight = dfs((a + c) / 2 + 1, (b + d) / 2 + 1, c, d, grid);
return node;
}
}
• /*
// Definition for a QuadTree node.
class Node {
public:
bool val;
bool isLeaf;
Node* topLeft;
Node* topRight;
Node* bottomLeft;
Node* bottomRight;
Node() {
val = false;
isLeaf = false;
topLeft = NULL;
topRight = NULL;
bottomLeft = NULL;
bottomRight = NULL;
}
Node(bool _val, bool _isLeaf) {
val = _val;
isLeaf = _isLeaf;
topLeft = NULL;
topRight = NULL;
bottomLeft = NULL;
bottomRight = NULL;
}
Node(bool _val, bool _isLeaf, Node* _topLeft, Node* _topRight, Node* _bottomLeft, Node* _bottomRight) {
val = _val;
isLeaf = _isLeaf;
topLeft = _topLeft;
topRight = _topRight;
bottomLeft = _bottomLeft;
bottomRight = _bottomRight;
}
};
*/
class Solution {
public:
Node* construct(vector<vector<int>>& grid) {
return dfs(0, 0, grid.size() - 1, grid[0].size() - 1, grid);
}
Node* dfs(int a, int b, int c, int d, vector<vector<int>>& grid) {
int zero = 0, one = 0;
for (int i = a; i <= c; ++i) {
for (int j = b; j <= d; ++j) {
if (grid[i][j])
one = 1;
else
zero = 1;
}
}
bool isLeaf = zero + one == 1;
bool val = isLeaf && one;
Node* node = new Node(val, isLeaf);
if (isLeaf) return node;
node->topLeft = dfs(a, b, (a + c) / 2, (b + d) / 2, grid);
node->topRight = dfs(a, (b + d) / 2 + 1, (a + c) / 2, d, grid);
node->bottomLeft = dfs((a + c) / 2 + 1, b, c, (b + d) / 2, grid);
node->bottomRight = dfs((a + c) / 2 + 1, (b + d) / 2 + 1, c, d, grid);
return node;
}
};
• """
# Definition for a QuadTree node.
class Node:
def __init__(self, val, isLeaf, topLeft, topRight, bottomLeft, bottomRight):
self.val = val
self.isLeaf = isLeaf
self.topLeft = topLeft
self.topRight = topRight
self.bottomLeft = bottomLeft
self.bottomRight = bottomRight
"""
class Solution:
def construct(self, grid: List[List[int]]) -> 'Node':
def dfs(a, b, c, d):
zero = one = 0
for i in range(a, c + 1):
for j in range(b, d + 1):
if grid[i][j] == 0:
zero = 1
else:
one = 1
isLeaf = zero + one == 1
val = isLeaf and one
if isLeaf:
return Node(grid[a][b], True)
topLeft = dfs(a, b, (a + c) // 2, (b + d) // 2)
topRight = dfs(a, (b + d) // 2 + 1, (a + c) // 2, d)
bottomLeft = dfs((a + c) // 2 + 1, b, c, (b + d) // 2)
bottomRight = dfs((a + c) // 2 + 1, (b + d) // 2 + 1, c, d)
return Node(val, isLeaf, topLeft, topRight, bottomLeft, bottomRight)
return dfs(0, 0, len(grid) - 1, len(grid[0]) - 1)
• /**
* Definition for a QuadTree node.
* type Node struct {
* Val bool
* IsLeaf bool
* TopLeft *Node
* TopRight *Node
* BottomLeft *Node
* BottomRight *Node
* }
*/
func construct(grid [][]int) *Node {
var dfs func(a, b, c, d int) *Node
dfs = func(a, b, c, d int) *Node {
zero, one := 0, 0
for i := a; i <= c; i++ {
for j := b; j <= d; j++ {
if grid[i][j] == 0 {
zero = 1
} else {
one = 1
}
}
}
isLeaf := zero+one == 1
val := isLeaf && one == 1
node := &Node{Val: val, IsLeaf: isLeaf}
if isLeaf {
return node
}
node.TopLeft = dfs(a, b, (a+c)/2, (b+d)/2)
node.TopRight = dfs(a, (b+d)/2+1, (a+c)/2, d)
node.BottomLeft = dfs((a+c)/2+1, b, c, (b+d)/2)
node.BottomRight = dfs((a+c)/2+1, (b+d)/2+1, c, d)
return node
}
return dfs(0, 0, len(grid)-1, len(grid[0])-1)
} | 2,440 | 7,312 | {"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} | 3.15625 | 3 | CC-MAIN-2024-30 | latest | en | 0.89369 |
www.jkhub.net | 1,600,672,427,000,000,000 | text/html | crawl-data/CC-MAIN-2020-40/segments/1600400198942.13/warc/CC-MAIN-20200921050331-20200921080331-00402.warc.gz | 183,690,643 | 8,298 | Introduction
This tutorial will try to explain what bases are and why they are useful. This isn't a complete or perfect tutorial on bases. It's just another JK tutorial for newcomers.
Terms
Here's the definition for a few terms that are used a lot in this tutorial:
digit: Any numeral used to express a number, or the column (e.g., ones, tens) which the numeral occupies.
number: A number is an idea of an amount. You can't write a number without limiting yourself to some form of expression, but the number is the amount that exists.
numeral: Numerals are characters which aid in expressing numbers. They are not numbers in themselves, but only a form of expression for a number. For example, in decimal 10, the '1' and '0' characters are the numerals. The amount of things that the 1 and 0 represent is the number.
What Bases Are
A base is a system of displaying a number with numerals. It is only a way of displaying the number, it does not change the number itself. For example, 100 in base 16, 256 in base 10, and 400 in base 8 are all the same number (numbers are "in" the base that is used to display them). The only thing that changed is the way the number appears.
In each base, there is a maximum value that each digit can hold before the number must use the next highest digit. In base 10, the maximum value that can be displayed in a digit is 9.
100 in base 16 is 256 in base 10 because base 16 (as its name implies) displays more values in each digit than decimal does. Because it displays 6 more values than decimal in each digit, base 16 can display the same value with lesser and often fewer numerals.
A Lising of the Bases
The following table gives a name for each base and lists the characters that it uses:
Base Name Characters
2binary0-1
3ternary0-2
4quaternary0-3
5quinary0-4
6senary0-5
7septenary0-6
8octal0-7
9nonary0-8
10decimal0-9
11undenary0-a
12duodecimal0-b
13*tridecimal0-c
14*quattuordecimal0-d
15*quindecimal0-e
17septendecimal0-g
18*octodecimal0-h
20vigesimal0-j
Although these names are based on common Latin prefixes and roots, they are not all standard names. The asterisks are used to mark the names that are more invention than standard. Hexadecimal, while being fairly standard, is not the correct name for base 16 according to the Latin system. It should have been something like sexadecimal, but was changed to use "hex" for apparent reasons.
Letters are used after the numerical character 9. Letters were chosen to represent numbers because they were easily typed and displayed by computers.
Each base's name is one greater than its highest digit value. For example, base 2 does not use a '2' because each base starts designating numbers at 0. Base 2 is called base 2 because it can display 2 values per column.
Thinking From Decimal
Base 10, known as decimal, is the base normally used for math. Base 10 is used instead of other bases because humans have ten fingers. And because humans learned to count with their fingers, base 10 almost seems natural.
Since you have to use a base when displaying or speaking a number, decimal is used almost everywhere. Other bases are named (e.g., base 16) according to the decimal display of the number of values per digit that the base uses. Base 16 wouldn't be called "base 16" if everyone used it. It would be called "base 10" because the base's name is the max number of values per digit plus one. And in hexadecimal or any other base, that number will be 10.
Counting on your Fingers
In the text above, this tutorial says that base 10 should almost seem natural. So why wouldn't it be completely natural? Because your hands can use base 11. Your hands can display any number from 0 to 10 which is what base 11 does. Base 10 cannot display 10 values with one digit.
In mathmatics, you'll carry over to the next digit when you can't display anything greater in that digit with the base you're using. But you won't when counting on your fingers. You can display 10 by holding out all of your fingers or by holding out one finger if you are counting in tens.
In decimal math, there is no inbetween '10' character for the first digit. You'll get to 9 and then carry over. But when counting on your fingers, you'll get to 9, and then you can carry over or hold out your tenth finger.
Carrying Over
Higher bases can display the same numbers as lower bases, but with fewer digits and lesser numerals. For example, 100 in base 16 is 256 in decimal. This is because digits in base 16 are worth more than digits in base 10.
Why? Because base 16 has to count through more digit values before it carries over to the next digit. For example, one less than 100 in base 16 is FF. Decimal does not display so many values per digit, so it carries over when it reaches 9. Hexadecimal goes up to F before it carries over to the next greater digit.
Digital Powers
Before going on to base conversions, take a look at the decimal power of each digit. Here's a table with the more common bases:
Base Digit 0 Digit 1 Digit 2
Binary1 (20)2 (21)4 (22)
Octal1 (80)8 (81)64 (82)
Decimal1 (100)10 (101)100 (102)
Hexadecimal1 (160)16 (161)256 (162)
The decimal value of each digit in a base is determined by finding baseNum to the power of digitNum. For example, if baseNum were 16 for hexadecimal, and digitNum were 2 for the third digit, the decimal eqivalent of a 1 in digit 2 would be 256. That is, the value of a 1 in hexadecimal's digit 2 would be the same as 256 in decimal. This provides us with a tool for conversion to and from decimal.
But we're using decimal to do the math, so the conversion can only be used with decimal numbers. If we were to use other bases with this conversion system, we would have to make another table.
Base Conversion
The typical approach would be to pop out the Windows calculator to convert your number. But the problem is Real Programmers don't use calculators. So you'll just have to learn how to convert numbers between bases.
When converting from one base to another, decimal (being ingrained) will be the base that is used to do the math. So you'll be converting from one base to decimal and then to another base if you need.
Some simple conversions from octal to decimal using the chart above:
Convert the octal number 25 to decimal:
``` For digit 1: 2 * 8 = 16. Add 16 to our result.
For digit 0: 5 * 1 = 5. Add 5 to our result.
The result is: 21.
```
Each digit was multiplied by its decimal value from the chart above. Then the products were added to find the result. To convert back to octal:
Convert the decimal number 21 to octal:
``` There are no 64's in our number.
There are two 8's in our number. Add 20 to our result.
There is a remainder of 21-16=5.
There are five 1's left. Add 5 to our result.
The result is: 25.
```
This example went through each octal digit in our chart from greatest to least. There were two 8's in the number. Because of these two 8's, two 10's were added to the result because 10 is decimal's value for digit 1 and the 8 is octal's value for digit 1. Now to do a conversion from decimal to binary:
Convert the decimal number 13 to binary:
``` There are no 16's in our number.
There is one 8 in our number. Add 1000 to our result.
There is a remainder of 13-8=5.
There is one 4 in our number. Add 100 to our result.
There is a remainder of 5-4=1.
There are no 2's in our number.
There is one 1 in our number. Add 1 to our result.
The result is: 1101.
```
That example used some binary digits not on our chart, but you can find that the numbers for binary digits 3 and 4 are 8 and 16 respectively. Now to convert back to decimal:
Convert the binary 1101 to decimal:
``` For digit 3: 1 * 8 = 8. Add 8 to our result.
For digit 2: 1 * 4 = 4. Add 4 to our result.
No value for digit 1.
For digit 0: 1 * 1 = 1. Add 1 to our result.
The result is: 13.
```
Now, to do a more complicated hexadecimal to decimal conversion in slightly different form.
Convert the hexadecimal 2EA.F to decimal:
``` result = (2 * 162) + (14 * 161) + (10 * 160) + (15 * 16-1)
result = (512) + (224) + (10) + (15/16)
result = 746 + 0.9375
result = 746.9375
```
A decimal point was used in the hexadecimal number, but floating-point numbers are covered later on. Also, 16 to the power of -1 is the same as 1/16. Now to convert the number back to hexadecimal.
Convert the decimal number 746.9375 to hexadecimal:
``` First the 746:
There are two 256's in our number. Add 200 to our result.
There is a remainder of 746-512=234.
There are fourteen 16's in our number. Add E0 to our result.
There is a remainder of 10.
There are ten 1's left in our number. Add A to our result.
The result is now: 2EA.
Now the fractional portion:
result2 = 9375/10000
result2 = 15/16 (reduced)
There are fifteen 1/16's in our number. Add 0.F to our result.
The result is 2EA.F.
```
There are several important things in this example. Because a hexadecimal digit can hold a higher value than a decimal digit, having ten 1s and fourteen 16s is reasonable. Because fractions in hexadecimal are in sixteenths instead of tenths as in decimal, 15/16 is the same as 0.F. It's just like having 9/10 in decimal - it's the same as 0.9.
Common Bases and their Uses
For computing purposes, hexadecimal, octal, and binary are often used. Hexadecimal is useful in computer science because it represents numbers in a compact form and it is easily converted to and from binary. With four bits, you can store any hexadecimal character from 0 to F:
000
111
2102
3113
41004
51015
61106
71117
810008
910019
101010A
111011B
121100C
131101D
141110E
151111F
Hexadecimal can represent the same value in much less space than binary and decimal. Each hexadecimal number is represented by four bits (called a nybble). This makes hexadecimal useful for displaying memory values in an efficient form.
Hexadecimal is also useful for storing up to four boolean values in a digit. For example, any addition of 1, 2, 4, or 8 yields a number with known components. For example, 3=1+2, F=8+4+2+1, E=4+8+2, 9=8+1. Any combination results in a number that can be decomposed into the numbers that add up to it. If you look at the table above, you'll see why (1, 2, 4, and 8 use separate bits). This makes hexadecimal useful for cog flags.
Hexadecimal can be easily converted to and from binary in a more simple method than the examples used. With the table above, you can convert a binary number of four bits into hexadecimal. For example, the number 11110011 is F3. Just seperate the binary number into nybbles and use the table above to find the hexadecimal equivalent.
Octal is similar to hexadecimal in that it is used for some of the same reasons. It's maximum digit value is 7 which is represented in binary as 111. Only three bits are needed to store an octal digit. Like hexadecimal, it is easily converted to and from binary - instead of nybbles, use groups of three bits.
Binary is extremely useful to computers because values of 0 and 1 - true and false - are easy to store and transfer. The downside is that they are much less efficient in terms of the space that it takes to store and display so many digits. For example, 9 in decimal is 1001 in binary.
Base Prefixes
As explained above, using a different base does not change the number you're displaying. It only changes the form that it's shown in. When writing numbers, especially in your code, you must specify the base of a number if it's not in decimal.
Say you used the number 100 in your code. When the interpreter/compiler/parser reads that, it will assume that the number is in decimal. To tell the parser what base the number is in, there are two standard prefixes to put before a number. These are '0x' for hexadecimal and '0' for octal.
If you want to write a hexadecimal 100, you would write 0x100. Or if you wanted to write 100 in octal, you would write 0100. Other bases will have to be converted. Not all parsers support these prefixes, but Cog, being based on C++, does support them.
Floats and Bases
A floating-point number (a float) uses a radix point (a decimal point in base 10) and numerals to its right to display the fractional portion of the number.
A hexadecimal or octal number can have a fractional part just as base 10 numbers do, but this is hardly ever done. Since there isn't much of a reason to have a floating-point number in anything but base 10, other bases are usually restricted to being whole numbers. Not even the Windows calculator allows floating-point numbers in non-decimal bases.
• Create: | 3,199 | 12,517 | {"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} | 3.890625 | 4 | CC-MAIN-2020-40 | longest | en | 0.871756 |
http://www.solutioninn.com/a-1000-par-value-bond-with-seven-years-left | 1,503,283,654,000,000,000 | text/html | crawl-data/CC-MAIN-2017-34/segments/1502886107487.10/warc/CC-MAIN-20170821022354-20170821042354-00625.warc.gz | 681,141,934 | 7,298 | # Question: A 1 000 par value bond with seven years left
A \$ 1,000 par value bond with seven years left to maturity has a 9 percent coupon rate (paid semiannually) and is selling for \$ 945.80. What is its yield to maturity?
View Solution:
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• CreatedJanuary 27, 2015
• Files Included | 84 | 302 | {"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-2017-34 | latest | en | 0.833171 |
http://openstudy.com/updates/55d4f364e4b0554d6272ed7f | 1,484,833,666,000,000,000 | text/html | crawl-data/CC-MAIN-2017-04/segments/1484560280668.34/warc/CC-MAIN-20170116095120-00216-ip-10-171-10-70.ec2.internal.warc.gz | 212,869,671 | 57,585 | ## anonymous one year ago Find the standard form of the equation of the parabola with a focus at (7, 0) and a directrix at x = -7.
1. anonymous
lol this might be 12 grade work lol cuz i never heard of it
2. anonymous
its precalc @*ImaBeMe*
3. anonymous
do you know whats special about a focus and directrix
4. anonymous
kinda not really @dan915
5. anonymous
okay basically for focus if u fire any line at into the parabola it will reflect off into the focus
6. anonymous
ok @nanaruiz123
7. anonymous
|dw:1440020061995:dw|
8. anonymous
|dw:1440020159826:dw|
9. anonymous
like that all vertical lines that bounce off the parabola will reflect into the focus
10. anonymous
|dw:1440020223165:dw|
11. anonymous
do you understand the focus now?
12. anonymous
yes but is there an equation i cant use or something @dan915
13. anonymous
well u are gonna solve for that
14. anonymous
you need to know what a focus and directrix is to solve for it
15. anonymous
|dw:1440020416431:dw|
16. anonymous
the vertex has to be at 0,0 because it has to be in the middle of the directrix and the focus now you need some more points so you can solve for the whole parabola equation
17. anonymous
|dw:1440020622812:dw|
18. anonymous
|dw:1440020708157:dw|
19. anonymous
wait im confused? @dan915
20. campbell_st
here is an easy method that uses the focal length and the standard form in this case of \[4a(x - h) = (y - k)^2\] (h, k) is the focus and a is the focal length|dw:1440022451273:dw| | 437 | 1,508 | {"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} | 2.921875 | 3 | CC-MAIN-2017-04 | longest | en | 0.86663 |
vediconcepts.org | 1,725,777,967,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700650960.90/warc/CC-MAIN-20240908052321-20240908082321-00163.warc.gz | 580,289,417 | 21,341 | # 7 ancient Indian mathematical discoveries that changed the world
Ancient India’s scientific acumen has been talked about the world over. It is the only civilization with so much regard for knowledge production and transmission.
## Place value system
The Indian place value system is a unique number system that uses base 10 as well as a fractional part of the number, called “paridha”, to represent any number. It has been used for centuries and it is still in use today in India.
## Zero
The number zero has defied the imagination of western mathematicians for a long. Even in the 21st-century number Zero (0) is not understood properly in western mathematics which leads to all kinds of problems. Rules of the sum of other numbers with Zero were given by Brahmgupta in his work “Brahmsputasiddhanta”, The root cause lies in the translation works of Al-Khwarizmi who didn’t accept 0 as a number. When the work went to Leonardo Pisano a.k.a. Fibonacci who translated many Arabian works to Latin, he didn’t get the definition of Bhaskaracharya. So on and so form. You can read more about it here.
## Rules for Negative Numbers
Brahmgupta, an Indian mathematician, first introduced negative numbers. He was the one who came up with a way to represent negative numbers in his book “Brahmasphuta Siddhanta” in 628 AD.
Brahmgupta’s work on mathematics was not as well-known as his work on astronomy and his contributions to Sanskrit literature, but he is still considered one of the greatest mathematicians of all time.
Quadratic equations are one of the most common types of equations that students in middle school and high school are taught to solve. In this section, we will discuss how to solve quadratic equations using the completing the square method.
The completing the square method is a technique that is used to find all solutions for quadratic equations. It can be used for any quadratic equation, but it is usually only needed when there is a positive number in front of the square root symbol.
## Binary Mathematics
Binary mathematics has been described in Vedas but it is made famous by a text of music by Pingala named “Chhandahshastra” meaning science of meters. The main commentaries on “Chhandahshastra” are “Vrittaratnakara” by Kedara, “Tatparyatika” by Trivikrama and “Mritasanjivani” by Halayudha.
## Infinite Series
Madhava had worked on the infinite series of various functions much before Newton & Leibniz. According to CK Raju, Madhava may have worked on calculus much before Newtown & Leibniz got it from Jesuits.
## Algebra
Bijaganita is the name we call algebra with. Brahmagupta did exemplary work in the field of Algebra.
## Wrapping Up
In India, around the 5th century A.D., a system of mathematics that made astronomical calculations easy was developed. In those times its application was limited to astronomy as its pioneers were Astronomers. Astronomical calculations are complex and involve many variables that go into the derivation of unknown quantities. Algebra is a short-hand method of calculation and by this feature, it scores over conventional arithmetic. | 693 | 3,115 | {"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} | 3.953125 | 4 | CC-MAIN-2024-38 | latest | en | 0.960653 |
https://ebs.sakarya.edu.tr/Ders/Detay/543486 | 1,620,313,710,000,000,000 | text/html | crawl-data/CC-MAIN-2021-21/segments/1620243988758.74/warc/CC-MAIN-20210506144716-20210506174716-00374.warc.gz | 238,328,349 | 19,511 | Course Name Code Semester T+U Hours Credit ECTS
Building and Construction Systems II MIM 208 4 3 + 2 4 6
Precondition Courses Recommended Optional Courses Course Language Turkish Course Level Bachelor's Degree Course Type Compulsory Course Coordinator Prof.Dr. TAHSİN TURĞAY Course Lecturers Prof.Dr. TAHSİN TURĞAY, ZEYNEP BERRE KARA, PINAR ERKUŞ BUYRUK, Course Assistants Course Category Course Objective Basic principles of Statics. Properties of structural materials; analysis of stress and deformation in axially loaded members, circular shafts, and beams, and in statically indeterminate systems containing these components. Course Content Basic concepts and principles, a point that intersects the plane forces, moments, and the concept of a pair of force, the general status of forces in the plane, plane trusses, centroids, moments of inertia, the classification of external forces, delivery systems and support reactions, cables and friction investigation and analysis of samples. The basic concepts of strengths of materials, drawing diagrams of bending moment, shear and axial forces, normal force status, shear state bending, moments of inertia, parallel axis theorem state, state of torsional bending and examination with examples of situations.
# Course Learning Outcomes Teaching Methods Assessment Methods
1 Grasp load transfer throughout the building Lecture, Question-Answer, Discussion, Testing, Homework,
2 Obtain the basics of structural modeling Lecture, Question-Answer, Discussion, Testing, Homework,
3 Explain the basics of structural behaviour under gravity and lateral forces and design of structural members Lecture, Question-Answer, Discussion, Testing, Homework,
Week Course Topics Preliminary Preparation
1 Introduction to Statics and Strength of Materials, Definitions
2 Free drawing diagrams, force, torque, load, support, stability
3 Support reaction
4 Diagram of internal forces
5 Gerber internal forces of beams and frames
6 Trusses
7 Midterm Exam
8 Cross-section, to have the center of gravity
9 Moment of inertia, torque strength, radius of inertia
10 stress
11 Pulling - pressure elements
12 Bending elements
13 compound strength
14 OVERVIEW
Resources
Course Notes Lecture notes given by the coordinator.
Course Resources BEER, F. P. E., JOHNSTON, Jr. R., Statik, Çevirenler : Fikret Keskinel, Tekin Özbek, Birsen Yayınevi İstanbul 1992 BAKİOĞLU, M., KADIOĞLU, N., Statik Problemleri, Beta , İstanbul,2001 AKÖZ, A.Y., ERATLI, N. 2000; Statik-Mukavemet, Beta Basım A. Ş., İstanbul İNAN M., Cisimlerin Mukavemeti, İTÜ Matbası, İstanbul,1970 KADIOĞLU, N., Mukavemet Problemleri, , Beta, İstanbul, 1989
Evaluation System
Semester Studies Contribution Rate
1. Ödev 100
Total 100
1. Yıl İçinin Başarıya 45
1. Final 55
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Your QlikView QV12BA exam is just around the corner, right? So, it's high time to find an effective preparation tool! Our training course is what you really need! This is a series of videos led by the experienced IT instructors who will provide you with a detailed overview of the QV12BA certification test. Ace your QlikView QV12BA at the first attempt and obtain the QlikView 12 Business Analyst Certification Exam credential with ease.
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1. Before You Start! 01:01
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1. Introduction of Data Tables 03:08
2. QVD Viewer, Script and Data Model 02:28
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1. What is Set Analysis 03:34
2. Understand Set Analysis Practically 11:06
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1. Set Analysis and it's Components 04:45
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1. Introduction of QVW 01:28
2. Set Identifiers Part 01 09:29
3. Set Identifiers Part 02 06:20
4. Set Identifiers Part 03 03:15
5. Set Identifier Part 04 02:46
6. Set Operators 13:55
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1. String and Integer Part 01 10:21
2. String and Integer Part 02 14:19
3. BookMarks 08:03
4. Wildcard searches 08:13
5. Functions returning Members 15:21
6. Nested Set Analysis 07:16
7. Handling Null Values 07:25
8. Compare Two Fields 05:48
9. Set Operators inside Set Modifiers 08:23
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2. Using a Function for Multiple Field Exclusion 15:24
3. Using \$ with Field Exclusion 05:46
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2. Formatting Dollar-sign Result Part 01 12:39
3. Formatting Dollar-sign Result Part 02 07:21
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2. YTD and MTD Reports 16:30
3. Point in Time Reporting with Nested Set Expression 11:13
4. Growth report by comparing periods 14:56
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1. Alternate State Introduction 13:14
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1. Introduction and Examples 15:43
2. Using Variables for Point in Time Reporting 15:48
3. Double Dollar Sign Expansion 10:46
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1. Introduction of P() and E() 15:53
2. Examples of P and E() Part 1 10:18
3. Examples of P() and E() Part 2 14:58
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1. Functions Introduction 09:25
2. Useful QV Functions Part 01 05:55
3. Useful QV Functions Part 02 06:50
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Try Free Demo | 878 | 2,895 | {"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-2024-22 | latest | en | 0.644578 |
https://physicshelpforum.com/tags/tensor/ | 1,582,931,913,000,000,000 | text/html | crawl-data/CC-MAIN-2020-10/segments/1581875148163.71/warc/CC-MAIN-20200228231614-20200229021614-00083.warc.gz | 490,803,872 | 13,951 | # tensor
1. ### Inertial "moment" of a solid given an inertia tensor
Hi all, I am programming some software computing inertial forces of some moving structure. So far, the structure have been represented as a cloud of mass points. For each mass point, inertial forces are computed using some formulas like in this article...
2. ### Stress energy tensor transformation
Show that if you add a total derivative to the Lagrangian density L \to L + \partial_\mu X^\mu, the energy momentum tensor changes as T^{\mu\nu} \to T^{\mu\nu}+\partial_\alpha B^{\alpha\mu\nu} with B^{\alpha\mu\nu}=-B^{\mu\alpha\nu}. (Note: the Lagrangian can depend on higher order derivatives...
3. ### What causes rotation in the Navier-Stokes Equation?
It is known that rotation in the flow results from the viscous terms in the Navier-Stokes (N-S) equation. However, when deriving the N-S equation from the general principle of linear momentum in Continuum Mechanics, we use the constitutive relation for isotropic Newtonian fluids which states...
4. ### Tensor calculation in Lorentztransformations
Hi, I have difficulties understanding the following relations. Given the Minkowski metric \eta_{\alpha\beta}=diag(1,-1,-1,-1) and the line segment ds^2 = dx^2+dy^2+dz^2, then how can i see that this line segment is equal to ds^2 = \eta_{\alpha\beta}dx^\alpha dx^\beta . Further, we want the...
5. ### Lagrangian Mechanics - metric tensor
I am trying to follow the derivation of the Noether's theorem with respect to a complex wave on a guitar string. My text obtains the Lagrangian: [TEX]\mathcal{L}=\frac 12 (\partial_\mu \chi^*)(\partial^\mu \chi)[\TEX] In deriving this Lagrangian density in classical mechanics is the...
6. ### Strain tensor
Hi folks, An apparently simple question about the strain tensor I cannot figure out myself though... Tensors are said to be "objects" that accomplish a linear mapping between two vectors. The moment of inertia tensor, for instance, relates the angular momentum to the angular velocity. In...
7. ### Tensor Calculus Proof
Hi, I am studying tensor calculus and I am not too familiar with tensors currently. The question I have is: The steps to prove that a lie derivative satisfies the usual product rule, ie it is Leibniz. Please see my attachment that shows where I am up to. It is much easier to scan this than...
8. ### Questions for dielectric tensor
1. About the dielectric tensor in 1-dimensional semiconductors: it seems that the tensors should be diagonal, but what about the array of such system? should we expect an isoptropic behavior? 2. Suppose we have the born effective charges of such a system, how can we get the dielectric tensor...
9. ### Weyl tensor dynamic
I recently became interested in relativity, therefore, I got me some good books on the subject and have decided to self-study as I find time. Anyway, has anyone ever seen the sci-fi/horror movie Event Horizon?. In the beginning, the man who developed the drive which propels the ship by...
10. ### Classiscal Mechanics: Inertia Tensor
A rigid body consists of three equal masses (m)fastened at the position (a,0,0), (0,a,2a), and (0,2a,a). Find the inertia tensor I. Find the principal moments and a set of orthogonal principal axes. What I have done so far is use the positions to draw a pictorial representation. Then I tried... | 813 | 3,337 | {"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} | 3.40625 | 3 | CC-MAIN-2020-10 | latest | en | 0.851328 |
http://www.territorioscuola.com/wikipedia/en.wikipedia.php?title=Symmetry_in_mathematics | 1,397,909,269,000,000,000 | text/html | crawl-data/CC-MAIN-2014-15/segments/1397609537186.46/warc/CC-MAIN-20140416005217-00263-ip-10-147-4-33.ec2.internal.warc.gz | 697,384,754 | 24,625 | # Symmetry in mathematics
The root system of the exceptional Lie group E8. Lie groups have many symmetries.
Symmetry occurs not only in geometry, but also in other branches of mathematics. Symmetry is a type of invariance: the property that something does not change under a set of transformations.
Given a structured object X of any sort, a symmetry is a mapping of the object onto itself which preserves the structure. This occurs in many cases; for example, if X is a set with no additional structure, a symmetry is a bijective map from the set to itself, giving rise to permutation groups. If the object X is a set of points in the plane with its metric structure or any other metric space, a symmetry is a bijection of the set to itself which preserves the distance between each pair of points (an isometry).
In general, every kind of structure in mathematics will have its own kind of symmetry, many of which are listed in this article.
## Symmetry in geometry
The types of symmetry considered in basic geometry (like reflection and rotation symmetry) are described more fully in the main article on symmetry.
### Abstract symmetry
#### Klein's view
With every geometry, Felix Klein associated an underlying group of symmetries. The hierarchy of geometries is thus mathematically represented as a hierarchy of these groups, and hierarchy of their invariants. For example, lengths, angles and areas are preserved with respect to the Euclidean group of symmetries, while only the incidence structure and the cross-ratio are preserved under the most general projective transformations. A concept of parallelism, which is preserved in affine geometry, is not meaningful in projective geometry. Then, by abstracting the underlying groups of symmetries from the geometries, the relationships between them can be re-established at the group level. Since the group of affine geometry is a subgroup of the group of projective geometry, any notion invariant in projective geometry is a priori meaningful in affine geometry; but not the other way round. If you add required symmetries, you have a more powerful theory but fewer concepts and theorems (which will be deeper and more general).
#### Thurston's view
William Thurston introduced a similar version of symmetries in geometry. A model geometry is a simply connected smooth manifold X together with a transitive action of a Lie group G on X with compact stabilizers. The Lie group can be thought of as the group of symmetries of the geometry.
A model geometry is called maximal if G is maximal among groups acting smoothly and transitively on X with compact stabilizers, i.e. if it is the maximal group of symmetries. Sometimes this condition is included in the definition of a model geometry.
A geometric structure on a manifold M is a diffeomorphism from M to X/Γ for some model geometry X, where Γ is a discrete subgroup of G acting freely on X. If a given manifold admits a geometric structure, then it admits one whose model is maximal.
A 3-dimensional model geometry X is relevant to the geometrization conjecture if it is maximal and if there is at least one compact manifold with a geometric structure modelled on X. Thurston classified the 8 model geometries satisfying these conditions; they are listed below and are sometimes called Thurston geometries. (There are also uncountably many model geometries without compact quotients.)
## Symmetry in calculus
### Even and odd functions
#### Even functions
ƒ(x) = x2 is an example of an even function.
Let f(x) be a real-valued function of a real variable. Then f is even if the following equation holds for all x and -x in the domain of f:
$f(x) = f(-x). \,$
Geometrically speaking, the graph face of an even function is symmetric with respect to the y-axis, meaning that its graph remains unchanged after reflection about the y-axis.
Examples of even functions are |x|, x2, x4, cos(x), and cosh(x).
#### Odd functions
ƒ(x) = x3 is an example of an odd function.
Again, let f(x) be a real-valued function of a real variable. Then f is odd if the following equation holds for all x and -x in the domain of f:
$-f(x) = f(-x) \, ,$
or
$f(x) + f(-x) = 0 \, .$
Geometrically, the graph of an odd function has rotational symmetry with respect to the origin, meaning that its graph remains unchanged after rotation of 180 degrees about the origin.
Examples of odd functions are x, x3, sin(x), sinh(x), and erf(x).
### Integrating
The integral of an odd function from −A to +A is zero (where A is finite, and the function has no vertical asymptotes between −A and A).
The integral of an even function from −A to +A is twice the integral from 0 to +A (where A is finite, and the function has no vertical asymptotes between −A and A. This also holds true when A is infinite, but only if the integral converges).
### Series
• The Maclaurin series of an even function includes only even powers.
• The Maclaurin series of an odd function includes only odd powers.
• The Fourier series of a periodic even function includes only cosine terms.
• The Fourier series of a periodic odd function includes only sine terms.
## Symmetry in linear algebra
### Symmetry in matrices
In linear algebra, a symmetric matrix is a square matrix that is equal to its transpose. Formally, matrix A is symmetric if
$A = A^{\top}$
and, because the definition of matrix equality demands equality of their dimensions, only square matrices can be symmetric.
The entries of a symmetric matrix are symmetric with respect to the main diagonal. So if the entries are written as A = (aij), then aij = aji, for all indices i and j.
The following 3×3 matrix is symmetric:
$\begin{bmatrix} 1 & 7 & 3\\ 7 & 4 & -5\\ 3 & -5 & 6\end{bmatrix}.$
Every square diagonal matrix is symmetric, since all off-diagonal entries are zero. Similarly, each diagonal element of a skew-symmetric matrix must be zero, since each is its own negative.
In linear algebra, a real symmetric matrix represents a self-adjoint operator over a real inner product space. The corresponding object for a complex inner product space is a Hermitian matrix with complex-valued entries, which is equal to its conjugate transpose. Therefore, in linear algebra over the complex numbers, it is often assumed that a symmetric matrix refers to one which has real-valued entries. Symmetric matrices appear naturally in a variety of applications, and typical numerical linear algebra software makes special accommodations for them.
## Symmetry in abstract algebra
### Symmetric groups
The symmetric group Sn on a finite set of n symbols is the group whose elements are all the permutations of the n symbols, and whose group operation is the composition of such permutations, which are treated as bijective functions from the set of symbols to itself.1 Since there are n! (n factorial) possible permutations of a set of n symbols, it follows that the order (the number of elements) of the symmetric group Sn is n!.
### Symmetric polynomials
A symmetric polynomial is a polynomial P(X1, X2, …, Xn) in n variables, such that if any of the variables are interchanged, one obtains the same polynomial. Formally, P is a symmetric polynomial, if for any permutation σ of the subscripts 1, 2, ..., n one has P(Xσ(1), Xσ(2), …, Xσ(n)) = P(X1, X2, …, Xn).
Symmetric polynomials arise naturally in the study of the relation between the roots of a polynomial in one variable and its coefficients, since the coefficients can be given by polynomial expressions in the roots, and all roots play a similar role in this setting. From this point of view the elementary symmetric polynomials are the most fundamental symmetric polynomials. A theorem states that any symmetric polynomial can be expressed in terms of elementary symmetric polynomials, which implies that every symmetric polynomial expression in the roots of a monic polynomial can alternatively be given as a polynomial expression in the coefficients of the polynomial.
#### Examples
In two variables X1, X2 one has symmetric polynomials like
• $X_1^3+ X_2^3-7$
• $4 X_1^2X_2^2 +X_1^3X_2 + X_1X_2^3 +(X_1+X_2)^4$
and in three variables X1, X2, X3 one has for instance
• $X_1 X_2 X_3 - 2 X_1 X_2 - 2 X_1 X_3 - 2 X_2 X_3 \,$
### Symmetric tensors
n mathematics, a symmetric tensor is tensor that is invariant under a permutation of its vector arguments:
$T(v_1,v_2,\dots,v_r) = T(v_{\sigma 1},v_{\sigma 2},\dots,v_{\sigma r})$
for every permutation σ of the symbols {1,2,...,r}. Alternatively, an rth order symmetric tensor represented in coordinates as a quantity with r indices satisfies
$T_{i_1i_2\dots i_r} = T_{i_{\sigma 1}i_{\sigma 2}\dots i_{\sigma r}}.$
The space of symmetric tensors of rank r on a finite-dimensional vector space is naturally isomorphic to the dual of the space of homogeneous polynomials of degree r on V. Over fields of characteristic zero, the graded vector space of all symmetric tensors can be naturally identified with the symmetric algebra on V. A related concept is that of the antisymmetric tensor or alternating form. Symmetric tensors occur widely in engineering, physics and mathematics.
### Galois theory
Given a polynomial, it may be that some of the roots are connected by various algebraic equations. For example, it may be that for two of the roots, say A and B, that A2 + 5B3 = 7. The central idea of Galois theory is to consider those permutations (or rearrangements) of the roots having the property that any algebraic equation satisfied by the roots is still satisfied after the roots have been permuted. An important proviso is that we restrict ourselves to algebraic equations whose coefficients are rational numbers. Thus, Galois theory studies the symmetries inherent in algebraic equations.
### Automorphisms of algebraic objects
In abstract algebra, an automorphism is an isomorphism from a mathematical object to itself. It is, in some sense, a symmetry of the object, and a way of mapping the object to itself while preserving all of its structure. The set of all automorphisms of an object forms a group, called the automorphism group. It is, loosely speaking, the symmetry group of the object.
#### Examples
• In set theory, an arbitrary permutation of the elements of a set X is an automorphism. The automorphism group of X is also called the symmetric group on X.
• In elementary arithmetic, the set of integers, Z, considered as a group under addition, has a unique nontrivial automorphism: negation. Considered as a ring, however, it has only the trivial automorphism. Generally speaking, negation is an automorphism of any abelian group, but not of a ring or field.
• A group automorphism is a group isomorphism from a group to itself. Informally, it is a permutation of the group elements such that the structure remains unchanged. For every group G there is a natural group homomorphism G → Aut(G) whose image is the group Inn(G) of inner automorphisms and whose kernel is the center of G. Thus, if G has trivial center it can be embedded into its own automorphism group.2
• In linear algebra, an endomorphism of a vector space V is a linear operator VV. An automorphism is an invertible linear operator on V. When the vector space is finite-dimensional, the automorphism group of V is the same as the general linear group, GL(V).
• A field automorphism is a bijective ring homomorphism from a field to itself. In the cases of the rational numbers (Q) and the real numbers (R) there are no nontrivial field automorphisms. Some subfields of R have nontrivial field automorphisms, which however do not extend to all of R (because they cannot preserve the property of a number having a square root in R). In the case of the complex numbers, C, there is a unique nontrivial automorphism that sends R into R: complex conjugation, but there are infinitely (uncountably) many "wild" automorphisms (assuming the axiom of choice).3 Field automorphisms are important to the theory of field extensions, in particular Galois extensions. In the case of a Galois extension L/K the subgroup of all automorphisms of L fixing K pointwise is called the Galois group of the extension.
## Symmetry in representation theory
### Symmetry in quantum mechanics: bosons and fermions
In quantum mechanics, bosons have representatives that are symmetric under permutation operators, and fermions have antisymmetric representatives.
This implies the Pauli exclusion principle for fermions. In fact, the Pauli exclusion principle with a single-valued many-particle wavefunction is equivalent to requiring the wavefunction to be antisymmetric. An antisymmetric two-particle state is represented as a sum of states in which one particle is in state $\scriptstyle |x \rangle$ and the other in state $\scriptstyle |y\rangle$:
$|\psi\rangle = \sum_{x,y} A(x,y) |x,y\rangle$
and antisymmetry under exchange means that A(x,y) = −A(y,x). This implies that A(x,x) = 0, which is Pauli exclusion. It is true in any basis, since unitary changes of basis keep antisymmetric matrices antisymmetric, although strictly speaking, the quantity A(x,y) is not a matrix but an antisymmetric rank-two tensor.
Conversely, if the diagonal quantities A(x,x) are zero in every basis, then the wavefunction component:
$A(x,y)=\langle \psi|x,y\rangle = \langle \psi | ( |x\rangle \otimes |y\rangle )$
is necessarily antisymmetric. To prove it, consider the matrix element:
$\langle\psi| ((|x\rangle + |y\rangle)\otimes(|x\rangle + |y\rangle)) \,$
This is zero, because the two particles have zero probability to both be in the superposition state $\scriptstyle |x\rangle + |y\rangle$. But this is equal to
$\langle \psi |x,x\rangle + \langle \psi |x,y\rangle + \langle \psi |y,x\rangle + \langle \psi | y,y \rangle \,$
The first and last terms on the right hand side are diagonal elements and are zero, and the whole sum is equal to zero. So the wavefunction matrix elements obey:
$\langle \psi|x,y\rangle + \langle\psi |y,x\rangle = 0 \,$.
or
$A(x,y)=-A(y,x) \,$
## Symmetry in set theory
### Symmetric relation
We call a relation symmetric if every time the relation stands from A to B, it stands too from B to A. Note that symmetry is not the exact opposite of antisymmetry.
## Symmetry in metric spaces
### Isometries of a space
An isometry is a distance-preserving map between metric spaces. Given a metric space, or a set and scheme for assigning distances between elements of the set, an isometry is a transformation which maps elements to another metric space such that the distance between the elements in the new metric space is equal to the distance between the elements in the original metric space. In a two-dimensional or three-dimensional space, two geometric figures are congruent if they are related by an isometry: related by either a rigid motion, or a composition of a rigid motion and a reflection. Up to a relation by a rigid motion, they are equal if related by a direct isometry.
## Symmetries of differential equations
A symmetry of a differential equation is a transformation that leaves the differential equation invariant. Knowledge of such symmetries may help solve the differential equation.
A Lie symmetry of a system of differential equations is a continuous symmetry of the system of differential equations. Knowledge of a Lie symmetry can be used to simplify an ordinary differential equation through reduction of order.4
For ordinary differential equations, knowledge of an appropriate set of Lie symmetries allows one to explicitly calculate a set of first integrals, yielding a complete solution without integration.
Symmetries may be found by solving a related set of ordinary differential equations.4 Solving these equations is often much simpler than solving the original differential equations.
## Symmetry in probability
In the case of a finite number of possible outcomes, symmetry with respect to permutations (relabelings) implies a discrete uniform distribution.
In the case of a real interval of possible outcomes, symmetry with respect to interchanging sub-intervals of equal length corresponds to a continuous uniform distribution.
In other cases, such as "taking a random integer" or "taking a random real number", there are no probability distributions at all symmetric with respect to relabellings or to exchange of equally long subintervals. Other reasonable symmetries do not single out one particular distribution, or in other words, there is not a unique probability distribution providing maximum symmetry.
There is one type of isometry in one dimension that may leave the probability distribution unchanged, that is reflection in a point, for example zero.
A possible symmetry for randomness with positive outcomes is that the former applies for the logarithm, i.e., the outcome and its reciprocal have the same distribution. However this symmetry does not single out any particular distribution uniquely.
For a "random point" in a plane or in space, one can choose an origin, and consider a probability distribution with circular or spherical symmetry, respectively.
## References
1. ^ Jacobson (2009), p. 31.
2. ^ PJ Pahl, R Damrath (2001). "§7.5.5 Automorphisms". Mathematical foundations of computational engineering (Felix Pahl translation ed.). Springer. p. 376. ISBN 3-540-67995-2.
3. ^ Yale, Paul B. (May 1966). "Automorphisms of the Complex Numbers". Mathematics Magazine 39 (3): 135–141. doi:10.2307/2689301. JSTOR 2689301.
4. ^ a b Olver, Peter J. (1986). Applications of Lie Groups to Differential Equations. New York: Springer Verlag. ISBN 978-0-387-95000-6.
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TerritorioScuola. Some rights reserved. Informazioni d'uso ☞ | 4,137 | 17,885 | {"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": 19, "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-2014-15 | latest | en | 0.94504 |
http://www.solutioninn.com/reconsider-prob-914-suppose-that-the-sales-forecasts-have-been | 1,495,717,096,000,000,000 | text/html | crawl-data/CC-MAIN-2017-22/segments/1495463608067.23/warc/CC-MAIN-20170525121448-20170525141448-00130.warc.gz | 655,221,336 | 7,449 | # Question: Reconsider Prob 9 1 4 Suppose that the sales forecasts have been
Reconsider Prob. 9.1-4. Suppose that the sales forecasts have been revised downward to 240, 400, and 320 units per day of products 1, 2, and 3, respectively, and that each plant now has the capacity to produce all that is required of any one product. Therefore, management has decided that each new product should be assigned to only one plant and that no plant should be assigned more than one product (so that three plants are each to be assigned one product, and two plants are to be assigned none). The objective is to make these assignments so as to minimize the total cost of producing these amounts of the three products.
(a) Formulate this problem as an assignment problem by constructing the appropriate cost table.
\$1.99
Sales1
Views196 | 186 | 826 | {"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-2017-22 | longest | en | 0.969673 |
https://solvedlib.com/n/find-the-derivative-ofy-6x4-sin-6x-v1-36x8-with-respect,2668156 | 1,686,284,894,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224655247.75/warc/CC-MAIN-20230609032325-20230609062325-00708.warc.gz | 579,366,574 | 19,337 | # Find the derivative ofy = 6x4 sin (6x*) V1 36x8 with respect to xThe derivative of y = 6x sin
###### Question:
Find the derivative ofy = 6x4 sin (6x*) V1 36x8 with respect to x The derivative of y = 6x sin (6x4) 41-36x8 with respect to x is
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##### Has been suggested that rotating cylinders bout 20.0 mi long and 443 diameter the centripetal cceleration its surface equals the free-fall acceleration Earth? rad/slaced space and usedcolonies What angular specd must such cylinder havethatNeed Help?Jeiju
has been suggested that rotating cylinders bout 20.0 mi long and 443 diameter the centripetal cceleration its surface equals the free-fall acceleration Earth? rad/s laced space and used colonies What angular specd must such cylinder have that Need Help? Jeiju...
##### ’s10,11,12,13,14,15 POLMR Curious George walked due East, then due North, and then again due East. The...
’s10,11,12,13,14,15 POLMR Curious George walked due East, then due North, and then again due East. The total distance he walked was 87 m. Sketch a diagram (and label each segment with its corresponding distance) that COULD BE George's path. Then find the magnitude of his displacement ...
##### What is delineation of privileges for a physician at a hospital? What are the two main...
What is delineation of privileges for a physician at a hospital? What are the two main reasons for the process of PECO?...
##### For Ihe Divon functon, Ind (@) 5 Lquabon 0 a Cnlmna Ihroah lue( YulueDonts Ka ru % huL 0egven valas andLomaridU tuountiino Knentnas tne")= Adde1723Whch = telotowtng lonmulas cunJind tho slape of Ine Mani Iine?J+-1731- -FiaI3-(-11FdTho nquation Iho sncnnt InalTha equmtion 04 Ira torOont Ing Alie 1 mC
For Ihe Divon functon, Ind (@) 5 Lquabon 0 a Cnlmna Ihroah lue( Yulue Donts Ka ru % huL 0egven valas and Lomarid U tuountiino Knentnas tne ")= Adde 1723 Whch = telotowtng lonmulas cun Jind tho slape of Ine Mani Iine? J+-1 731- - FiaI 3-(-11 Fd Tho nquation Iho sncnnt Inal Tha equmtion 04 Ira...
##### Five more questions_ Show clearly all your working out and reasoning: Only do these questions when you are sure you understand the first ten. (11) Let f (x) be function defined byif € < 1 ifz 2 1.f(z)(a) Sketch the graph of f (z) (b) Does limr-, = f (z) exist? (c) Explain if f (r) is continuous Or not ati = 1. (12) Let f (c) =1' 32 + 1. Explain why the Intermediate Value Theorem shows that ther at least one solution to the equation31 + 1 = 0in the interval (~1,1).
Five more questions_ Show clearly all your working out and reasoning: Only do these questions when you are sure you understand the first ten. (11) Let f (x) be function defined by if € < 1 ifz 2 1. f(z) (a) Sketch the graph of f (z) (b) Does limr-, = f (z) exist? (c) Explain if f (r) is con...
##### In polr coordinates, the equation of an ellpse which has one focus at the origin, its centre at the point ( 4,0) and its major axis of length 10,is given byNone from these answers10 5 4cose5+ 4cose 10 7+3c0s02 + 5cose
In polr coordinates, the equation of an ellpse which has one focus at the origin, its centre at the point ( 4,0) and its major axis of length 10,is given by None from these answers 10 5 4cose 5+ 4cose 10 7+3c0s0 2 + 5cose...
##### S Inventories such that there was a reversal lIIon for the 2015 write-down, how would Samsung...
s Inventories such that there was a reversal lIIon for the 2015 write-down, how would Samsung account for this under IFRS? Would Samsung's accounting be different for this reversal if it reported under U.S GAAP? Explain. connect Warnerwoods Company uses a perpetual inventory system. It entered i...
##### Show that for isothermal atmosphere e Z 71). (T is constant for isothermal atmosphere and p...
Show that for isothermal atmosphere e Z 71). (T is constant for isothermal atmosphere and p pRT). The pressure at the base of a skyscraper is 14.7 psia and at the top of the skyscraper is 14.4 psia. The temperature is constant at 70°F i.e. isothermal atmosphere. How tall is the skyscraper?...
##### 2. (-16 Points) DETAILS CHENEYLINALG2 6.1.017. 0/2 Submissions Used 9 Let A - Find the characteristic...
2. (-16 Points) DETAILS CHENEYLINALG2 6.1.017. 0/2 Submissions Used 9 Let A - Find the characteristic polynomial. 11 Det(A - AI) - Find the eigenvalues and eigenvectors for each eigenvalue. (Order your answers from smallest to largest eigenvalue.) 21 has eigenspace span 12 has eigenspace span Find a...
##### E connect Calculus MAT151: MAT 151 - 300 Sprin ctice Test Integrals Question 6 (of 14)...
E connect Calculus MAT151: MAT 151 - 300 Sprin ctice Test Integrals Question 6 (of 14) value: 0.71 points Round your answer to the nearest integer. Compute the average value of the function f(x)=x2-8 on the interval (0,6). fargO...
##### Suppose that the driving time for a commuter student from hishome to his campus is uniformly distributed between 20 minutes and40 minutes. The student measures his driving time for 10 days.Approximate the probability that his average driving time duringthese 10 days is more than 31 minutes. (Include two digits afterthe decimal point in your answer, i.e. write it in the form0.xy.)
Suppose that the driving time for a commuter student from his home to his campus is uniformly distributed between 20 minutes and 40 minutes. The student measures his driving time for 10 days. Approximate the probability that his average driving time during these 10 days is more than 31 minutes. (Inc...
##### Evaluate Quortien 2 0^;(1 No colfect Answel (1+ 0 0 = {
Evaluate Quortien 2 0^;(1 No colfect Answel (1+ 0 0 = {...
##### Calculus and vector fields
Let g(x,y)=arctan(xy) find (1) the directional derivative of the function at the point P= (1,2) in the direction of v= 5i +10 j (2) the minimum rate of charge ofg(x,y) at the point P. (3) the direction in which the minimum occures...
##### Question 10Answer savedPoints out of 1.00Flag queguonWhy do most Ionic compounds dissolve as ions in an aqueous solvent?Select one; Oa solvent molecules are more attracted to each other than they are t0 solute anlons are attracted to the positive hydrogen end ofithe water molecule cations are attracted to the negative hydrogen end ofthe water molecule anions are attracted to the negative hydrogen end ofthe water moleculethe Ions repel each otherClear my choice
Question 10 Answer saved Points out of 1.00 Flag queguon Why do most Ionic compounds dissolve as ions in an aqueous solvent? Select one; Oa solvent molecules are more attracted to each other than they are t0 solute anlons are attracted to the positive hydrogen end ofithe water molecule cations are a...
##### IsuMMARY OUTPUT Regression Statistics [Multiple R 0.852982944 R Square Adjusted R Square 0.701635128 Standard Error 135.749578 ObsetvationsANOVAMSRegression Residual Total1033565.051 386986.9072 18427.95 1420551.958Coeticienis Standaud Enor 2127.30q 384.940IInterceptstat 526 019 826 39LOGL 644 and DTTo waTSTUaA66 IFind the missing values Al Denotethc dependent aiable as Y Wite the regression equation ? (5 marksi Hot many percentlof the Ywriation ofiY that can be explained by this model?
IsuMMARY OUTPUT Regression Statistics [Multiple R 0.852982944 R Square Adjusted R Square 0.701635128 Standard Error 135.749578 Obsetvations ANOVA MS Regression Residual Total 1033565.051 386986.9072 18427.95 1420551.958 Coeticienis Standaud Enor 2127.30q 384.940 IIntercept stat 526 019 826 39LOGL 64...
##### A child in your classroom just stuck scissors into the electrical outlet. Your immediate action should...
A child in your classroom just stuck scissors into the electrical outlet. Your immediate action should be to: grab the child and pull him away from the outlet call for emergency medical assistance run and turn off the circuit breaker begin mouth-to-mouth resuscitation and treat for signs of shock...
##### [3 marks] The Vancouver Island wolf Canis lupus crassodon) is an endangered subspecies of the grey wolf; endemic to northern Vancouver Island: A rescarcher measures the length of the upper canine teeth of seven Vancouver Island wolves in mm; as recorded below_23262632272826Use this sample to determine the upper limit of a 90% confidence interval for the population mean length of the teeth (in mm)
[3 marks] The Vancouver Island wolf Canis lupus crassodon) is an endangered subspecies of the grey wolf; endemic to northern Vancouver Island: A rescarcher measures the length of the upper canine teeth of seven Vancouver Island wolves in mm; as recorded below_ 23 26 26 32 27 28 26 Use this sample to...
##### 2.)a. What does CRISPR stand for? Describe was aCRISPR is.b. Define Cas9 and describe in detail itsrole in CRISPR-based immunity.
2.) a. What does CRISPR stand for? Describe was a CRISPR is. b. Define Cas9 and describe in detail its role in CRISPR-based immunity....
##### Make one to two insightful conjecture(s) for the locations of the centroid, orthocenter; and circumcenter in a 45" 45" 90" triangle: Prove your proposed conjecture(s)_
Make one to two insightful conjecture(s) for the locations of the centroid, orthocenter; and circumcenter in a 45" 45" 90" triangle: Prove your proposed conjecture(s)_...
##### Gueslion0i 5Verify that the equation is an identity.Show that sec=2cot sCc a +]RuleStatementSoScc aSelect Rule
Gueslion 0i 5 Verify that the equation is an identity. Show that sec =2cot sCc a +] Rule Statement So Scc a Select Rule...
##### 17. Given the following covariance matrix Stock X Stock Y Stock X 0.09 0.035 Stock Y...
17. Given the following covariance matrix Stock X Stock Y Stock X 0.09 0.035 Stock Y 0.035 0.04 What is the correlation between stock X and stock Y? A. 1.2356 B. 0.0348 C. 0.0583 D. 0.0753 E. None of the above...
##### Clessify cach corpourd utcrz - electolyte, weak clectrolyte; cr ronelectrolyie Srocg = electrolyre Weak electrolytcNenclccuclyceAnsie Bonk37CA1533
Clessify cach corpourd utcrz - electolyte, weak clectrolyte; cr ronelectrolyie Srocg = electrolyre Weak electrolytc Nenclccuclyce Ansie Bonk 37CA 1533...
##### Six hundred fish of a non-native species is introduced to an isolated pond. After t =...
Six hundred fish of a non-native species is introduced to an isolated pond. After t = 2 years, there are 900 of these fishes in the pond. The pond can support up to 4500 of these fishes. Model this behavior using logistic growth (i.e. find the formula for the number of fish after t years assuming th...
##### Comozny [ cridcized because Only 15 ol 40 erecubves at a local branch are women The company explains that albiough this proporbon Ine comoany nas more than 500 erecubves wondwade Aodronnate hypothesis ano 5aplnp coccltsicnValue niyenmalont 4046 olall5 emaloveesDetermina ine hypoiheses Ior ihis testproporton of lemale akacumxasre enure companydendied 0Y p |Ho 0=04 HA 0<04Ho P=0 0 >0 2Ho 0s04 Ha d=04 0r0 * HA p =Ho P H 00 4Calculata nne test stabsuc 2-Diround two decimal places necutoAnd i
comozny [ cridcized because Only 15 ol 40 erecubves at a local branch are women The company explains that albiough this proporbon Ine comoany nas more than 500 erecubves wondwade Aodronnate hypothesis ano 5aplnp coccltsicn Value niyenmalont 4046 olall5 emalovees Determina ine hypoiheses Ior ihis tes...
##### How do you solve 3( x - 2 ) ^ { 2 } - 2 0 = 5 5?
How do you solve 3( x - 2 ) ^ { 2 } - 2 0 = 5 5#?...
##### Practice the Skill 19.34 Predict the major product for each of the following reactions. Get help...
Practice the Skill 19.34 Predict the major product for each of the following reactions. Get help answering Molecular Drawing questions. V pphs Edit Get help answering Molecular Drawing questions. Edit The following reaction is from a synthesis of the natural product salinipyrone A. After being synth...
##### Initial volume 309.7 L at 96.4 C and pressure of781.8 torr. What temp, in C, does balloon need to be cooled down toreduce its volume to 296.2 L if pressure remains constant.
initial volume 309.7 L at 96.4 C and pressure of 781.8 torr. What temp, in C, does balloon need to be cooled down to reduce its volume to 296.2 L if pressure remains constant....
##### Fill in the Table: Special Conditions condition Obese Patient Facts and/or Additional Equipment or Supplies that...
Fill in the Table: Special Conditions condition Obese Patient Facts and/or Additional Equipment or Supplies that may be needed: 1. Sequential devices to prevent 2. - lifting devices and additional personnel to prevent - and 3.- suture devices or larger looped to prevent wound- Pregnant Patient Diabe...
##### Question Completion Status: A Moving to the next question prevents changes to this answer. Question S...
Question Completion Status: A Moving to the next question prevents changes to this answer. Question S The nurse is testing the visual acuity with the Snellen chart. The findings are that the right eye is 20/150. What does this mean? O The dient didn't remove their glasses for the test O That at ...
##### Skill name:: Two step BP method All questions must be answered based on the skill listed...
Skill name:: Two step BP method All questions must be answered based on the skill listed above: what is the Description of this skill? what are the indicators? what are the nursing interventions (pre, intra, post)? what are the outcomes/evaluation? what is the client education for this skill? what a...
##### Let f(e) = c*e". Only one of the following is true0 f' (2) = 32?e"0 322 re?-1f' (2) =2ez + 3r2e"Nonc of these
Let f(e) = c*e". Only one of the following is true 0 f' (2) = 32?e" 0 322 re?-1 f' (2) =2ez + 3r2e" Nonc of these...
##### QUESTION 18Which of the following statements correctly describes osmosis?A. Osmosis only takes place in red blood cells_B. Osmosis is an energy-demanding or active' processC.In osmosis, water moves across membrane from areas of lower solute concentration to areas of higher solute concentration: DIn osmosis solutes move across membrane from areas of lower water concentration to areas of higher water concentration.QUESTION 19Which organelle is the primary site of ATP synthesis in eukaryotic c
QUESTION 18 Which of the following statements correctly describes osmosis? A. Osmosis only takes place in red blood cells_ B. Osmosis is an energy-demanding or active' process C.In osmosis, water moves across membrane from areas of lower solute concentration to areas of higher solute concentrat... | 4,123 | 14,803 | {"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} | 2.796875 | 3 | CC-MAIN-2023-23 | latest | en | 0.836783 |
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If one travels at 450 miles per hour and the other at 550 miles per hour, how long will it take for them to be 4000 miles apart? 2. Two cyclists start from the same point at the same time and move in opposite directions. One cyclist is traveling at 8 miles per hour, and the other cyclist is traveling at 11 miles per hour. After 30 minutes, how far apart are the two cyclists? | 127 | 509 | {"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-2021-49 | latest | en | 0.905544 |
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# BigDaddy's Pi Formula: X/n + YYY
Topic closed. 216 replies. Last post 1 year ago by GwizQ1.
Page 2 of 15
New Mexico
United States
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January 29, 2010
11483 Posts
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Posted: March 29, 2016, 3:01 pm - IP Logged
I back tested NC , Va and Texas with results not worth talking about
To the contrary:
NC results 315 sum 9
27-9=18
3.14159*18=5.654862
Look at those first 3 digits 565
Mirror the six to one and a few draws later 155.
Bam!
The message is think outside the box!
United States
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February 11, 2016
515 Posts
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Posted: March 29, 2016, 3:25 pm - IP Logged
To the contrary:
NC results 315 sum 9
27-9=18
3.14159*18=5.654862
Look at those first 3 digits 565
Mirror the six to one and a few draws later 155.
Bam!
The message is think outside the box!
That's just ridiculous.
California
United States
Member #164727
March 12, 2015
3347 Posts
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Posted: March 29, 2016, 3:58 pm - IP Logged
That's just ridiculous.
What's ridiculous is that you have nothing to offer. You have as much imagination as a bowl of spaghetti with ketchup on it.
Maybe if you try my system you would win in your state of Wisconsin.
Wed, Mar 23, 2016 1-6-5Prize Payouts Tue, Mar 22, 2016 3-8-6Prize Payouts
386
3+8=1...8+6=4
14
8-3=5...8-6=2
52
Use the 15 and add the 4+2=6.....156-561-str/bx
Use the 42...and add the 5+1=6...426-642-str8/bx
14
52
United States
Member #172977
February 11, 2016
515 Posts
Offline
Posted: March 29, 2016, 4:04 pm - IP Logged
What's ridiculous is that you have nothing to offer. You have as much imagination as a bowl of spaghetti with ketchup on it.
Maybe if you try my system you would win in your state of Wisconsin.
Wed, Mar 23, 2016 1-6-5Prize Payouts Tue, Mar 22, 2016 3-8-6Prize Payouts
386
3+8=1...8+6=4
14
8-3=5...8-6=2
52
Use the 15 and add the 4+2=6.....156-561-str/bx
Use the 42...and add the 5+1=6...426-642-str8/bx
14
52
That's ridiculous too.
United States
Member #172977
February 11, 2016
515 Posts
Offline
Posted: March 29, 2016, 4:05 pm - IP Logged
What's ridiculous is that you have nothing to offer. You have as much imagination as a bowl of spaghetti with ketchup on it.
Maybe if you try my system you would win in your state of Wisconsin.
Wed, Mar 23, 2016 1-6-5Prize Payouts Tue, Mar 22, 2016 3-8-6Prize Payouts
386
3+8=1...8+6=4
14
8-3=5...8-6=2
52
Use the 15 and add the 4+2=6.....156-561-str/bx
Use the 42...and add the 5+1=6...426-642-str8/bx
14
52
New Mexico
United States
Member #86099
January 29, 2010
11483 Posts
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Posted: March 29, 2016, 5:17 pm - IP Logged
If you can't see outside of your negative world than you will never see what the forum has to offer. You still have not produced any thing but you are quick to give your 2 cents worth of garbage. As a result, no one respects what you have to say.
The River Walk NC Coast
United States
Member #170590
December 8, 2015
65 Posts
Offline
Posted: March 29, 2016, 5:19 pm - IP Logged
To the contrary:
NC results 315 sum 9
27-9=18
3.14159*18=5.654862
Look at those first 3 digits 565
Mirror the six to one and a few draws later 155.
Bam!
The message is think outside the box!
I guess I'll have to cone outside my glass house lol. Did not think about mirrors. Thanks for the suggestion
People who stay in glass hotels shouldn’t throw parties
New Mexico
United States
Member #86099
January 29, 2010
11483 Posts
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Posted: March 29, 2016, 5:24 pm - IP Logged
I guess I'll have to cone outside my glass house lol. Did not think about mirrors. Thanks for the suggestion
United States
Member #172977
February 11, 2016
515 Posts
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Posted: March 29, 2016, 5:29 pm - IP Logged
I guess I'll have to cone outside my glass house lol. Did not think about mirrors. Thanks for the suggestion
You did not think about mirrors because mirrors were not part of the Pi formula. That is, until laker wanted to make it fit your recent draw history somehow.
BETWEEN OAKRIDGE AND WRIGHT-PATTERSON AFB
United States
Member #1647
June 10, 2003
2830 Posts
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Posted: March 29, 2016, 5:31 pm - IP Logged
The yyy integer can be looked at as 3 separate digit each controls one space of the integer 0-9 ...
in pick 4 the first y controls the fourth number too but very loosely..I run my pick 4 with 3 and 4 integers like yyy and yyyy..adding the fourth number to the integer adds control and flexibility to adjustment ..
Pi is the way...
turning \$30 or less into thousands everyday!!
here we go steelers ..here we go---------stairway to seven
TIME FOR THE LOMBARDI TROPHY TO COME HOME..
The River Walk NC Coast
United States
Member #170590
December 8, 2015
65 Posts
Offline
Posted: March 29, 2016, 5:31 pm - IP Logged
You did not think about mirrors because mirrors were not part of the Pi formula. That is, until laker wanted to make it fit your recent draw history somehow.
I'll have to agree with you ..... True
cheers
People who stay in glass hotels shouldn’t throw parties
BETWEEN OAKRIDGE AND WRIGHT-PATTERSON AFB
United States
Member #1647
June 10, 2003
2830 Posts
Offline
Posted: March 29, 2016, 5:34 pm - IP Logged
You did not think about mirrors because mirrors were not part of the Pi formula. That is, until laker wanted to make it fit your recent draw history somehow.
Mirrors are not pi and not necessary
Pi is the way...
turning \$30 or less into thousands everyday!!
here we go steelers ..here we go---------stairway to seven
TIME FOR THE LOMBARDI TROPHY TO COME HOME..
The River Walk NC Coast
United States
Member #170590
December 8, 2015
65 Posts
Offline
Posted: March 29, 2016, 6:03 pm - IP Logged
The yyy integer can be looked at as 3 separate digit each controls one space of the integer 0-9 ...
in pick 4 the first y controls the fourth number too but very loosely..I run my pick 4 with 3 and 4 integers like yyy and yyyy..adding the fourth number to the integer adds control and flexibility to adjustment ..
Can you give us an example of an actual draw (any draw any state) with step by step instructions. Although you may have valuable information with yyy and yyyy this is still extreamly Greek and shows no added value to a win on an up coming draw
cheers
People who stay in glass hotels shouldn’t throw parties
United States
Member #172977
February 11, 2016
515 Posts
Offline
Posted: March 29, 2016, 6:52 pm - IP Logged
Mirrors are not pi and not necessary
There ya go laker, right from the big guy himself.... Bam!!
BETWEEN OAKRIDGE AND WRIGHT-PATTERSON AFB
United States
Member #1647
June 10, 2003
2830 Posts
Offline
Posted: March 29, 2016, 6:53 pm - IP Logged
Can you give us an example of an actual draw (any draw any state) with step by step instructions. Although you may have valuable information with yyy and yyyy this is still extreamly Greek and shows no added value to a win on an up coming draw
cheers
I have given enough information about pi that you can tinker with it to find what works for your state..do the work and I will guide your efforts.pi works in any 0-9 digits game pick 3,4 and 5 which should be true in any system for daily games | 2,247 | 7,245 | {"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} | 2.984375 | 3 | CC-MAIN-2017-26 | latest | en | 0.820693 |
www.atoha.com | 1,722,646,263,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722640353668.0/warc/CC-MAIN-20240802234508-20240803024508-00340.warc.gz | 534,558,039 | 66,963 | # Tổng hợp Estimating: Analogous Estimating vs. Parametric Estimating vs. Three-point estimating vs. Bottom-Up Estimating
Bài viết tổng hợp bên dưới giúp học viên Atoha phân biệt Analogous Estimating vs. Parametric Estimating vs. Three-point estimating vs. Bottom-Up Estimating
Đây là một số tools & techniques phổ biến trong Estimate Duration và Estimate Cost.
One-point estimating Three-point estimating Bottom-Up Estimating Analogous Estimating(Top-Down) Parametric Estimating Heuristics Triangular distribution(Simple Average) Beta distribution / PERT(Weighted Average) using historical data from a previous, similar activity or project using a statistical relationship between historical data and other variables A heuristic means a generally accepted rule, or best practice Using three-point estimates helps define an approximate range => cover risk.Most likely (M): realistic expectationsOptimistic (O): best-casePessimistic (P): worst-case Doing this type of estimating well requires an accurate WBS - relies on the actual duration of previous, similar projects to estimate duration of the current project.- a gross value estimating approach, adjusted for known differences in project complexity.- less costly, less time-consuming, and less accurate. This technique quantifies duration by multiplying the quantity of work to be performed by the number of labor hours per unit of work.Regression analysis (scatter diagram): This diagram tracks two variables to see if they are related; the diagram is then used to create a mathematical formula to use in future parametric estimating. E = (O + M + P) / 3Depending on the assumed distribution of values within the range of the three estimates, the expected duration (E) can be calculated E = (O + 4M + P) / 6This method gives stronger consideration to the most likely (M) estimate (x 4)SD = (P – O)/ 6Activity standard deviation (SD) is the possible range for the estimate. SD = sigma (σ). aggregating the estimates of the lower-level components of the WBS (activity or work package (if activities are not defined) Uses this if the scenario indicates that you don’t have a lot of experience or historical info,Exam keyword: new project, no experience, not much reliable data, simple, straight. Uses this if scenario indicates there are historical data or samples to work withExam keyword: experts, similar to previous projects, need a more accurate estimate the last five projects similar to this one each took eight months, so this one should as well. If the assigned resource is capable of installing 25 meters of cable per hour, the duration required to install 1,000 meters is 40 hours Design work is always 15 percent of the total project length or 80/20 rule Terms like “simple” or “straight” refer to triangular distribution,“weighted” refers to beta distribution.Beta distribution leverages the benefits of risk management in reducing the uncertainty of estimates.
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Liên hệ ngay với Atoha để được tư vấn về chương trình phù hợp | 931 | 3,961 | {"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-2024-33 | latest | en | 0.763923 |
https://ssbcrackexams.com/nda-1-2024-exam-maths-sequence-series-class-1/ | 1,716,418,574,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971058575.96/warc/CC-MAIN-20240522224707-20240523014707-00750.warc.gz | 466,151,123 | 49,513 | Search
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# NDA 1 2024 Exam Maths Sequence & Series Class 1
In the vast landscape of mathematics, sequences and series play a pivotal role, offering insights into patterns, progressions, and the summation of terms. In Class 1 of the Sequence &...
In the vast landscape of mathematics, sequences and series play a pivotal role, offering insights into patterns, progressions, and the summation of terms. In Class 1 of the Sequence & Series session for the NDA 1 2024 Exam, students delved into the world of arithmetic progression (AP), geometric progression (GP), and harmonic progression (HP). Let’s embark on a journey to explore the key highlights of this class and unravel the mysteries of sequences and series.
Understanding Arithmetic Progression (AP)
The class commenced with an in-depth exploration of arithmetic progression, a fundamental concept in mathematics. Students revisited the definition of AP and learned about its properties, including the common difference between consecutive terms. Through engaging discussions and illustrative examples, students gained a deeper understanding of how APs evolve and the significance of their properties in problem-solving.
Exploring Geometric Progression (GP)
Next, students ventured into the realm of geometric progression, another essential concept in the study of sequences and series. They examined the defining characteristics of GP, such as the common ratio between consecutive terms, and explored its properties and behavior. By analyzing geometric sequences and their terms, students developed a keen appreciation for the geometric patterns that underpin GP.
Unraveling Harmonic Progression (HP)
In Class 1, students also encountered harmonic progression, a less common but equally significant concept in mathematics. They learned about the reciprocal terms in HP and explored its properties, including the harmonic mean and the relationship between terms. Through insightful discussions, students grasped the unique nature of HP and its applications in various mathematical contexts.
Summation of Terms and Formulas
A key focus of the class was the summation of terms in sequences and series. Students revisited important formulas for finding the sum of the first ( n ) terms of AP, GP, and HP. They learned how to apply these formulas to calculate the total sum of terms efficiently and accurately. By practicing with MCQs, students reinforced their understanding of these formulas and their applications in real-world scenarios.
Engaging with MCQs
The class concluded with an interactive session featuring multiple-choice questions (MCQs) designed to test students’ comprehension of AP, GP, and HP. Through these MCQs, students applied their knowledge of sequences and series, identified patterns, and solved problems involving the summation of terms. This hands-on practice enhanced their problem-solving skills and prepared them for the challenges of the upcoming exam.
Preparing for Exam Success
In summary, Class 1 of the Sequence & Series session for the NDA 1 2024 Exam provided students with a solid foundation in arithmetic, geometric, and harmonic progressions. By understanding the properties of AP, GP, and HP and mastering the formulas for the summation of terms, students are well-equipped to tackle exam questions with confidence. Armed with a comprehensive understanding of sequences and series, students are poised for success in the upcoming exam and beyond. | 656 | 3,459 | {"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} | 3.671875 | 4 | CC-MAIN-2024-22 | latest | en | 0.924138 |
https://wickedspoon.ca/strain_stress_handbook_formulas/l3s892k_invest.zrd | 1,670,374,952,000,000,000 | text/html | crawl-data/CC-MAIN-2022-49/segments/1669446711121.31/warc/CC-MAIN-20221206225143-20221207015143-00371.warc.gz | 655,557,464 | 16,390 | # Handbook Of Formulas For Stress And Strain
The deformation in oil or and of formulas for stress strain measures the beam equation numbering and makes reasonable efforts to reactor vessel code can all the mission of end.
Print friendly version of for stress in the physics and formatted. UNIQUENESS THEOREM The plane completely described must satisfy Eqs. Material is selected for various applications in a reactor facility based on its physical and chemical properties. Se, can be arbitrarily specified provided they consistent with work is Sec.
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Kobo customer service to exhibit less susceptible than displacements. For shear stress, clockwise is positive and counterclockwise is negative. The usage of those codes, however, still requires a background in mathematical physics and numerical algorithms. Here x is a vector containing the points.
Join the of for from these problems at the average diameter of materials. The ductility of many metals can change if conditions are altered. Soft steel, when tested in tension, frequently displays a peculiar characteristic, known as a yield point. This is found by dividing the relevant maximum load by the original area of cross section of the component. However, due to transit disruptions in some geographies, deliveries may be delayed.
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Shear Modulus; all the coefficients may be expressed in terms of them. In matrix notation the equation for obtaining strain from stress is. This may be zero stress for stress strain of formulas and display static response, called the boundary condition. When the geometry of the material changes, the flow lines move closer together or farther apart to accommodate. Then the addition of a tensile eccentric toward the concave edge of the beam.
The rectangular area the strain formulas and grow your membership? To include every level and strain energy density george green sec. The first solution to the total may be fast enough to stress for and strain of requests from the steps eqs. Orthorhombic crystals is stress for and strain of formulas for all the distance through axial compression. Eo of stresses, and animation functionality, adequate knowledge of subjects a handbook and company codes. Web of science core collection.
Flaws tend to the bending loads or fracture and calculator spread sheet of energy can have not small error occurred while computer coding in static loads for stress and of strain formulas and propagate approximately at the knovel without working of size.
Customarily the metal temperatures, and see vip membership is used is the strain and display distinctly viscous characteristics of normal shearing small. | 606 | 3,228 | {"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} | 3.046875 | 3 | CC-MAIN-2022-49 | latest | en | 0.933971 |
https://forum.xojo.com/t/when-is-an-enum-not-an-enum/79926 | 1,721,079,215,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763514713.74/warc/CC-MAIN-20240715194155-20240715224155-00781.warc.gz | 236,467,293 | 7,176 | When is an enum not an enum?
I may be misunderstanding what is meant by a datatype but:
What should the expected output be from the following code:?
``````
di = New Dictionary
di.Value(type1.a) = "a"
di.Value(type1.b) = "b"
di.Value(type1.c) = "c"
di.Value(type1.d) = "d"
di.Value(type2.e) = "e"
di.Value(type2.f) = "f"
di.Value(type2.g) = "g"
di.Value(type2.h) = "h"
Var ss() As String
For Each v As Variant In di.Values
Next
textarea1.Text = join(ss, ",")
``````
Where type1 and type2 are different enums.
The answer I get is e,f,g,h as the dictionary just saves the enum as its integer value, whereas I was hoping for a,b,c,d,e,f,g,h.
An enum give a list of labels to some base value. Such value usually is a Integer. So it is possible to have infinite different enums with the same values.
First you need to show us those enums definitions.
But let me assume a default simple definition where type1 a to d = 0 to 3 and type2 e to h = 0 to 3
The result should be “e,f,g,h”
To get what you wanted, your definitions should be:
``````Public Enum type1
a
b
c
d
End Enum
Public Enum type2
e = 4
f
g
h
End Enum
``````
1 Like
Thanks Rick. Even after 10 years I’m still learning basics.
I’ve solved it in a slightly different way using extends for each enum to add a constant range for each enum. This allows me to add or remove enums without having to worry about renumbering.
``````
di = New Dictionary
di.Value(type1.a.tointeger) = "a"
di.Value(type1.b.tointeger) = "b"
di.Value(type1.c.tointeger) = "c"
di.Value(type1.d.tointeger) = "d"
di.Value(type2.e.tointeger) = "e"
di.Value(type2.f.tointeger) = "f"
di.Value(type2.g.tointeger) = "g"
di.Value(type2.h.tointeger) = "h"
Var ss() As String
For Each v As Variant In di.Values
Next
textarea1.Text = join(ss, ",")
Public Function toInteger(extends e as type1) As Integer
return 100 + integer(e)
End Function
Public Function toInteger(extends e as type2) As Integer
return 200 + integer(e)
End Function``````
I think you may be misusing enums. There’s got to be a better approach. What problem are you trying to sove?
You appear to be using two different enum types in the same context to represent the same information. Maybe this is just an example to illustrate what you’ve noticed in some other context, but that seems like an anti-pattern to me.
Yes, this is just an example to illustrate that the enums are saved as integers in a dictionary. The actual code does nothing like this example.
In my code I have several different areas of code, each with their own enums that define particular events. As I build the code I want the ability to drop in different parts of code, separately tested, that include their own enum.events. But all the enum.events can be sent to a common dispatching structure to allow separation of UI and data processing. Rather than using Variants, I want the code to be a bit more auto-completing and testing in the IDE.
So for each area of code, I had defined its own enums, not realising at the time that they would lose their identify when put into a dictionary. So by adding a constant range to each enum, I can use common code.
You’re setting the dictionary values to string constants. The fact that the keys are enums or anything else is irrelevant - the values should be “a” - “h”. If you were collecting the keys, then I could see maybe integers showing up. Something seems wrong here.
You might consider using string constants instead of enumerations. This would let you namespace them, eliminating name conflicts:
``````fooClass.kProcessDataCommandKey = "fooClass.ProcessData"
``````
1 Like
I think James and Rick are right, the enums assigned to the Dictionary are saving the keys as Integers. If both Enums have no assigned values, then the default range for each set is 0, 1, 2, 3.
So when the second set of Enums are being assigned to the Dictionary, they are overriding the values of the first set, which is why the results were e, f, g, h.
I think there is only 4 entries in the Dictionary, not 8.
1 Like
I guess that would also work - but I like enums as they are more compact in the IDE - and, because they sit in their own Module, they are easy to refer to.
I think the answer is that enums are for ease of IDE and compiling, whereas they are just integers when compiled.
That has always been the case.
1 Like
That’s expected. I misunderstood the OP, read too quickly.
1 Like | 1,144 | 4,437 | {"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-2024-30 | latest | en | 0.681189 |
https://www.physicsforums.com/threads/damped-oscillator.112069/ | 1,524,681,041,000,000,000 | text/html | crawl-data/CC-MAIN-2018-17/segments/1524125947939.52/warc/CC-MAIN-20180425174229-20180425194229-00158.warc.gz | 838,386,994 | 14,583 | # Homework Help: Damped oscillator!
1. Feb 24, 2006
### DanaBug28
I am really struggling with this question...:yuck:
Question: Consider a damped oscillator, with natural frequency w_0 (omega_0) and damping constant B (beta) both fixed, that is driven by a force F(t)= F_0*cos(wt). Find the rate P(t) at which F(t) does work and show that the average < P > over any number of complete cycles is mBw^2*A^2.
any help would be amazing!!
2. Feb 24, 2006
### Tide
I think the rules here stipulate that you need to show some of your own work before you can get specific help on homework problems.
3. Feb 24, 2006
### DanaBug28
work
F(t)=m*f_0*cos(wt) in general
long term motion x(t)=A*cos(wt-delta)
delta= arctan((2Bw)/(w_0^2-w^2))
A^2= (f_0^2)/((w_0^2-w^2)^2+4*B^2*w^2)
< P >=mBw^2*A^2
= m*f_0*cos(wt)*distance
mBw^2*A^2 = mBw^2*(f_0^2)/((w_0^2-w^2)^2+4*B^2*w^2) = m*f_0*cos(wt)*distance
cancel stuff...
B*w^2*(f_0)/((w_0^2-w^2)^2+4*B^2*w^2) = cos(wt)*distance
uh......help? :uhh:
4. Feb 24, 2006
### Tide
To calculuate the average power over a period you need to evaluate the integral
$$<P> = \frac {1}{T} \int_0^T F v dt$$ | 431 | 1,140 | {"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} | 3.609375 | 4 | CC-MAIN-2018-17 | longest | en | 0.822686 |
https://pythonmana.com/2020/11/20201113185729192f.html | 1,653,171,445,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662541747.38/warc/CC-MAIN-20220521205757-20220521235757-00746.warc.gz | 546,535,458 | 10,384 | Is there such a problem that you really understand python programming from now on?
Tianyuan prodigal son 2020-11-13 09:09:30
problem really understand python programming
When I write down this topic , In my mind, I couldn't help but hear Zhou Huajian's slightly hoarse voice ：
The familiar song came from afar ,
Why are those voices so weak .
long time no see , Are you all right now ？
Is there such a song ,
Will let you follow and ,
With the ups and downs of our lives ,
A theme song to sing together ;
Is there such a song ,
It will remind you of me ,
Make you happy and worry ,
Such a me ……
The music is over , Back to the point . Browse recently LeetCode, I found an interesting little topic . When I try Python When you answer , Actually used the assembly 、map function 、zip function 、lambda function 、sorted function , The debugging process also involves iterators 、 generator 、 The concept of list derivation . A seemingly simple topic , Although the final code can be combined into one line , But almost put Python I used the programming skills of , It can be said. “ The subtlety is the spirit ”！ Through this topic , Maybe it will make you really understand Python Programming .
This question , be known as 《 The lucky number in the list 》. What is the lucky number ？ In the list of integers , If a number appears at the same frequency as its value , We call this number 「 Lucky number 」. for example , In the list [1, 2, 2, 3] in , Numbers 1 And number 2 The number of times they appear is 1 and 2, So they are lucky numbers , but 3 Only ever 1 Time ,3 It's not a lucky number .
I understand the concept of lucky number , Let's try to find out the list [3, 5, 2, 7, 3, 1, 2 ,4, 8, 9, 3] The lucky number in . This process can be divided into the following steps ：
1. Find out the numbers that are not repeated in the list
2. Count the number of times each number appears in the list
3. Find out the numbers that appear equal to the number itself
The first 1 Step , Find out the numbers that are not repeated in the list
Find out the numbers that are not repeated in the list , That is, to remove duplicate elements from the list , abbreviation “ duplicate removal ”. The simplest way to de duplicate is to use sets .
``````>>> arr = [3,5,2,7,3,8,1,2,4,8,9,3]
>>> unique = set(arr)
>>> unique
{
1, 2, 3, 4, 5, 7, 8, 9}
``````
The first 2 Step , Count the number of times each number appears in the list
We know , The list object comes with a count() Method , Can return the number of times an element appears in the list , The usage is as follows ：
``````>>> arr = [3,5,2,7,3,8,1,2,4,8,9,3]
>>> arr.count(8) # Elements 8 In the array arr There has been 2 Time
2
``````
Next , We only need to traverse the elements after de duplication , Count the number of times they appear one by one , And save it into a suitable data structure , This step of the work will be all right .
``````>>> arr = [3,5,2,7,3,8,1,2,4,8,9,3]
>>> unique = set(arr) # Remove duplicate elements
>>> pairs = list() # An empty list , Used to hold tuples of array elements and occurrence times
>>> for i in unique:
pairs.append((i, arr.count(i)))
>>> pairs
[(1, 1), (2, 2), (3, 3), (4, 1), (5, 1), (7, 1), (8, 2), (9, 1)]
``````
As a rookie , Code like this , Has been very good . however , A aspiring programmer will never be complacent about it 、 come to a standstill . Their favorite thing to do is to do everything possible to eliminate for loop , For example, using mapping functions 、 Filter function instead of for loop ; Even if you can't refuse for loop , They also try to hide the cycle as much as possible , For example, hiding in list derivation . Since this is to call the list for every element count() This method , That's the best way to use map Function instead of for Circulated .
``````>>> m = map(arr.count, unique)
>>> m
<map object at 0x0000020A2D090E08>
>>> list(m) # Generators can be converted to lists
[1, 2, 3, 1, 1, 1, 2, 1]
>>> list(m) # The generator can only be used once , After use , It's automatically cleaned up
[]
``````
map The function returns a generator （generator）, It can be traversed like a list , But you can't see the elements as intuitively as a list , Unless we use list() Turn this generator into a list （ You don't actually need to turn the generator into a list ）. Please note that , Generators are different from iterators , Or a generator is a special kind of iterator , Can only be traversed once , End of traversal , It's gone . Iterators can iterate over and over . such as ,range() Function returns iterator ：
``````>>> a = range(5)
>>> list(a)
[0, 1, 2, 3, 4]
>>> list(a)
[0, 1, 2, 3, 4]
``````
Say generator and iterator , We have to go back to the original topic . Use map Mapping function , We get the number of occurrences of each element , You also need to form a tuple with the corresponding elements . Now , Just use zip() Function .zip() Function to create a generator , Used to aggregate every iteratable object （ iterator 、 generator 、 list 、 Tuples 、 aggregate 、 String, etc. ） The elements of , Elements aggregate according to the same subscript , If the length is different, elements larger than the shortest iteration object length will be ignored .
``````>>> m = map(arr.count, unique)
>>> z = zip(unique, m)
>>> z
<zip object at 0x0000020A2D490508>
>>> list(z)
[(1, 1), (2, 2), (3, 3), (4, 1), (5, 1), (7, 1), (8, 2), (9, 1)]
>>> list(z)
[]
``````
Obviously ,zip() The function also returns the generator , It can only be used once , Then it disappears .
The first 3 Step , Find out the numbers that appear equal to the number itself
With each element and its number of occurrences , We just need to loop through …… No , One moment please , Why do we have to cycle ？ We just need to filter every element , Find out the tuples that have the same number of occurrences as the element itself , Why not try the filter function filter() Well ？
``````>>> def func(x): # Parameters x It's a tuple type
if x[0] == x[1]:
return x
>>> m = map(arr.count, unique)
>>> z = zip(unique, m)
>>> f = filter(func, z)
>>> f
<filter object at 0x0000020A2D1DD908>
>>> list(f)
[(1, 1), (2, 2), (3, 3)]
>>> list(f)
[]
``````
Filter function filter() Take two parameters , The first 1 A parameter is a function , Used to determine whether an element meets the filtering conditions , The first 2 One parameter is the iteratable object to be filtered .filter() The function also returns the generator , It can only be used once , Then it disappears .
Write here , We're almost done . however , As a pursuing programmer , You can tolerate func() Such a strange looking function ？ The answer is no ！ You must be able to use lambda Function to replace it . in addition , Maybe we need to sort the results by the size of the elements . Add sorting , The complete code is as follows ：
``````>>> arr = [3,5,2,7,3,8,1,2,4,8,9,3]
>>> unique = set(arr)
>>> m = map(arr.count, unique)
>>> z = zip(unique, m)
>>> f = filter(lambda x:x[0]==x[1], z)
>>> s = sorted(f, key=lambda x:x[0])
>>> print(' The lucky number is ：', [item[0] for item in s])
The lucky number is ： [1, 2, 3]
``````
The ultimate code , One line fix
If you've ever been written in one line by those 、 But it can achieve complex functions 、 The painful experience of code ravaging that looks like a heavenly book , that , Now you can also write the above code in one line , To ravage others .
``````>>> arr = [3,5,2,7,3,8,1,2,4,8,9,3]
>>> print(' The lucky number is ：', [item[0] for item in sorted(filter(lambda x:x[0]==x[1], zip(set(arr), map(arr.count, set(arr)))), key=lambda x:x[0])])
The lucky number is ： [1, 2, 3]
``````
Dramatic reversal , I really understand this time Python 了 ！
This blog has not been published for two days , Some netizens left a message saying , Why bother ？ It's not easier to write like this 、 Is it easier to read ？ Sure enough , I really want to ！
``````>>> arr = [3,5,2,7,3,8,1,2,4,8,9,3]
>>> [x for x in set(arr) if x == arr.count(x)]
[1, 2, 3]
`````` | 2,236 | 8,004 | {"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} | 3.296875 | 3 | CC-MAIN-2022-21 | latest | en | 0.871613 |
https://www.coursehero.com/file/6590195/multivariable-17-Differential-Equations-2up/ | 1,493,421,870,000,000,000 | text/html | crawl-data/CC-MAIN-2017-17/segments/1492917123097.48/warc/CC-MAIN-20170423031203-00093-ip-10-145-167-34.ec2.internal.warc.gz | 882,890,385 | 24,426 | multivariable_17_Differential_Equations_2up
# multivariable_17_Differential_Equations_2up - 17...
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Unformatted text preview: 17 Differential Equations Many physical phenomena can be modeled using the language of calculus. For example, observational evidence suggests that the temperature of a cup of tea (or some other liquid) in a room of constant temperature will cool over time at a rate proportional to the difference between the room temperature and the temperature of the tea. In symbols, if t is the time, M is the room temperature, and f ( t ) is the temperature of the tea at time t then f ′ ( t ) = k ( M − f ( t )) where k > 0 is a constant which will depend on the kind of tea (or more generally the kind of liquid) but not on the room temperature or the temperature of the tea. This is Newton’s law of cooling and the equation that we just wrote down is an example of a differential equation . Ideally we would like to solve this equation, namely, find the function f ( t ) that describes the temperature over time, though this often turns out to be impossible, in which case various approximation techniques must be used. The use and solution of differential equations is an important field of mathematics; here we see how to solve some simple but useful types of differential equation. Informally, a differential equation is an equation in which one or more of the derivatives of some function appear. Typically, a scientific theory will produce a differential equation (or a system of differential equations) that describes or governs some physical process, but the theory will not produce the desired function or functions directly. Recall from section 6.2 that when the variable is time the derivative of a function y ( t ) is sometimes written as ˙ y instead of y ′ ; this is quite common in the study of differential equations. 425 426 Chapter 17 Differential Equations 7F iÖ ×ØÖd eÖD iffeÖ eÒØ ia ÐE ÕÙaØ iÓÒ × We start by considering equations in which only the first derivative of the function appears. DEFINITION 17.1 A first order differential equation is an equation of the form F ( t,y, ˙ y ) = 0. A solution of a first order differential equation is a function f ( t ) that makes F ( t,f ( t ) ,f ′ ( t )) = 0 for every value of t . Here, F is a function of three variables which we label t , y , and ˙ y . It is understood that ˙ y will explicitly appear in the equation although t and y need not. The term “first order” means that the first derivative of y appears, but no higher order derivatives do. EXAMPLE 17.2 The equation from Newton’s law of cooling, ˙ y = k ( M − y ) is a first order differential equation; F ( t,y, ˙ y ) = k ( M − y ) − ˙ y . EXAMPLE 17.3 ˙ y = t 2 +1 is a first order differential equation; F ( t,y, ˙ y ) = ˙ y − t 2 − 1....
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## This note was uploaded on 12/01/2011 for the course MATH 305 taught by Professor Guichard during the Fall '11 term at Whitman.
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# Liquids and Solids - PowerPoint PPT Presentation
Liquids and Solids. Changes of State. Objectives. Explain the relationship between equilibrium and changes of state Define Le Chatelier’s Principle. Predict changes in equilibrium using Le Chatelier’s Principle. Dry Ice Balloon Explosion (Very Loud Bang) - YouTube. Equilibrium.
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### Liquids and Solids
Changes of State
Objectives
• Explain the relationship between equilibrium and changes of state
• Define Le Chatelier’s Principle.
• Predict changes in equilibrium using Le Chatelier’s Principle.
Dry Ice Balloon Explosion (Very Loud Bang) - YouTube
Equilibrium
Equilibrium – a dynamic state in which two opposing changes occur at equal rates in a closed system.
Changes of State
solid liquid melting
solid gas sublimation
liquid solid freezing
liquid gas vaporization
gas liquid condensation
gas solid deposition
An Equilibrium Equation
• Evaporation of a liquid
Liquid + energy vapor
• Condensation of a liquid
Vapor liquid + energy
• Liquid-vapor equilibrium
liquid + energy vapor
Le Chatelier’s Principle
A system at equilibrium will shift to offset a stress or change in conditions imposed on the system.
Equilibrium and Temperature
liquid + energy vapor
Equilibrium and Concentration
liquid + energy vapor
Equilibrium Vapor Pressure
• Pressure exerted by a vapor in equilibrium with its corresponding liquid at a given temperature
-an increase in temperature causes an increase in equilibrium vapor pressure; result of increased K.E. of the liquid particles.
Boiling
Boiling…
…occurs when the equilibrium vapor pressure of a liquid equals the atmospheric pressure
…conversion of a liquid to a vapor within the liquid as well as at the surface.
Normal Boiling Point: boiling point at standard atmospheric pressure (100oC for water)
Molar Heat of Vaporization
• The amount of energy needed to vaporize 1 mole of a liquid at its boiling point
Freezing and Melting
Freezing:
Liquid solid + heat energy
Melting:
Solid + heat energy liquid
Normal freezing point: temperature at which a solid and liquid are at equilbrium at standard pressure (0oC for water
Molar Heat of Fusion – energy required to melt one mole of a solid at its melting point.
Phase Diagram
Triple Point – temperature and pressure conditions at which the solid, liquid, and gas phases of a substance can coexist at equilibrium
Critical temperature - temperature above which a substance cannot exist in the liquid phase.
Critical pressure – the lowest pressure at which a substance can exist as a liquid at the critical temperature. | 755 | 3,355 | {"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-2018-34 | longest | en | 0.76941 |
https://www.maplesoft.com/support/help/Maple/view.aspx?path=examples/DataFrame/Statistics | 1,718,887,426,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198861940.83/warc/CC-MAIN-20240620105805-20240620135805-00401.warc.gz | 760,053,389 | 25,569 | Statistics with DataFrames - Maple Help
Statistics with DataFrames
A DataFrame is one of the basic data structures in Maple. Data frames are a list of variables, known as DataSeries, which are displayed in a rectangular grid. Every column (variable) in a DataFrame has the same length; however, each variable can have a different type, such as integer, float, string, name, truefalse, etc., which makes data frames an ideal storage device for heterogeneous data.
When printed, Data frames resemble matrices in that they are viewed as a rectangular grid, but a key difference is that the first row corresponds to the column (variable) names and the first column corresponds to the row (individual) names. These row and columns are treated as header meta-information and are not a part of the data. Moreover, the data stored in a DataFrame can be accessed using these header names, as well as by the standard numbered index.
This example page shows a number of common statistical operations with data frames. For more information, including a list of Statistics commands that can be run on data frames, see DataFrames in Statistics.
Getting Started
To begin, the Statistics package is loaded.
> with(Statistics):
A new DataFrame can be created based on randomly generated data. The following generates a DataFrame with 3 DataSeries. The first two columns are generated by randomly sampling from a Uniform(0,1) distribution. The third DataSeries also has randomly generated data, which is sampled from 4 distinct levels: 0, 1, 2, 3.
> data := DataFrame( < Sample(Uniform(0, 1), [20, 2]) | LinearAlgebra:-RandomVector(20, generator = rand(0 .. 3) ) >, columns = [a,b,c] );
DataFrames and the Context Panel The Maple programming language provides many commands that are useful for exploring DataFrames. The Context Panel provides easy access to a selection of these commands, displaying context-specific commands that can be applied to DataFrames or DataSeries. The DataFrame context-sensitive options include many commands that can be applied to entire DataFrames as well as to a single DataSeries in a DataFrame. The second section of the DataFrame menu in the Context Panel includes commands for conversions, operations, queries, and visualization of DataFrames and DataSeries. The third section includes more commands relating to statistics and data analysis, including data analysis, data manipulation, properties and quantities, and summary and tabulation. A useful feature of the context-sensitive options is the ability to quickly filter the DataFrame by value or to select columns to apply operations to. This can be beneficial when dealing with heterogeneous data that includes non-numeric DataSeries. In many cases, commands in Statistics assumes an entirely numeric DataFrame. Selectively removing the non-numeric data makes it possible to use the routines natively on the given DataFrame.
Computing Summary Statistics
One of the most fundamental statistical tasks is to generate summary statistics, such as the mean or standard deviation, for a given data set. The DataSummary command returns the mean, standard deviation, skewness and kurtosis, as well as the minimum and maximum values, and the cumulative weight. When all of the elements in the DataSeries have weight = 1, the cumulative weight corresponds to the total number of observations in the DataSeries.
> DataSummary(data, summarize = embed):
a b c mean ${0.642033244375975753}$ ${0.492561671718578453}$ ${1.64999999999999969}$ standarddeviation ${0.329931930346065327}$ ${0.334466425079465335}$ ${1.26802789276975481}$ skewness ${-0.535097906770228615}$ ${-0.223319664925291123}$ ${-0.259820705584549505}$ kurtosis ${1.62899290839617339}$ ${1.41288760741544195}$ ${1.38747927386886905}$ minimum ${0.0975404049994095246}$ ${0.0318328463774206760}$ ${0.}$ maximum ${0.970592781760615697}$ ${0.950222048838354927}$ ${3.}$ cumulativeweight ${20.}$ ${20.}$ ${20.}$
Individual summary statistics can also be returned. For example, the variance of each of the DataSeries in the DataFrame is:
> Variance(data);
${\mathrm{DataSeries}}{}\left(\left[\begin{array}{ccc}0.1088550786618809& 0.1118677895054376& 1.6078947368421048\end{array}\right]{,}{\mathrm{labels}}{=}\left[{a}{,}{b}{,}{c}\right]{,}{\mathrm{datatype}}{=}{{\mathrm{float}}}_{{8}}\right)$ (1)
It is important to note that a DataSeries is returned from requesting any individual summary statistic. Each row corresponds to each of the columns in the DataFrame. In this case, column "a" has a variance of 0.11, column "b" has a variance of 0.11, and column "c" has a variance of 1.61.
Aggregate Statistics
The defined DataFrame has a third column which has 3 distinct levels: 0, 1, 2, and 3. The distinct levels in a DataSeries can easily be seen by collapsing the DataSeries into a set:
> convert(data[3], set);
$\left\{{0}{,}{1}{,}{2}{,}{3}\right\}$ (2)
When a DataFrame contains a DataSeries that has a fixed number of distinct levels, it can be useful to compute aggregate statistics based on the levels in a given DataSeries. Using the example DataFrame, since the column "c" has 4 distinct levels, aggregate statistics can be computed using the Aggregate command, that show values for a given statistic for each of the levels.
The following shows the mean for each of the levels in column "c":
> Aggregate(data, 3);
${\mathrm{DataFrame}}{}\left(\left[\begin{array}{ccc}0.789176927985601& 0.5715716569968473& 0\\ 0.5312144700993431& 0.4644634091949476& 1\\ 0.6209018764709715& 0.6098719860151968& 2\\ 0.562666428150338& 0.34907382056065794& 3\end{array}\right]{,}{\mathrm{rows}}{=}\left[{1}{,}{2}{,}{3}{,}{4}\right]{,}{\mathrm{columns}}{=}\left[{a}{,}{b}{,}{c}\right]\right)$ (3)
The default summary statistic for the Aggregate command is the mean. By specifying a function, any summary statistic can be returned for the levels in column "c":
> Aggregate(data, 3, function = Median);
${\mathrm{DataFrame}}{}\left(\left[\begin{array}{ccc}0.9354413457866585& 0.7394678592524246& 0\\ 0.5312144700993431& 0.4644634091949476& 1\\ 0.6323592462254095& 0.6787351548577735& 2\\ 0.5468815192049838& 0.31709948006086053& 3\end{array}\right]{,}{\mathrm{rows}}{=}\left[{1}{,}{2}{,}{3}{,}{4}\right]{,}{\mathrm{columns}}{=}\left[{a}{,}{b}{,}{c}\right]\right)$ (4)
The tally option can be optionally specified in order to tally up the number of observations in each of the levels:
> Aggregate(data, 3, function = Range, tally);
${\mathrm{DataFrame}}{}\left(\left[\begin{array}{cccc}0.8287064431334004& 0.9183892024609343& 0& 6\\ 0.867348130199867& 0.5865534427667717& 1& 2\\ 0.6786687293758972& 0.4662094831640262& 2& 5\\ 0.788748708895561& 0.8134176272945876& 3& 7\end{array}\right]{,}{\mathrm{rows}}{=}\left[{1}{,}{2}{,}{3}{,}{4}\right]{,}{\mathrm{columns}}{=}\left[{a}{,}{b}{,}{c}{,}{\mathrm{Tally}}\right]\right)$ (5)
Data Manipulation
The Statistics package has many commands for manipulating statistical data including data selection, scaling and more. For example, the Scale command can be used to center and scale numeric DataSeries:
> data[[1, 2]] := Scale(data[[1, 2]]);
> data;
Data Analysis
There are many commands in Maple for analyzing data, including commands for regression analysis, principal component analysis, analysis of variance and more.
Principal Component Analysis (PCA) aims to identify patterns in data by reducing the dimensionality of multivariate data to a few key explanatory variables called principal components. Performing a principal component analysis on our data returns a record, which can be queried for the principal components, transformation matrix, singular values and more.
> pca := PCA(data, summarize = true);
summary:
Values proportion of variance St. Deviation 1.7667 0.4897 1.3292 1.5158 0.4201 1.2312 0.3254 0.0902 0.5704
> Biplot(pca, pointlabels = true, points = false);
Visualizing DataFrames
Many statistical visualizations support DataFrames and DataSeries:
> BoxPlot(data);
> AreaChart(data);
The colorscheme option is useful when a DataSeries has a fixed number of distinct levels in a given column. In the following, the points are colored based on the 4 levels {0, 1, 2, 3} found in the column "c".
> ScatterPlot(data[.., 1], data[.., 2], symbolsize = 20, symbol = solidbox, colorscheme = ["valuesplit", data[.., 3], [0 = "Red", 1 = "Blue", 2 = "Green", 3 = "Purple"]]);
Sampling a DataFrame
A typical way of sampling a dataset stored in a Matrix is to make a new empirical distribution based on the dataset and sample it directly. The same process can be used for numeric DataSeries:
> Sample(EmpiricalDistribution(data[1]), 10);
$\left[\begin{array}{cccccccccc}6.0& 14.0& 14.0& 4.0& 3.0& 10.0& 20.0& 7.0& 12.0& 5.0\end{array}\right]$ (6)
This method is however only valid for type numeric DataSeries. In the case that we have a non-numeric OR numeric DataSeries, the RandomTools[Generate] command can be used to sample the DataSeries. This does however require a conversion of the DataSeries to a list:
> RandomTools:-Generate('list'('choose'(convert(data[3], list)), 10));
$\left[{0}{,}{1}{,}{0}{,}{0}{,}{1}{,}{3}{,}{3}{,}{0}{,}{3}{,}{3}\right]$ (7)
> RandomTools:-Generate('list'('choose'(convert(DataSeries(["m", "a", "p", "l", "e"]), list)), 10));
$\left[{"e"}{,}{"e"}{,}{"l"}{,}{"p"}{,}{"p"}{,}{"e"}{,}{"p"}{,}{"p"}{,}{"e"}{,}{"p"}\right]$ (8)
More examples
There are several examples for working with DataFrames and DataSeries:
• DataFrame Guide : Examples of working with DataFrames
• Iris Data : Examples of summarizing data, computing aggregate statistics, and principal component analysis
• Subsets of DataFrames : Examples of indexing and filtering columns and rows of a DataFrame | 2,703 | 9,805 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 29, "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} | 3.3125 | 3 | CC-MAIN-2024-26 | latest | en | 0.884611 |
https://plugincafe.maxon.net/topic/10496/13947_best-way-to-get-vertices-from-a-point/6 | 1,597,470,699,000,000,000 | text/html | crawl-data/CC-MAIN-2020-34/segments/1596439740679.96/warc/CC-MAIN-20200815035250-20200815065250-00165.warc.gz | 432,077,854 | 14,863 | # Best way to get vertices from a point
• On 05/12/2017 at 03:04, xxxxxxxx wrote:
I'm looking for a "best-practice" approach to this problem. I need to read out an object and convert it to its vertex positions (not point positions! vertices.). As for the why: this appears to be the only way to retain UV coordinates for each vertex (using points' UVs will cause issues because a point is shared between multiple polygons, usually). So far it looks like making it editable and calling Disconnect on it seems like the only way to do this - however I was wondering whether there might be a more elegant solution whereby I could get the vertices per point?
Cheers
Michael
• On 05/12/2017 at 04:10, xxxxxxxx wrote:
For some understanding purpose, and to be sure we talk about the same.
Polygon is define by his edge.
Edge is 2 Vertexs.
c4d.CPolygon actually represent a polygon.
c4d.CPolygon get in maximum 4 points (a, b, c, d) if it's triangle c and d are egual.
c4d.CPolygon vertex (a,b,c,d presented in the last sentence) are VertexID
c4d.PolygonObject inherite from c4d.PointObject
VertexID are shared accross the PointObject
UVVertexID are shared accross CPolygon
To get position of a specific point you have to do
``````#op is c4d.PolygonObject
localPointPos = op.GetPoint(0) # Get the local position of the VertexID 0
globalPointPos = op.GetPoint(0) * op.GetMg() # Get the world position of the VertexID 0
``````
If you want to go from PolygonID to VertexID
``````#op is c4d.PolygonObject
poly = op.GetPolygon(0) #Get the c4d.CPolygon with the polygonID 0
localPointPos = op.GetPoint(poly.a) # Get the local position of the first VertexID inside CPolygon (called Cpolygon.a)
``````
About UV since they belong to CPolygon you have to use GetPointPolys to find all the shared CPolygon accross a given VertexID. Then for each CPolygon you have to iterate over (a,b,c,d) to get the desired VertexID. Then you have to move it using SetSlow.
I hope it's andwerd your question.
• On 05/12/2017 at 04:26, xxxxxxxx wrote:
Hi,
no, it's not quite it. I'm aware of all the steps to get UVs and Points from the geometry. The problem is that in Cinema all the points usually are treated as shared points. So if you have two polygons next to each other, their bordering points (on the same edge) are shared point IDs.
1 - 2 - 3
| | |
4 - 5 - 6
So you get CPolygon with 1245 and 2356. Now if you UV map a texture onto this, with a repeating UV for example, you end up with these UV coordinates for _each_ of the two polygons.
(0,0) - (1,0)(0,0) - (1,0)
| | |
(0,1) - (1,1)(0,1) - (1,1)
This results in point 2, for example, having two UVs: (1,0) (from the left polygon) and (0,0) from the right polygon.
To properly handle this, you need to have two vertices (or more, depending on how many polygons share this point), where each vertex stores the position of the Point and also its individual UV (and normal).
This is something that apparently is handled entirely internally in Cinema - my question now is, can I get this data through the means of the Python API somehow, without jumping through hoops for it (e.g. Make Editable, then Triangulate, the Disconnect (which may even screw up the normals?)).
Michael
• On 05/12/2017 at 05:04, xxxxxxxx wrote:
Originally posted by xxxxxxxx
To properly handle this, you need to have two vertices (or more, depending on how many polygons share this point), where each vertex stores the position of the Point and also its individual UV (and normal).
It's actually the case since as said in my previous post, UVVertexID belong to CPolygon vertex(a,b,c,d). Maybe I missunderstand something about how you do your UV stuff but basicly here is a code that show you that you have 2 UVVertexID for VertexID 1 (2 in your schema, since ID start at 0 and not 1)
``````import c4d
def CreateObject() :
obj = c4d.BaseObject(c4d.Opolygon)
points = [c4d.Vector(0, 0, -100), # Coordonnées des points
c4d.Vector(0, 0, 0),
c4d.Vector(0, 0, 100),
c4d.Vector(100, 0, -100),
c4d.Vector(100, 0, 0),
c4d.Vector(100, 0, 100)]
polys = [c4d.CPolygon(0, 1, 4, 3), # Points ABCD du polygone
c4d.CPolygon(1, 2, 5, 4)]
obj.ResizeObject(len(points), len(polys))
obj.SetAllPoints(points)
for i, p in enumerate(polys) :
obj.SetPolygon(i, p)
obj.Message(c4d.MSG_UPDATE)
doc.InsertObject(obj)
return obj
def CreateUVTag(obj) :
tag = c4d.UVWTag(obj.GetPolygonCount())
obj.InsertTag(tag)
return tag
def main() :
obj = CreateObject()
if not obj: return
uvTag = CreateUVTag(obj)
if not uvTag: return
# Now everything is setup, let's change VertexID 1 (2 in your schema, since ID start at 0 and not 1)
nbr = c4d.utils.Neighbor()
nbr.Init(obj)
polys = nbr.GetPointPolys(1) # Get all the PolygonID shared with vertexID 1
polys_data = obj.GetAllPolygons()
# Loop for each CPolygon and add to list_id, the PolygonID["poly_id"], and the actual CPolygon vertex ID (a,b,c,d are mapped to 0,1,2,3)["pt_num"]
list_id = list()
for poly_id in polys:
poly = polys_data[poly_id]
found_id = poly.Find(1) # here we search for want VertexID 1
if found_id != c4d.NOTOK:
buffer_data = dict()
buffer_data["poly_id"] = poly_id
buffer_data["pt_num"] = found_id
list_id.append(buffer_data)
# Now we get list of all Cpolygon with the corresponding (a,b,c,d) that are equal to VertexID 1
for pt in list_id:
buffer_uv = uvTag.GetSlow(pt["poly_id"])
list_uv = [buffer_uv["a"],
buffer_uv["b"],
buffer_uv["c"],
buffer_uv["d"]]
# change the value only for the corresponding CPolygon vertexID look comment at line 48
list_uv[pt["pt_num"]] = c4d.Vector(0.5, 0.0, 0.0)
# Set the point where you want
uvTag.SetSlow(pt["poly_id"],
list_uv[0],
list_uv[1],
list_uv[2],
list_uv[3]
)
if __name__=='__main__':
main()
``````
Please take a look at my script linked in my previous post
But maybe I complettly missunderstand your question and someone else get it ! ;)
• On 05/12/2017 at 05:17, xxxxxxxx wrote:
No, it's not a complete misunderstanding, but it's not the result I'm looking for :)
What I am looking for is simply a simple way to say "for Point X, return an Array of Vertices and their UVs" but I think it's just not there and I'll write my own.
Thanks anyway :)
• On 07/12/2017 at 14:06, xxxxxxxx wrote:
Hi Michael, thanks for writing us.
if I correctly understood your request, the following code should satisfy your need.
``````
import c4d
def main() :
obj = doc.GetActiveObject()
# check something is active
if obj is None:
print "No object selected"
return
# check the object to be an editable polygon object
if obj.GetType() != c4d.Opolygon:
print "Selected object is a generator, please make it editable"
return
# attempt to retrive a UVWTag
uvwTag = obj.GetTag(c4d.Tuvw)
if uvwTag is None:
print "uvwTag doesn't exists"
return
# attempt to access points and polygons lists
points = obj.GetAllPoints()
polygons = obj.GetAllPolygons()
if polygons is None or points is None:
print "points or polygons don't exist"
return
# store the polygons count
polyCnt = len(polygons)
# preallocate the list containing the final pos and uvw data
alldata = [None] * polyCnt
# loop through the polygons
for i in xrange(polyCnt) :
polygon = polygons[i]
# access the UVW data for the current polygon
uvwPolygon = uvwTag.GetSlow(i)
# check whatever the polygon has three or four vertices
if polygon.IsTriangle() :
# cycle over all the poiygon data and store in alldata
pos = points[polygon.a]
uvw = uvwPolygon["a"]
data = [[pos, uvw]]
pos = points[polygon.b]
uvw = uvwPolygon["b"]
data.append([pos, uvw])
pos = points[polygon.c]
uvw = uvwPolygon["c"]
data.append([pos, uvw])
alldata[i] = data
else:
pos = points[polygon.a]
uvw = uvwPolygon["a"]
data = [[pos, uvw]]
pos = points[polygon.b]
uvw = uvwPolygon["b"]
data.append([pos, uvw])
pos = points[polygon.c]
uvw = uvwPolygon["c"]
data.append([pos, uvw])
pos = points[polygon.d]
uvw = uvwPolygon["d"]
data.append([pos, uvw])
alldata[i] = data
# just print out to check the result
for j in xrange(len(alldata)) :
data = alldata[j]
print "Polygon["+str(j) +"]"
for k in xrange(len(data)) :
spacer = " ---> vtx [" + str (k) + "]"
posString = " pos:[" + str(data[k][0].x) + ", " + str(data[k][0].y) +", "+ str(data[k][0].z) + "]"
uvwString = " uvw:[" + str(data[k][1].x) + ", " + str(data[k][1].y) +", "+ str(data[k][1].z) + "]"
print spacer, posString, uvwString
if __name__=='__main__':
main()
``````
Best, Riccardo | 2,444 | 8,414 | {"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-2020-34 | latest | en | 0.880931 |
https://www.semanticscholar.org/paper/The-Goldbach-problem-Iwaniec-Kowalski/c89ef3a3bb6cae356a9e28ef17dc28a960bdbc63 | 1,632,742,270,000,000,000 | text/html | crawl-data/CC-MAIN-2021-39/segments/1631780058415.93/warc/CC-MAIN-20210927090448-20210927120448-00033.warc.gz | 960,327,856 | 43,795 | # The Goldbach problem
@inproceedings{Iwaniec2004TheGP,
title={The Goldbach problem},
author={Henryk Iwaniec and Emmanuel Kowalski},
year={2004}
}
• Published 2004
• Mathematics
This is a project for a student who likes problems about the distribution of prime numbers and who enjoyed the last part of the undergraduate course Analytic Number Theory related to the representation of every large enough positive integer as the sum of nine positive integer cubes. One of the most well-known open problems in all of mathematics is the Goldbach conjecture: every even integer greater than two is the sum of two primes. If true, it implies that every odd integer greater than five… Expand
The ternary Goldbach problem
The ternary Goldbach conjecture, or three-primes problem, states that every odd number n greater than 5 can be written as the sum of three primes. The conjecture, posed in 1742, remained unsolvedExpand
The ternary Goldbach conjecture is true
The ternary Goldbach conjecture, or three-primes problem, asserts that every odd integer $n$ greater than $5$ is the sum of three primes. The present paper proves this conjecture. Both the ternaryExpand
Minor arcs for Goldbach's problem
The ternary Goldbach conjecture states that every odd number n>=7 is the sum of three primes. The estimation of sums of the form \sum_{p\leq x} e(\alpha p), \alpha = a/q + O(1/q^2), has been aExpand
A Rigorous Proof for the Strong Goldbach Conjecture
• Computer Science
• 2016
It is shown that it is always possible to find at least one pair of prime numbers according to the former two expressions for any given even number greater or equal to 6. Expand
Major arcs for Goldbach's problem
The ternary Goldbach conjecture, or three-primes problem, asserts that every odd integer n greater than 5 is the sum of three primes. The present paper proves this conjecture. Both the ternaryExpand
eu AN EXPLORATION ON GOLDBACH ’ S CONJECTURE
This paper divides the set of natural numbers in six equivalence classes and determines two of them as candidate to include all prime numbers. Concerning the even numbers themselves, these wereExpand
Some Considerations in Favor of the Truth of Goldbach's Conjecture
This article presents some considerations about the Goldbach's conjecture (GC). The work is based on analytic results of the number theory and it provides a constructive method that permits, given anExpand
Explicit Estimates in the Theory of Prime Numbers
It is the purpose of this thesis to enunciate and prove a collection of explicit results in the theory of prime numbers. First, the problem of primes in short intervals is considered. We prove thatExpand
On the existence of a non-zero lower bound for the number of Goldbach partitions of an even integer
• S. Davis
• Mathematics, Computer Science
• Int. J. Math. Math. Sci.
• 2004
It will be shown how to determine by the method of induction the existence of a non-zero lower bound for the number of Goldbach partitions of all even integers greater than or equal to 4. Expand
Some Issues on Goldbach Conjecture
• Mathematics
• 2012
This paper presents a deterministic process of finding all pairs (p,q) of odd numbers (composites and primes) of natural numbers ≥ 3 whose sum (p + q) is equal to a given even natural number 2n ≥ 6.Expand
#### References
Multiplicative Number Theory
From the contents: Primes in Arithmetic Progression.- Gauss' Sum.- Cyclotomy.- Primes in Arithmetic Progression: The General Modulus.- Primitive Characters.- Dirichlet's Class Number Formula.- TheExpand | 818 | 3,535 | {"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": 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} | 3.40625 | 3 | CC-MAIN-2021-39 | latest | en | 0.884213 |
https://solvedlib.com/which-factor-self-interest-or-idealism-was-more,162875 | 1,696,345,145,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233511106.1/warc/CC-MAIN-20231003124522-20231003154522-00075.warc.gz | 573,086,341 | 16,607 | # Which factor, self-interest or idealism, was more important in driving American foreign policy 1895-1920
###### Question:
Which factor, self-interest or idealism, was more important in driving American foreign policy 1895-1920?
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Brief Exercise 14-08 In alphabetical order below are current asset items for Roland Company's balance sheet at December 31, 2020. Accounts receivable Cash Finished goods Prepaid expenses Raw materials Work in process $207,000 70,000 97,000 39,000 91,000 94,000 Prepare the current assets section.... 1 answer ##### You are looking to buy a car. You can afford$730 in monthly payments for five...
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Use the table to the right to find the given derivative. f(x) X+7 f(x) X+7 X=1 (Simplify your answer )... | 4,095 | 14,019 | {"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": 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} | 2.734375 | 3 | CC-MAIN-2023-40 | latest | en | 0.91885 |
http://www.cs.cmu.edu/~claytronics/software/aggregates.html | 1,542,574,951,000,000,000 | text/html | crawl-data/CC-MAIN-2018-47/segments/1542039744649.77/warc/CC-MAIN-20181118201101-20181118223101-00525.warc.gz | 404,929,800 | 4,647 | Aggregate Engineering - Compiling Ensemble-level Specifications into Catom-level Instructions
The practical use of Claytronics requires that we deal with ensembles at a high level; programming individual catoms is like coding all of Windows in assembly. Engineers will need a convenient way to specify aggregate behavior, and tools that can compile these specs into programs for each catom. The code must be robust to component failure, hardware irregularities and other engineering concerns. Ensembles must operate at reasonable time scales. The techniques must carry over to future versions of the hardware. And finally, the set of programmable phenomena must be rich enough for the wide range of uses to which Claytronics will be put.
An analogy is found in gases, where properties like pressure and temperature function as ``universal knobs'' that specify large-scale behavior and are governed by the ideal gas law. Similarly, Claytronics engineers should be able to specify ``sphere with radius = 3. Now double the radius'', or ``create the shape in file human.cly. No, make it taller than that''. We want to design, from first principles, ensembles with the ``universal knobs'' needed for applications, and to understand the laws that govern them.
This is no small task; applications will involve dozens to thousands of parameters, and reverse-engineering them is far harder than ground-up approaches. So in pursuit of the overarching goal, we are starting smaller. Simple solids like spheres and regular polyhedra are highly symmetrical and can be easily described using mathematics; we seek algorithms which will form Claytronic matter into these shapes while meeting the necessary criteria for robustness and generality. Common patterns in these algorithms will point the way to general rules underlying the ``universal knobs'' that will be needed in the future. Starting from these smaller problems, we seek to lay the foundation for all aggregate Claytronic programming.
Our work will have ramifications far beyond Claytronics. Large distributed systems, in the form of sensor nets, communication networks, and even the power grid, already have a prominent role in the modern world. Self-assembling systems, like synthetic biology and designer materials, are just around the corner. These are all examples where high-level behavior is needed from a system that is too complex for an engineer to understand, and the solutions we develop for Claytronics will provide the conceptual framework for this more general class of systems.
What methods can we apply to understand Claytronic ensembles? Statistical physics already has a rich literature on ensembles, but they have not considered complex engineering tasks. Electrical engineers have done much work in distributed systems, but the number of components is dwarfed by our problems. The spatial nature of Claytronics suggests that classical geometry will play a role, as may topology and differential geometry. Our work draws inspiration from all of these fields, as well as seeking fundamentally new ideas to address the problems of scale and engineering that make Claytronics such a (for the time being) unique challenge. | 600 | 3,190 | {"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-2018-47 | latest | en | 0.903428 |
http://www.primidi.com/skew_symmetric | 1,571,229,876,000,000,000 | text/html | crawl-data/CC-MAIN-2019-43/segments/1570986668569.22/warc/CC-MAIN-20191016113040-20191016140540-00238.warc.gz | 301,754,043 | 3,309 | # Skew Symmetric
### Some articles on skew, skew symmetric:
Bivector - Three Dimensions - Matrices
... Bivectors are isomorphic to skew-symmetric matrices the general bivector B23e23 + B31e31 + B12e12 maps to the matrix This multiplied by vectors on both sides gives the ... Skew symmetric matrices generate orthogonal matrices with determinant 1 through the exponential map ... with a rotation is a rotation matrix, that is the rotation matrix MR given by the above skew-symmetric matrix is The rotation described by MR is the same as that described by the rotor R given by and the ...
Parallel Axes Rule - Moment of Inertia Matrix - Identities For A Skew-symmetric Matrix
... In order to compare formulations of the parallel axis theorem using skew-symmetric matrices and the tensor formulation, the following identities are useful ... Let be the skew symmetric matrix associated with the position vector R=(x, y, z), then the product in the inertia matrix becomes This product can be ...
Charts On SO(3) - Parametrizations - Problems of The Parametrizations
... If we use a skew-symmetric matrix, every 3×3 skew-symmetric matrix is determined by 3 parameters, and so at first glance, the parameter space is R3 ... holds for applying a Cayley transform to the skew-symmetric matrix ...
Riemannian Connection On A Surface - Example: The 2-sphere
... The Lie algebra of SO(3) consists of all skew-symmetric real 3 x 3 matrices ... The group SU(2) has a 3-dimensional Lie algebra consisting of complex skew-hermitian traceless 2 x 2 matrices, which is isomorphic to ... function on matrices and thus the geodesics through I are have the form exp Xt where X is a skew-symmetric matrix ...
Skew-symmetric Matrix
... mathematics, and in particular linear algebra, a skew-symmetric (or antisymmetric or antimetric) matrix is a square matrix A whose transpose is also its negative that is, it satisfies the equation A = −AT ... A = (aij) then the skew symmetric condition is aij = −aji ... For example, the following matrix is skew-symmetric ... | 462 | 2,041 | {"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} | 3.09375 | 3 | CC-MAIN-2019-43 | latest | en | 0.854051 |
https://kmla.co.za/wp-includes/sodium_compat/lemon-cheesecake-abvge/page.php?id=pentagon-inscribed-in-a-circle-angles-4d3839 | 1,618,111,445,000,000,000 | text/html | crawl-data/CC-MAIN-2021-17/segments/1618038060927.2/warc/CC-MAIN-20210411030031-20210411060031-00466.warc.gz | 457,498,382 | 20,095 | # pentagon inscribed in a circle angles
/ January 22, 2021/ Uncategorized
In the above illustration, ∠ AOB is the inscribed angle. First off, a definition: A and C are \"end points\" B is the \"apex point\"Play with it here:When you move point \"B\", what happens to the angle? CISCE ICSE Class 10. These radii divide the pentagon into five isosceles triangles each with a center angle of 360/5 = 72 degrees (once around the circle, divided by five triangles) and two sides of length 8 cm. Polygons that are not regular are considered to be irregular polygons with unequal sides, or angles or both. We studied interior angles and exterior angles of triangles and polygons before. If you have that, are opposite angles of that quadrilateral, are they always supplementary? If you have a quadrilateral, an arbitrary quadrilateral inscribed in a circle, so each of the vertices of the quadrilateral sit on the circle. Polygons are regular if all of their sides and angles are equal. We are assuming regular pentagons (each side is equal and all central angles are the same). In geometry, an arc is one of the parts of the circumference of a circle. CISCE ICSE Class 10. From the above figure, {eq}PENTA {/eq} is a regular pentagon inscribed in a circle, so each of the angles labeled with x have the same measure.. \\[0.3cm]5 \ x &= 360^{\circ} \end{align*} A triangle (black) with incircle (blue), incentre (I), excircles (orange), excentres (J A,J B,J C), internal angle bisectors (red) and external angle bisectors (green) In geometry, the incircle or inscribed circle of a polygon is the largest circle contained in the polygon; it touches (is tangent to) the many sides. Galleries. Male or Female ? So a polygon inscribed in a circle means the polygon is inside. I'll denote it by psi -- I'll use the psi for inscribed angle and angles in this video. Question Bank Solutions 24848. Therefore, each inscribed angle creates an arc of 216° Use the inscribed angle formula and the formula for the angle of a tangent and a secant to arrive at the angles Find angle $x$ and $y$. Keywords. How to Find the Measure of an Angle? Each central angle is equal to 360 / 5 = 72 … To improve this 'Regular polygons inscribed to a circle Calculator', please fill in questionnaire. Inscribed Angles in Circles. {/eq}. It has 5 central angles. Question 888882: a regular pentagon is inscribed in a circle whose radius is 18cm. If the circle is circumscribed about the polygon inside the circle, it can be any sized polygon in this case I have a hexagon inside it) so I would say the circle is circumscribed about the polygon. Hence angle ADC+angle DCB=180° Since angle DCB=72 ° Hence angle ADC=180°-72°=108° Also angle DAB+angle DCB=180° (Cyclic quadrilateral) Illustration showing a circle inscribed in a regular pentagon. When a circle is inscribed inside a polygon, the edges of the polygon are tangent to the circle.-- In the given figure, ABCDE is a pentagon inscribed in a circle. Male Female Age Under 20 years old 20 years old level 30 years old level 40 years old level 50 years old level 60 years old level or over Occupation Elementary school/ Junior high-school student C. 6. So a polygon inscribed in a circle means the polygon is inside. Get Instant Solutions, 24x7. If we have one angle that is inscribed in a circle and another that has the same starting points but its vertex is in the center of the circle then the second angle is twice the angle that is inscribed: 2 ∠ A B C = ∠ A D C Arc AE subtends ∠AOE at the centre and ∠ADE at the remaining part of the circle. Illustration showing a circle inscribed in a regular pentagon. Given a pentagon $ABCDE$ inscribed in a circle with centre $O$. Applications of Right Triangles. answr. Why? Syllabus. In a regular pentagon ABCDE, Inscribed in a circle; find ratio between angle EDA and angle ADC. What is the length of one side? Favorite Answer. I am trying to calculate the left over area that the triangle makes with the pentagon which are both inscribed in a circle radius 1. And if a quadrilateral is inscribed in a circle, then both pairs of opposite angles are supplementary. A regular pentagon is inscribed in a circle of radius $15.8 \mathrm{cm} .$ Find the perimeter of the pentagon. Find x. circle P with points A, B, and C on the circle and inscribed angle A C B drawn Question 4 answers -2 -4 -6 -8 Geometry A regular pentagon has side length 12cm.the perimeter of the pentagon is 60cm and the area is 247.7cm2 .a second. Description. A regular polygon is inscribed in a circle. The radius of the circle is 5 cm and each side AB = BC = CD = DE = EA = 6 cm. 5. In the mathematics exam of geometry, the examiners make the questions complex by inscribing a […] If we let O be the point at the center of the circle, then we can also draw a triangle AOB inside the circle. Inscribed Shapes. From the above figure, {eq}PENTA {/eq} is a regular pentagon inscribed in a circle, so each of the angles labeled with x have the same measure.. In both cases, the outer shape circumscribes, and the inner shape is inscribed. angle, angles, circle, circles, circumscribed, five 5 sides, inscribed, length, line segment, pentagon, pentagons, radius. As is the case repeatedly in discussions of polygons, triangles are a special case in the discussion of inscribed & circumscribed. You can find the length of the third side in one of two ways. Relevance. About $92.9 \mathrm{cm}$ Topics. (Use radians, not degrees.) % Progress . Time Tables 15. 02:05. {/eq} using all of this information: \begin{align*} Square given one side; Square inscribed in a circle; Hexagon given one side; Hexagon inscribed in a given circle; Pentagon inscribed in a given circle; Non-Euclidean constructions. So that is the difference between inscribed and circumscribed. You should be able to link the points together. The sum of the angle measures (each marked as x in the figure) corresponding to the five sides of the pentagon is equal to the total angle measure of the circle. This means that all the corners, or ... of a regular polygon will lie on a circle. Please show how you work it out as I want to be able to apply this to n-sided inscribed polygons. The inner shape is called "inscribed," and the outer shape is called "circumscribed." They both intercept this arc right over here. And it even looks that way right over here. All other trademarks and copyrights are the property of their respective owners. Earn Transferable Credit & Get your Degree, Get access to this video and our entire Q&A library. Usually the simplest method, then, to construct a regular polygon is to inscribe it in a circle. Chapter 6. Number of sides of polygon = 6 0 o 3 6 0 = 6 0 o 3 6 0 o = 6. Section 2. All regular polygons can be inscribed in a circle. And we know from the inscribed angle theorem that an inscribed angle that intercepts the same arc as a central angle is going to have half the angle measure. find the perimeter of the pentagon Answer by Theo(11113) (Show Source): You can put this solution on YOUR website! Thank you so much! Theorem 1 : If a right triangle is inscribed in a circle, then the hypotenuse is a diameter of the circle. No Related Subtopics. Polygons are closed plane figures whose edges are straight lines. Each triangle would have one 72-degree angle in the middle, and 2 54-degree angles ((180-72)/2). {/eq}. Polygon Inscribed in a Circle : If all of the vertices of a polygon lie on acircle, the polygon is inscribed in the circle and the circle is circumscribedabout the polygon. {/eq} is a regular pentagon inscribed in a circle, so each of the angles labeled with x have the same measure. In a Regular Pentagon Abcde, Inscribed in a Circle; Find Ratio Between Angle Eda and Angle Adc. A regular pentagon is made of five congruent triangles whose congruent vertex angles form a circle and add to 360. Important Solutions 2865. The regular pentagon (5-sided polygon) divides the 360 degrees of the circle into 5 equal arcs. In this case, this inscribed angle ( | 1,979 | 8,016 | {"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} | 4.5 | 4 | CC-MAIN-2021-17 | longest | en | 0.897165 |
https://tex.stackexchange.com/questions/35295/how-can-i-number-a-few-equations-together | 1,721,145,652,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763514759.37/warc/CC-MAIN-20240716142214-20240716172214-00874.warc.gz | 487,439,948 | 39,747 | How can I number a few equations together
i would like to write few equations, but all the equations will get only once numbered and in the middle (right side) of the equations. e.q. if i write 3 equations, the number will be to the right of the second equation line and if i have 2 equations, then the number will between the two equations and at the right side.
in addition i would like to have something like "&" (align) that i could align my equations at certain points.
Example:
a = x_{ij}
(1)
b_j = y_j
where of course the number of equation doesn't take a all line space.
• Would simply using \notag in conjucture with \begin{align*} or \tag with \begin{align} solve your problem ? Commented Nov 18, 2011 at 15:04
• Commented Nov 18, 2011 at 15:10
• @N3buchadnezzar but then the tag won't be vertically centered if there's an even number of lines in the equation. Commented Nov 18, 2011 at 15:12
3 Answers
The amsmath package provides the split environment. You can use a split environment inside an align environment or inside an equation environment; a little example:
\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{align}
\begin{split}
a &= x_{ij} \\
b_j &= y_j
\end{split}
\end{align}
\end{document}
• You do not need align to get alignment, your example will work fine with an equation instead of align. Commented Nov 18, 2011 at 15:14
• @TorbjørnT. Yes; however, for consistency reasons, I always use array when I use the alignment characters &. I will rephrase my answer. Commented Nov 18, 2011 at 15:22
• I wouldn't advise to use align other than when it's necessary and moreover the usage of split is "wrong", as LaTeX will never use \abovedisplayshortskip with it. With aligned inside equation it will, if the line preceding the alignment is short; this is preferable for a singly numbered display. Commented Nov 18, 2011 at 16:08
The amsmath package has many facilities, among which the aligned environment that does similarly to align, but produces a block usable in a bigger formula:
\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{aligned} a &= x_{ij} \\ b_j &= y_j \end{aligned}
\end{document}
What's the difference with split? That aligned, like align, allows many alignment points.
Although amsmath functionality is preferred, there are a multitude of ways this can be achieved. Here's one using only an array:
\documentclass{article}
\begin{document}
$$\renewcommand{\arraystretch}{1.2}% To spread out the equations \begin{array}{r@{\;}l} a =& x_{ij} \\ b_j =& y_j \end{array} \label{eq}$$
\end{document}
It has the same layout - in terms of input - to the align environment. Moreover, it now also straight-forward to combine the equations using a brace (say) - achieved using a \left. and \right\} pair:
\documentclass{article}
\begin{document}
$$\renewcommand{\arraystretch}{1.2}% To spread out the equations \left.\begin{array}{r@{\;}l} a =& x_{ij} \\ b_j =& y_j \end{array}\right\} \label{eq}$$
\end{document}
rcases (from mathtools) also provides the above functionality, but is usually intended for a different purpose. As such, the spacing/alignment is not as expected. One can use the undocumented \newcases to define a comparable alternative. Below I've adapted rcases to have a right-aligned first column, and introduce a \thickmuskip between the two "columns", similar to what one would expect around ordinary and relation atoms:
\documentclass{article}
\usepackage{mathtools}% http://ctan.org/pkg/mathtools
\makeatletter
\newcases{Rcases}{$\mskip\thickmuskip$}{%
\hfil$\m@th{##}$}{$\m@th{##}$\hfil}{.}{\rbrace}
\makeatother
\begin{document}
$$\begin{Rcases} a &= x_{ij} \\ b_j &= y_j \end{Rcases} \label{eq}$$
\end{document}
• could also mention rcases from mathtools... Commented Mar 29, 2012 at 8:53 | 1,050 | 3,816 | {"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": 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": 1, "equation": 4, "x-ck12": 0, "texerror": 0} | 2.640625 | 3 | CC-MAIN-2024-30 | latest | en | 0.90468 |
http://byjus.com/right-triangle-formula | 1,506,242,575,000,000,000 | text/html | crawl-data/CC-MAIN-2017-39/segments/1505818689900.91/warc/CC-MAIN-20170924081752-20170924101752-00398.warc.gz | 55,485,726 | 17,426 | ## Enter your keyword
In geometry, you come across different types of figures which properties that set them apart from one another. One common figure among them is a triangle. A triangle is a closed figure, a polygon, with three sides. It has 3 vertices and its 3 sides enclose 3 interior angles of the triangle. The sum of the three interior angles in a triangle is always 180 degrees.
The most common types of triangle that we study about are equilateral, isosceles, scalene and right angled triangle. In this section, we will talk about the right angled triangle, also called right triangle, and the formulas associated with it.
A right triangle is the one in which the measure of any one of the interior angles is 90 degrees. It is to be noted here that since the sum of interior angles in a triangle is 180 degrees, only 1 of the 3 angles can be a right angle. If the other two angles are equal, that is 45 degrees each, the triangle is called an isosceles right angled triangle. However, if the other two angles are unequal, it is a scalene right angled triangle.
The most common application of right angled triangles can be found in trigonometry. In fact, the relation between its angles and sides forms the basis for trigonometry.
## Formulas
• $Area of a right triangle = \frac{1}{2} bh$
Where b and h refers to the base and height of triangle respectively.
• $Perimeter of a right triangle = a+b+c$
Where a, b and c are the measure of its three sides.
• Pythagoras Theorem defines the relationship between the three sides of a right angled triangle. Thus, if the measure of two of the three sides of a right triangle is given, we can use the Pythagoras Theorem to find out the third side.
$Hypotenuse^{2} = Perpendicular^{2} + Base^{2}$
In the figure given above, ∆ABC is a right angled triangle which is right angled at B. The side opposite to the right angle, that is the longest side, is called the hypotenuse of the triangle. In ∆ABC, AC is the hypotenuse. Angles A and C are the acute angles. We name the other two sides (apart from the hypotenuse) as the ‘base’ or ‘perpendicular’ depending on which of the two angles we take as the basis for working with the triangle.
Derivation:
Consider a right angled triangle ABC which has B as 90 degrees and AC is the hypotenuse.
Now we flip the triangle over its hypotenuse such that a rectangle ABCD with width h and length b is formed.
You already know that area of a rectangle is given as the product of its length and width, that is, length x breadth.
Hence, area of the rectangle ABCD = b x h
As you can see, the area of the right angled triangle ABC is nothing but one-half of the area of the rectangle ABCD.
Thus, $Area of \Delta ABC = \frac{1}{2} Area of rectangle ABCD$
Hence, area of a right angled triangle, given its base b and height
$h= \frac{1}{2} bh$
Solved Examples:
Question 1: The length of two sides of a right angled triangle is 5 cm and 8 cm. Find:
• Length of its hypotenuse
• Perimeter of the triangle
• Area of the triangle
Solution: Given,
One side a = 5cm
Other side b = 8 cm
• The length of the hypotenuse is,
Using Pythagoras theorem,
$Hypotenuse^{2} = Perpendicular^{2} + Base^{2}$
$c^{2} = a^{2} +b^{2}$
$c^{2} = 5^{2} +8^{2}$
$c= \sqrt{25+64}= \sqrt{89}= 9.43cm$
• Perimeter of the right triangle = a + b + c = 5 + 8 + 9.43 = 22.43 cm
• $Area of a right triangle = \frac{1}{2} bh$
Here, area of the right triangle =
$\frac{1}{2} (8*5)= 20cm^{2}$
Question 2: The perimeter of a right angled triangle is 32 cm. Its height and hypotenuse measure 10 cm and 13cm respectively. Find its area.
Solution: Given,
Perimeter = 32 cm
Hypotenuse a= 13 cm
Height b= 10 cm
Third side, c=?
We know that perimeter = a+ b+ c
32 cm = 13 + 10 + c
Therefore, c = 32 – 23 = 9 cm
$Area = \frac{1}{2} bh = \frac{1}{2} (9*10)= 45cm^{2}$
To solve more problems on the topic and for video lessons, download Byju’s -The Learning App.
Related Formulas Radius Formula Signal to Noise Ratio Formula Square Root Property Formula Sum of Squares Formula Tangent Formula Trigonometry Formulas Vector Projection Formula Volume of a Triangular Prism Formula | 1,116 | 4,161 | {"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": 12, "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} | 4.84375 | 5 | CC-MAIN-2017-39 | latest | en | 0.939458 |
https://nl.mathworks.com/matlabcentral/cody/problems?action=index&controller=problems&sort=&term=tag%3A%22sum%22+difficulty_rating_bin%3Aeasy | 1,670,565,038,000,000,000 | text/html | crawl-data/CC-MAIN-2022-49/segments/1669446711390.55/warc/CC-MAIN-20221209043931-20221209073931-00725.warc.gz | 448,929,961 | 21,656 | # Problems
1 – 44 of 44
Problem Title Likes Solvers Difficulty
#### Problem 55520. Find the remainder - 02
Created by: Asif Newaz
Tags easy, sum, mod
0
30
#### Problem 47280. Find Sum of array
Created by: Dev Gupta
Tags cody, sum, contest
0
59
#### Problem 44977. Sum sum!!!
Created by: Xiao Zehn
Tags sum, 1 and n
1
70
#### Problem 47159. Simple sum 1
Created by: Mayank Bajpai
1
37
#### Problem 47533. Summy's odd sum
Created by: Viplav Patel
Tags vector, sum
0
69
#### Problem 42808. Sum of logarithms
Created by: HH
Tags sum, logarithm
1
82
#### Problem 47538. Summy's even sum
Created by: Viplav Patel
Tags vectors, sum
0
64
#### Problem 46868. Row avg
Created by: Payam Morsali
Tags sum, avg
1
59
#### Problem 44225. Sum of self power series
Created by: MathReallyWorks
2
70
#### Problem 44303. Find the sum of the largest two elements in a vector
Created by: Brian
0
98
#### Problem 2972. Sum of the Multiplication of Vectors
Created by: Marco
Tags vector, sum, uab
1
245
#### Problem 43304. Find sum of negative elements in row.
Created by: Andriy Kavetsky
1
101
#### Problem 1655. Sum of first n positive integers
Created by: MKN
Tags sum, sequence
3
522
#### Problem 44035. determine the sum of the squares
Created by: Zakaria Makhlouki
0
101
#### Problem 42663. Sum the squares of numbers from 1 to n
Created by: ANAND KUMAR
Tags sum
2
218
#### Problem 45484. Finding sum of even numbers in a vector.
Created by: Rahul Gulia
Tags vector, sum, even
2
69
#### Problem 47083. sum of binomial series
Created by: Mayank Bajpai
1
21
#### Problem 44650. determine the sum of decimal part for given matrix
Created by: Jamal Nasir
2
35
#### Problem 46863. Row sum
Created by: Payam Morsali
Tags sum
1
70
#### Problem 46105. Find sum of numbers on the cornice of a matrix.
Created by: Riccardo Consolo
1
49
#### Problem 42085. Sum of digits of powers of 2
Created by: Mayuri Patil
Tags sum, digit
0
65
#### Problem 44818. Add consecutive integer numbers
Created by: GT
Tags sum, sequence
0
52
#### Problem 2579. Sum of series V
Created by: Grzegorz Knor
Tags series, sum
5
648
#### Problem 44974. Sum Sum Sum!
Created by: Banana
Tags sum, n
0
51
#### Problem 43144. BASICS - sum part of vector
Created by: Jakub Mrowka
26
294
#### Problem 43123. Sum of cubes
Created by: Abhishek Jain
Tags numbers, sum, cube
6
94
#### Problem 2575. Sum of series I
Created by: Grzegorz Knor
Tags series, sum, vvvd
9
797
#### Problem 314. Find the sum of the elements in the "second" diagonal
Created by: Roy Fahn
4
1081
#### Problem 2577. Sum of series III
Created by: Grzegorz Knor
Tags series, sum
3
695
#### Problem 3015. Sum all integers from 1 to 2^x
Created by: Mycah Robinson
Tags series, sum, integer
0
102
#### Problem 45364. Sum of series
Created by: Asif Newaz
Tags basic, easy, series
4
406
#### Problem 44554. The maximum sum of squares
Created by: ddd ppp
Tags sum
2
40
#### Problem 2576. Sum of series II
Created by: Grzegorz Knor
Tags series, sum
7
712
#### Problem 44287. sum all digits
Created by: Zakaria Makhlouki
Tags digits, numbers, sum
1
100
#### Problem 2580. Sum of series VI
Created by: Grzegorz Knor
Tags series, sum
3
619
#### Problem 42653. Generate the sum of Squares of the given number
Tags sum, squares
0
95
#### Problem 2240. Sum the 'edge' values of a matrix
Created by: Dimitrios
Tags easy, matrix, sum
8
307
#### Problem 42850. Sum two real numbers
Created by: Daniel Pereira
3
45
#### Problem 2274. Find the square of the sum of the digits of a number
Created by: Debopam
Tags square, number, sum
1
143
#### Problem 2578. Sum of series IV
Created by: Grzegorz Knor
Tags series, sum
5
630
1
24
#### Problem 43639. Counting candies
Created by: Chaya N
0
65
#### Problem 42382. Combined Ages 1 - Symmetric, n = 3
Created by: goc3
Tags matrix, sum, linear
1
175
#### Problem 45384. Sum! Sum! Sum!
Created by: Asif Newaz
2
35
1 – 44 of 44 | 1,269 | 4,063 | {"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-2022-49 | latest | en | 0.704261 |
https://www.freelancewritersplanet.com/physics-including-earth-and-space-sciences-geometric-optics-2/ | 1,628,192,366,000,000,000 | text/html | crawl-data/CC-MAIN-2021-31/segments/1627046157039.99/warc/CC-MAIN-20210805193327-20210805223327-00132.warc.gz | 797,052,523 | 19,132 | Uncategorized
Physics (including Earth and space sciences geometric optics)
Physics (including Earth and space sciences geometric optics)
Don't use plagiarized sources. Get Your Custom Essay on
Physics (including Earth and space sciences geometric optics)
Just from \$13/Page
Project description
You must do Activity B (page 5) number 2,3,4 (especially 2,4) without the data from the experiment. Do page 6 (Question section) on number 1a,b,c,d. If you can also do questions in Activity A without the data.
Activity A: Measuring the focal length of a lens
Your goal is to measure the focal length of a converging lens using the lens equation. You’ll also check
the magnification relationship.
The image for t
his experiment is a card with a lett
er F punched out as holes. The object is illuminated
from behind with a light bulb.
1)
Construct the pictured setup using a meterstick
and the lens and screen clips provided. The object
screen should be at the 10 cm mark, the lens at the 30 cm mark.
2) Measure the height of your object (the letter F) and record it in the data table.
3) Adjust the image screen position until the imag
e is as sharp as possible. You’ll probably need to
move
the image screen
back and forth a few times to find the location that gives the sharpest image.
4) Record the following in the data table:
?
Object distance (distance between the object and the lens)
?
Image distance (distance between the lens and the image screen)
?
Image height (height of the image on the screen)
?
Image orientation (upright or inverted)
5) Calculate the observed magnification (image height / object height)
6) Calculate
?
the focal len
gth of the lens using the lens equation
?
the theoretical magnification (
s
i
/s
o
)
?
the magnification percent error
7) Repeat steps 3
6 for the object distances
given in the table
plus at least 3 others of your choosing
Object Height h
o
= ____________
S
0
(cm)
S
i
(cm)
H
i
(cm)
Orientation
(inverted/upright)
Observed
Magnification
(h
i
/h
o
)
Theoretical
Magnification
(
s
i
/s
o
)
Magnification
% error
Calculated
focal length
(cm)
20
25
30
40
50
Average
f
= __________ cm
Accepted
f
= __________ cm
% error = _____________
Calculate the average focal length of the lens from all your trials. Obtain the accepted value from your
instructor and report a percent error for your measurements. Show | 585 | 2,355 | {"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} | 3.28125 | 3 | CC-MAIN-2021-31 | latest | en | 0.827513 |
https://freecoursesite.com/linear-programming-for-data-science-and-machine-learning/ | 1,725,722,173,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700650883.10/warc/CC-MAIN-20240907131200-20240907161200-00203.warc.gz | 251,631,070 | 17,513 | # Linear Programming for Data Science and Machine Learning
## What you’ll learn
• Coordinate system
• Locations of points in coordinate system
• Linear Inequalities
• Practical examples of linear inequalities
• Graphing of linear inequalities
• Solution of linear inequalities
• Properties of linear inequality
• Linear programming
• Objective functions
• Optimal Solutions
• Linear Programming theorem
• Solution regions
• Solution regions of constrains with respect to objective functions
## Requirements
• Basics of mathematics
## Description
How to become a pro in Linear Programming?
In this course, you will learn all about the mathematical optimization of linear programming. This course is very unique and has its own importance in its respective disciplines. Data science and machine learning study heavily rely on optimization. Optimization is the study of analysis and interpreting mathematical data under special rules and formulas. Thousands of students worldwide are searching this topic of Linear Programming but they can’t find the complete courses in Linear Programming.
The length of the course is more than 6 hours and there are a total of more than 4 sections in this course. The quality and quantity of the course are super and you will enjoy the course all the way during the course.
The course is prepared according to the current needs of the students and I was much time asked to prepare this course and then finally I started working on it and now it is life. Many students around the globe are taking this type of course and there was nothing in the online learning platform including YouTube and I think it is good for Udemy that they have such types of courses.
In the first section of the course, we have discussed the coordinate system to develop an understanding of the basics of linear programming. While in the second section you will master the basics and advance concepts of linear inequality and finally you will get jump into Linear Programming for Data Science and Business Analysis
The question-answer section is available for the students where they can ask as many questions as they can ask and I will respond to each of your questions promptly. The more questions that you will ask the more are learning to master your concepts. It is found that the students who ask more questions are more likely to be favorite students in their learning perspectives.
Linear optimization or linear programming is considered the mathematical study of data science and business analytics. Therefore the students which are good at mathematics can take this course in an efficient way. However, I have tried my best to complete each section in an easy way. The most important thing is when you are being asked for the questions as you can put as many you want then why not you should put? So just keep in touch with your instructor and don’t feel shy or hesitant to talk with your instructor.
Remember that I am teaching on Udemy for the past 3 years and have a total of 18 years of teaching experience. I am a master in applied mathematics and give solutions to the people where Math has its applications. I have changed the life of many students around the world from my experience and polishing my world which has math difficulty.
## Who this course is for:
• Data science, machine learning, deep learning, artificial intelligence
Created by AD Chauhdry (AD Maths Plus Academy), Peter Alkema
Last updated 6/2022
English
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Size: 1.40 GB
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1 Comment
1. bipin thapa says
please seed this download. i really need this class. | 713 | 3,660 | {"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-2024-38 | latest | en | 0.936579 |
https://www.physicsforums.com/threads/prove-lim-x9-x-5-2.527347/ | 1,527,274,976,000,000,000 | text/html | crawl-data/CC-MAIN-2018-22/segments/1526794867173.31/warc/CC-MAIN-20180525180646-20180525200646-00252.warc.gz | 808,358,042 | 16,173 | # Homework Help: Prove Lim x→9 √(x-5) = 2
1. Sep 5, 2011
### djh101
1. The problem statement, all variables and given/known data
Prove the limit. I'm not entirely sure how to prove limits, the book doesn't go into much detail.
2. Relevant equations
Lim x→9 √(x-5) = 2
3. The attempt at a solution
Prove |x - 9| < δ
|√(x-5) - 2| < ε
2 - ε < √(x - 5) < 2 + ε
ε2 - 4ε + 4 < x - 5 < ε2 + 4ε + 4
ε2 - 4ε < x - 9 < ε2 + 4ε
δ = ε2 + 4ε
2. Sep 5, 2011
### tylerc1991
For proving limits, you need to show that, for all $\varepsilon > 0$, there exists a $\delta > 0$ such that
$|x - 9| < \delta \implies |\sqrt{x - 5} - 2| < \varepsilon$
So to begin, choose an $\varepsilon > 0$. Then you need to choose a $\delta > 0$ such that the above implication is true.
3. Sep 5, 2011
### LCKurtz
No, that isn't what you are trying to prove. The problem is to figure out a δ > 0 that will make your next inequality true if 0 < |x - 9| < δ.
You can tell by looking that if x is close to 9 then |√(x-5) - 2| will be close to zero, but how close x needs to be to 9 depends on how small ε is. The next few steps might be called an exploratory argument
Without multiplying those squares out you have
(2-ε)2 - 4 < x - 9 < (2+ε)2 - 4
Notice that the left side is negative (at least if ε < 2) and the right side is positive, so this is almost n the form
-δ < x - 9 < δ
but the δ on the left would be 4 - (2-ε)2 and the δ on the right is (2+ε)2 - 4
Figure out which of those is the smaller and use it for δ. Then you can reverse your argument like this:
Given ε > 0 let δ = [your minimum value here]. Then if |x - 9| < δ [work your steps backwards here to end up with |√(x-5) - 2| < ε.
Last edited: Sep 5, 2011
4. Sep 5, 2011
### djh101
Okay, so I've come down to δ1 = -ε2 + 4ε and δ2 = ε2. δ1 will be smaller so δ = -ε2 + 4ε.
So, $\forall$ ε > 0, $\exists$ δ = -ε2 + 4ε > 0 such that |$\sqrt{x - 5}$ - 2| < ε whenever |x - 9| < δ, therefore Lim x→4 (9-x) = 5.
Am I on the right track?
5. Sep 5, 2011
### LCKurtz
Word it like this. Given ε > 0, let δ = -ε2 + 4ε. (People will think WOW! Where did that come from because you aren't going to show them that scratch paper with the exploratory argument.) But at this point, you can't just assert |$\sqrt{x - 5}$ - 2| < ε whenever |x - 9| < δ because why would anyone believe you? You have to show the steps working backwards in your exploratory argument. So the next step would be to show, explaining how you know, that if |x - 9| < δ then
(2-ε)2 - 4 < x - 9 < (2+ε)2 - 4
so you can proceed working backwards to your conclusion:
|$\sqrt{x - 5}$ - 2| < ε
6. Sep 5, 2011
### djh101
Okay, I think I get it. Thanks you. | 967 | 2,667 | {"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} | 4.1875 | 4 | CC-MAIN-2018-22 | latest | en | 0.855129 |
https://www.jiskha.com/display.cgi?id=1361893742 | 1,516,794,392,000,000,000 | text/html | crawl-data/CC-MAIN-2018-05/segments/1516084894125.99/warc/CC-MAIN-20180124105939-20180124125939-00695.warc.gz | 905,382,179 | 3,534 | # Physics
posted by .
The radius of the earth is 6.37*10^6 m and its mass is 5.975*10^24 kg. Find the earth's average density to appropriate significant figure.
## Similar Questions
1. ### PHYSICS
Search: a 1.0 kg mass weighs 9.8 n on earths surface and the radius of the earth is roughly 6.4x10 to the 6 m. what is the mass of the earth and the average density of Earth
2. ### earth
The radius of the Earth is approximately 6370 km. If one could dig down straight towards the center of the Earth, one would find that the outermost 2890 km (the crust and the mantle) has an average density of about 4.5 g/cm3. Farther …
3. ### Physics
A 1.0kg mass weighs 9.8 Newton on earth's surface, and the radius of Earth is roughly 6.4 x 10 to the power of 6. The mass of the earth is 6.02 x 10 to the power of 24. Calculate the average density of Earth?
4. ### Physics-mechanics
A 1.0 kg mass weighs 9.8 N on Earth's surface, and the radius of the Earth is roughly 6.4 x 10^6 m. Calculate the average density of Earth. (Show how you would calculate for density; don't just give the answer because L wan't to understand …
5. ### physics-mechanics
A 1.0 kg mass weighs 9.8 N on Earth's surface, and the radius of Earth is roughly 6.4 x 10^6 m. Calculate the average density of Earth
6. ### Physics
The radius of the earth is 6.37*10^6 m and its mass is 5.975*10^24 kg. Find the earth's average density to appropriate significant figure.
7. ### Physics
The radius of the earth is 6.37*10^6 m and its mass is 5.975*10^24 kg. Find the earth's average density to appropriate significant figure.
8. ### Physics
The radius of the earth is 6.37*10^6 m and its mass is 5.975*10^24 kg. Find the earth's average density to appropriate significant figure.
9. ### Physics ( using earth to find pressure of planet y
3. A model of Earth’s interior: Look up the radius and mass of the Earth. Radius is 6,371 km Mass is 5.974 x 10^24 kg Calculate its average density. p_e = (5.974 x 10^24 kg)/ (4/3)pi r^3 = (5.974 x 10^24 kg)/ (4/3)pi (6371)^3 = 5.54 …
10. ### Physics Using hydrostatic equilbrium)
3. A model of Earth’s interior: Look up the radius and mass of the Earth. Radius is 6,371 km Mass is 5.974 x 10^24 kg Calculate its average density. p_e = (5.974 x 10^24 kg)/ (4/3)pi r^3 = (5.974 x 10^24 kg)/ (4/3)pi (6371)^3 = 5.54 …
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Maths is a helpful program that allows you to learn algebra, hear learning lessons and solve particular problems of this subject. while discrete mathematics is a part of mathematics involving mathematical reasoning from discrete objects. Statistics involves the collection, interpretation, presentation, and analysis of data. But when you want to purchase maths notes for Plus 2 you need to be careful about how things are explained.
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Board SCERT, Kerala Text Book NCERT Based Class Plus Two Subject Math's Notes Chapter Chapter 3 Chapter Name Matrices Category Plus Two Kerala
## Kerala Syllabus Plus Two Math's Notes Chapter 3: Matrices
### Topics covered:
The significant points discussed in this chapter are:
• Introduction
• Types of Matrice
• Operations on Matrice
• Transpose of matrice
• Symmetric and skew-symmetric matrices
• Elementary operations (Transpose) of matrices
• Invertible Matrices
#### Chapter 3: Matrices Notes - Preview
Feel free to comment and share this article if you found it useful. Give your valuable suggestions in the comment session or contact us for any details regarding HSE Kerala Plus Two syllabus, Previous year question papers, and other study materials.
### Plus Two Math's Related Links
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Topic Review (Newest First)
02-09-2013 07:35 AM shift That makes a little more sense. so 4 X20 = 80 * .056 = 4.48 GH and 9*10 - 90*.056 = 5.04 KH Those numbers seem make a little more sense. Than you for explaining that! 02-09-2013 07:22 AM Darkblade48 Quote: Originally Posted by shift View Post Found it! http://www.plantedtank.net/forums/sh...ad.php?t=61148 so if i multiply it by .56 GH = 44.8 KH = 50.4 No do those numbers sound right? If so its off the charts for shrimp You multiply by 0.056; you are off by an order of magnitude. To convert from German degrees to mg/L (ppm), multiply by 17.8. To go the other way, divide by 17.8 (or multiply by the inverse, which is 0.056). Also, regarding your kH, I am unsure how you managed to measure 0.9 of a drop, so I would interpret your results with caution. 02-09-2013 06:41 AM shift Found it! http://www.plantedtank.net/forums/sh...ad.php?t=61148 so if i multiply it by .56 GH = 44.8 KH = 50.4 No do those numbers sound right? If so its off the charts for shrimp 02-09-2013 06:33 AM shift Its a hagen/nutrifin test kit. Says 61-100 is slightly hard. My test said 80 (by counting drops) Its still not making much sense to me (atleast versus any of the results i normal see posted.) 02-09-2013 06:28 AM acitydweller sort of high but depends on what the mfg states. also are these results measured in PPM or by another? 02-09-2013 06:25 AM shift GH and KH and shrimp? So today i tested GH and KH. GH said to multiple the # of drops by 20.. 4 drops = 80 KH said multiple # of drops by 10. .9 drops = 90 When i'm looking at specs for shrimp they say GH 1-4.. is this drops? or an excessively low GH? Same goes for KH. specs are low (which would seem more like drops, not results?) Am i looking at this the right way?
Posting Rules You may post new threads You may post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is On HTML code is Off Forum Rules
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https://www.jiskha.com/display.cgi?id=1349236622 | 1,503,537,781,000,000,000 | text/html | crawl-data/CC-MAIN-2017-34/segments/1502886126017.3/warc/CC-MAIN-20170824004740-20170824024740-00255.warc.gz | 912,808,819 | 4,053 | math
posted by .
Mary wants to put all of her stamps on a single page. she has one page with 3 rows of 8 stamps, another page woth 4 rows of 5 stamps, and a third page with 6 rows of 4 stamps. her new single page has 7 rows and can fit 10 stamps across. can she fit all her stamps on the new page? explain.
• math -
3*8 = 24
4*5 = 20
6*4 = 24
total stamps: 68
new page holds 7*10 = 70 stamps
Similar Questions
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7. P6 maths
40% of Amy's stamps is equal to 75% of Mary's stamps. After Mary has given 25% of her stamps away , Amy has 90 more stamps than Mary. Find the total number of stamps they have at first | 472 | 1,794 | {"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} | 3.921875 | 4 | CC-MAIN-2017-34 | latest | en | 0.968863 |
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(Ab)using fo(u)r...
by chargrill (Parson)
on Feb 14, 2006 at 00:38 UTC Need Help??
This probably isn't a heavily obfuscated as others of its ilk (There can be only one!, My 2 cents worth) , and totally wasn't the original direction I was heading with this... but I saw myself writing for loops inside of for loops, and I just couldn't help myself.
```#!/usr/bin/perl
\$ four=44;\$ fore=\$four*\$
fore ;for \$ fore(1..\$ #4
four){\$ for ||(\$ \= pack
'c',\$ fore) } \$ fourteen
=14; \$ fjor =\$ four-\$ #4
fourteen ;\$ f=1;\$ or=2;\$
Or=\$ f+\$or+ \$ f+\$ or; #4
\$ foreteen= \$fourteen- \$
or;\$ fOr= \$ four+\$four -
4 *2;\$ a= \$ fior = sub {
return [ \$ fjor+\$four ,
--\$ four,-\$ or,\$f,-\$ fOr
-4,\$ fOr -\$ foreteen-\$ f
-\$ or]};\$b= \$ fore=sub {
return[ --\$ fourteen,\$ f
,\$ or *\$ or + \$ f,-\$ #42
foreteen ,- \$ f- \$ or, \$
fourteen]};\$c=\$fyor=sub{return[-\$ fOr-\$ or,++\$four+4
,(\$f+\$Or)*(\$f+\$or),\$fourteen,-\$Or,-\$fOr+4]};\$d=\$foer
=sub{return[\$ fOr-4-4,-\$ Or-\$ f,\$ or,\$ or+\$ Or,-\$Or,
\$fourteen]};for(a..d){if(ref(\$\$_)=~m\$AR\$){for(\$\$_){\$
for=\$fourten
*\$fjor;\$fore
+=\$fjor;for(
@\$_){\$for.=\$
fore;\$foor+=
\$ _ ;\$ for.=
pack 'a' , \$
foor}}}else{
for(\$\$_){for
(@{&{\$_}}){\$
foor+=\$ _; \$
for.=pack'c'
,\$ foor} }}}
print \$ for
--chargrill
```\$/ = q#(\w)# ; sub sig { print scalar reverse join ' ', @_ }
+ sig
map { s\$\\$/\\$/\$\\$2\\$1\$g && \$_ } split( ' ', ",erckha rlPe erthnoa stJu
+" );
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Re: (Ab)using fo(u)r...
by jdalbec (Deacon) on Feb 14, 2006 at 03:34 UTC
Create A New User
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Notices? | 948 | 2,934 | {"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-2017-51 | latest | en | 0.609388 |
http://vincenttam.github.io/blog/2015/09/04/stuck-at-two-trigonometric-inequalities/ | 1,561,597,413,000,000,000 | text/html | crawl-data/CC-MAIN-2019-26/segments/1560628000609.90/warc/CC-MAIN-20190626234958-20190627020958-00354.warc.gz | 181,216,236 | 7,750 | # Stuck at Two Trigonometric Inequalities
## Problem
Suppose that $z = x + iy, x,y \in \R$. Then $\abs{\sin z} \ge \abs{\sin x}$ and $\abs{\sin z} \ge \abs{\sinh y}$.
## Forgotten facts
I’ve forgotten many facts about complex variables learnt almost two years ago. For example, the defhinition of sines and cosines. Eight years ago, I can memorize well the trigonometric formulae. Now, I have difficulties in proving them.
\begin{align} \cos z &= \frac{e^{iz}+e^{-iz}}{2} \label{defa} \\ \sin z &= \frac{e^{iz}-e^{-iz}}{2i} \label{defb} \end{align}
## Look at the hint
In the book that I’m reading, there’re two formulae.
\begin{align} \abs{\sin z}^2 &= \sin^2 x + \sinh^2 y \label{hint1a} \\ \abs{\cos z}^2 &= \cos^2 x + \sinh^2 y \label{hint1b} \end{align}
Even though the problem can be solved once these two formulae are accepted, I don’t know why they’re true.
## Look further up
I found another two formulae.
\begin{align} \sin z &= \sin x \cosh y + i \cos x \sinh y \label{hint2a} \\ \cos z &= \cos x \cosh y - i \sin x \sinh y \label{hint2b} \end{align}
I tried to verify \eqref{hint2a} after having read \eqref{defhb}.
## First failed attempt
\begin{aligned} &\quad\: \sin z \\ &= \frac{e^{iz} - e^{-iz}}{2i} \\ &= \frac{e^{i(x + iy)} - e^{-i(x + iy)}}{2i} \\ &= \frac{e^{ix} e^{-y} - e^{-ix} e^{y}}{2i} \\ &= \frac{e^{ix} - e^{-ix}}{2i} e^{-y} + \frac{e^{-ix - y}}{2i} - \frac{e^{-ix} e^{y}}{2i} \\ &= \sin x \cdot e^{-y} + \frac{e^{-ix}}{i} \cdot \frac{e^{-y} - e^{y}}{2}\\ &= \sin x \cdot e^{-y} + i e^{-ix} \frac{e^{y} - e^{-y}}{2} \\ &= \sin x \cdot e^{-y} + i e^{-ix} \sinh y \end{aligned} \label{fail1}
I was stuck at this point because I didn’t know how to change \eqref{fail1} to \eqref{hint2a}.
## More forgotten facts
In fact, some simple identities involving hyperbolic functions can simplify matters.
\begin{align} \cosh z &= \frac{e^{y}+e^{-y}}{2} \label{defha} \\ \sinh z &= \frac{e^{y}-e^{-y}}{2} \label{defhb} \\ \cos(iy) &= \cosh y \label{idha} \\ \sin(iy) &= i \sinh y \label{idhb} \end{align}
Then I realised that \eqref{hint2a} follows from the compound angle formula.
\begin{aligned} \sin(x + iy) &= \sin x \cos(iy) + \cos x \sin(iy) \\ &= \sin x \cosh y + i \cos x \sinh y \end{aligned} \label{link}
Thus, I need to prove something more general.
## Compound angle formulae
\begin{align} \cos(z_1 + z_2) &= \cos z_1 \cos z_2 - \sin z_1 \sin z_2 \label{cpda} \\ \sin(z_1 + z_2) &= \sin z_1 \cos z_2 + \cos z_1 \sin z_2 \label{cpdb} \end{align}
I tried proving \eqref{cpdb} in the same way like \eqref{fail1}.
## Second failed attempt
\begin{aligned} &\quad\: \sin(z_1 + z_2) \\ &= \frac{e^{i(x_1 + iy_1 + x_2 + iy_2)} - e^{-i(x_1 + iy_1 + x_2 + iy_2)}}{2i} \\ &= \frac{1}{2i} [e^{i(x_1 + x_2)} e^{-(y_1 + y_2)} - e^{-i(x_1 + x_2)} e^{y_1 + y_2}] \end{aligned} \label{fail2}
Then I didn’t know how to continue.
## Reasons for the above failures
• \eqref{fail1} and \eqref{fail2} involve fractions, which are more difficult to deal with than those without fractions.
• In order to change \eqref{fail1} to \eqref{hint2a}, some sort of factorisation is needed, and this requires creating a term that fits the puzzle. Again, this isn’t so easy.
## Just use ‘+’, ‘-‘ and ‘×’, no ‘÷’
From \eqref{defa} and \eqref{defb}, one should know that cosines, sines and exponents are related. For any $z_1, z_2 \in \C$, the formula for $\sin(z_1 + z_2)$ and $\cos(z_1 + z_2)$ aren’t so easy, but the one for $e^{z_1 + z_2}$ is simple. Making use of the Euler’s formula for complex numbers, one has
\begin{align} e^{iz_1} &= \cos z_1 + i \sin z_1 \label{eulerz1} \\ e^{iz_2} &= \cos z_2 + i \sin z_2 \label{eulerz2} \end{align}
Multiply \eqref{eulerz1} by \eqref{eulerz2}.
\begin{aligned} &\quad\: e^{i(z_1 + z_2)} \\ &= (\cos z_1 \cos z_2 - \sin z_1 \sin z_2) \\ &\quad\: + i(\cos z_1 \sin z_2 + \sin z_1 \cos z_2) \end{aligned} \label{eiz12a}
Remembering Euler’s formula
$e^{i(z_1 + z_2)} = \cos(z_1 + z_2) + i \sin(z_1 + z_2),$
can we say immediately that \eqref{hint2a} and \eqref{hint2b} are true? No, since there’s no guarantee that $\cos(z_1 + z_2)$ and $\sin(z_1 + z_2)$ are real. However, I kept working on \eqref{eiz12a} so that \eqref{hint2a} and \eqref{hint2b} were proved.
From \eqref{defa} and \eqref{defb}, it’s trivial that
$\sin(-z) = -\sin z \text{ and } \cos(-z) = \cos z.$
Therefore, we write an analog of \eqref{eiz12a} for $e^{-i(z_1 + z_2)}$.
\begin{aligned} &\quad\: e^{-i(z_1 + z_2)} \\ &= [\cos (-z_1) \cos (-z_2) - \sin (-z_1) \sin (-z_2)] \\ &\quad\: + i[\cos (-z_1) \sin (-z_2) + \sin (-z_1) \cos (-z_2)] \\ &= (\cos z_1 \cos z_2 - \sin z_1 \sin z_2) \\ &\quad\: - i(\cos z_1 \sin z_2 + \sin z_1 \cos z_2) \end{aligned} \label{eiz12b}
\begin{aligned} &\quad\: \cos(z_1 + z_2) \quad (\text{by } \frac{\eqref{eiz12a} + \eqref{eiz12b}}{2}) \\ &= \frac{e^{i(z_1 + z_2) - e^{-i(z_1 + z_2)}}}{2} \\ &= \cos z_1 \cos z_2 - \sin z_1 \sin z_2 \end{aligned}
\eqref{hint2a} can be derived in a similar way.
## Remaining work
\eqref{hint1b} can be derived from \eqref{hint2b} by using $\sin^2 x + \cos^2 x = 1$ and $\cosh^2 x - \sinh^2 x = 1$.
\begin{aligned} &\quad\, \abs{\cos z}^2 \\ &= \cos^2 x \cosh^2 y + \sin^2 x \sinh^2 y \\ &= \cos^2 x (1 + \sinh^2 y) + (1 - \cos^2 x) \sinh^2 y \\ &= \cos^2 x + \sinh^2 y \end{aligned}
The derivation of \eqref{hint1a} from \eqref{hint2a} is left as exercise. | 2,182 | 5,378 | {"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": 6, "equation": 5, "x-ck12": 0, "texerror": 0} | 4.4375 | 4 | CC-MAIN-2019-26 | latest | en | 0.519708 |
https://en.m.wikipedia.org/wiki/Parallelogram_identity | 1,579,493,172,000,000,000 | text/html | crawl-data/CC-MAIN-2020-05/segments/1579250597230.18/warc/CC-MAIN-20200120023523-20200120051523-00021.warc.gz | 434,047,078 | 15,953 | # Parallelogram law
(Redirected from Parallelogram identity)
A parallelogram. The sides are shown in blue and the diagonals in red.
In mathematics, the simplest form of the parallelogram law (also called the parallelogram identity) belongs to elementary geometry. It states that the sum of the squares of the lengths of the four sides of a parallelogram equals the sum of the squares of the lengths of the two diagonals. Using the notation in the diagram on the right, the sides are (AB), (BC), (CD), (DA). But since in Euclidean geometry a parallelogram necessarily has opposite sides equal, or (AB) = (CD) and (BC) = (DA), the law can be stated as,
${\displaystyle 2(AB)^{2}+2(BC)^{2}=(AC)^{2}+(BD)^{2}\,}$
If the parallelogram is a rectangle, the two diagonals are of equal lengths (AC) = (BD) so,
${\displaystyle 2(AB)^{2}+2(BC)^{2}=2(AC)^{2}\,}$
and the statement reduces to the Pythagorean theorem. For the general quadrilateral with four sides not necessarily equal,
${\displaystyle (AB)^{2}+(BC)^{2}+(CD)^{2}+(DA)^{2}=(AC)^{2}+(BD)^{2}+4x^{2},\,}$
where x is the length of the line segment joining the midpoints of the diagonals. It can be seen from the diagram that, for a parallelogram, x = 0, and the general formula simplifies to the parallelogram law.
## Proof
In the parallelogram on the left, let AD=BC=a, AB=DC=b, ∠BAD = α. By using the law of cosines in triangle ΔBAD, we get:
${\displaystyle a^{2}+b^{2}-2ab\cos(\alpha )=BD^{2}}$
In a parallelogram, adjacent angles are supplementary, therefore ∠ADC = 180°-α. By using the law of cosines in triangle ΔADC, we get:
${\displaystyle a^{2}+b^{2}-2ab\cos(180^{\circ }-\alpha )=AC^{2}}$
By applying the trigonometric identity ${\displaystyle \cos(180^{\circ }-x)=-\cos x}$ to the former result, we get:
${\displaystyle a^{2}+b^{2}+2ab\cos(\alpha )=AC^{2}}$
Now the sum of squares ${\displaystyle BD^{2}+AC^{2}}$ can be expressed as:
${\displaystyle BD^{2}+AC^{2}=a^{2}+b^{2}-2ab\cos(\alpha )+a^{2}+b^{2}+2ab\cos(\alpha )}$
After simplifying this expression, we get:
${\displaystyle BD^{2}+AC^{2}=2a^{2}+2b^{2}}$
## The parallelogram law in inner product spaces
Vectors involved in the parallelogram law.
In a normed space, the statement of the parallelogram law is an equation relating norms:
${\displaystyle 2\|x\|^{2}+2\|y\|^{2}=\|x+y\|^{2}+\|x-y\|^{2}.\,}$
In an inner product space, the norm is determined using the inner product:
${\displaystyle \|x\|^{2}=\langle x,x\rangle .\,}$
As a consequence of this definition, in an inner product space the parallelogram law is an algebraic identity, readily established using the properties of the inner product:
${\displaystyle \|x+y\|^{2}=\langle x+y,x+y\rangle =\langle x,x\rangle +\langle x,y\rangle +\langle y,x\rangle +\langle y,y\rangle ,\,}$
${\displaystyle \|x-y\|^{2}=\langle x-y,x-y\rangle =\langle x,x\rangle -\langle x,y\rangle -\langle y,x\rangle +\langle y,y\rangle .\,}$
${\displaystyle \|x+y\|^{2}+\|x-y\|^{2}=2\langle x,x\rangle +2\langle y,y\rangle =2\|x\|^{2}+2\|y\|^{2},\,}$
as required.
If x is orthogonal to y, then ${\displaystyle \langle x,\ y\rangle =0}$ and the above equation for the norm of a sum becomes:
${\displaystyle \|x+y\|^{2}=\langle x,x\rangle +\langle x,y\rangle +\langle y,x\rangle +\langle y,y\rangle =\|x\|^{2}+\|y\|^{2},}$
which is Pythagoras' theorem.
## Normed vector spaces satisfying the parallelogram law
Most real and complex normed vector spaces do not have inner products, but all normed vector spaces have norms (by definition). For example, a commonly used norm is the p-norm:
${\displaystyle \|x\|_{p}=\left(\sum _{i=1}^{n}|x_{i}|^{p}\right)^{\frac {1}{p}},}$
where the ${\displaystyle x_{i}}$ are the components of vector ${\displaystyle x}$ .
Given a norm, one can evaluate both sides of the parallelogram law above. A remarkable fact is that if the parallelogram law holds, then the norm must arise in the usual way from some inner product. In particular, it holds for the p-norm if and only if p = 2, the so-called Euclidean norm or standard norm.[1][2]
For any norm satisfying the parallelogram law (which necessarily is an inner product norm), the inner product generating the norm is unique as a consequence of the polarization identity. In the real case, the polarization identity is given by:
${\displaystyle \langle x,y\rangle ={\|x+y\|^{2}-\|x-y\|^{2} \over 4},\,}$
or, equivalently, by:
${\displaystyle {\|x+y\|^{2}-\|x\|^{2}-\|y\|^{2} \over 2}{\text{ or }}{\|x\|^{2}+\|y\|^{2}-\|x-y\|^{2} \over 2}.\,}$
In the complex case it is given by:
${\displaystyle \langle x,y\rangle ={\|x+y\|^{2}-\|x-y\|^{2} \over 4}+i{\|ix-y\|^{2}-\|ix+y\|^{2} \over 4}.}$
For example, using the p-norm with p = 2 and real vectors ${\displaystyle x,\ y\,}$ , the evaluation of the inner product proceeds as follows:
{\displaystyle {\begin{aligned}\langle x,y\rangle &={\|x+y\|^{2}-\|x-y\|^{2} \over 4}\\&={\tfrac {1}{4}}\left[\sum |x_{i}+y_{i}|^{2}-\sum |x_{i}-y_{i}|^{2}\right]\\&={\tfrac {1}{4}}\left[4\sum x_{i}y_{i}\right]\\&=(x\cdot y),\end{aligned}}}
which is the standard dot product of two vectors.
1. ^ Cantrell, Cyrus D. (2000). Modern mathematical methods for physicists and engineers. Cambridge University Press. p. 535. ISBN 0-521-59827-3. if p ≠ 2, there is no inner product such that ${\displaystyle {\sqrt {\langle x,\ x\rangle }}=\|x\|_{p}}$ because the p-norm violates the parallelogram law. | 1,800 | 5,413 | {"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} | 4.71875 | 5 | CC-MAIN-2020-05 | latest | en | 0.785967 |
https://www.doorsteptutor.com/Exams/NEET/Physics/Questions/Topic-Rotational-Motion-4/Subtopic-Torque-4/Part-3.html | 1,508,229,330,000,000,000 | text/html | crawl-data/CC-MAIN-2017-43/segments/1508187820930.11/warc/CC-MAIN-20171017072323-20171017092323-00583.warc.gz | 924,147,999 | 17,206 | # Rotational Motion-Torque (NEET (National Eligibility cum Medical Entrance Test) Physics): Questions 11 - 15 of 25
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## Question number: 11
» Rotational Motion » Torque
MCQ▾
### Question
A constant torque of 1000 N -m, turns a wheel of moment of inertia 200 kg -m 2 about an axis passing through the center. Angular velocity of the wheel after 3 s will be
### Choices
Choice (4) Response
a.
b.
c.
d.
## Question number: 12
» Rotational Motion » Torque
MCQ▾
### Question
A constant torque acting on a uniform circular wheel changes its angular momentum from Aq to 5Aq in 4 seconds. The magnitude of this torque is
### Choices
Choice (4) Response
a.
b.
c.
d.
## Question number: 13
» Rotational Motion » Torque
MCQ▾
### Question
A wheel having moment of inertia 2 kg -m 2 about its vertical axis, rotates at the rate of 60 rpm about this axis. The torque which can stop the wheel’s rotation in 1 minute would be
### Choices
Choice (4) Response
a.
b.
c.
d.
## Question number: 14
» Rotational Motion » Torque
MCQ▾
### Question
A horizontal force F is applied such that the block remains stationary, then which of the following statement is false
### Choices
Choice (4) Response
a.
F = N [where N is the normal reaction]
b.
F will not produce torque
c.
N will not produce torque
d.
f = mg [where f is the friction force]
## Question number: 15
» Rotational Motion » Torque
MCQ▾
### Question
A wheel having moment of inertia 5 kg -m 2 about its vertical axis, rotates at the rate of 60 rpm about this axis. The torque which can stop the wheel’s rotation in 1 minute would be
### Choices
Choice (4) Response
a.
b.
2 π 15 N m
c.
d.
f Page | 519 | 1,940 | {"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} | 3.484375 | 3 | CC-MAIN-2017-43 | longest | en | 0.760914 |
https://www.physicsforums.com/threads/physics-finding-total-distance.590519/ | 1,545,188,718,000,000,000 | text/html | crawl-data/CC-MAIN-2018-51/segments/1544376830479.82/warc/CC-MAIN-20181219025453-20181219051453-00264.warc.gz | 976,241,237 | 18,129 | # Homework Help: Physics Finding Total Distance?
1. Mar 26, 2012
### RichardT
1. The problem statement, all variables and given/known data
John had 5 dogs pulling his sled at full speed for 24 hours. 2 dogs than escaped. however, the journey continued at 3/5 the original velocity and reached his destination 48 hours later. if the two dogs did not escape for an additional 50km he would have reached 24 hours late instead. What is the distance he covered??
3. The attempt at a solution
Well so far heres what i got:
I think i can assume(not sure) that with 5 dogs he traveled 50km in 24 hours according to the last bit of information.
So than that means in the previous 24 hours he would have went 50km with 3 dogs - this is what i dont understand, how can 5 dogs travel 50km in 24 hours while 3 dogs travel 50km in 24 hours as well??
And therefore in the first 24 hours the dogs traveled (50/3) x 5 = 83.333km
and for my total I get 50 + 83.333 = 133.33
Please explain to me the part where 3 dogs travel the same distance in the same time as 5 dogs...
Thanks!
The possible answers are 100, 133, 167, 200, or 267 (all kilometers)
Last edited: Mar 26, 2012
2. Mar 26, 2012
### Staff: Mentor
No, you don't know how long it took the five dogs to cover the 50km. All you know is that it takes a total of 24 hours to cover the "second stretch" if the first 50km are done with a full team of 5 dogs, and 48 hours if done with 3 dogs.
So if v is the "top speed" with 5 dogs, then to cover the second stretch:
$$\frac{50 km}{v} + \frac{x}{\frac{3}{5}v} = 24 hours$$
where x is the currently unknown portion of the second stretch: d2 = 50 km + x
You should be able to write another equation for d2 for the case where only three dogs are employed for the whole second stretch. Substitute for x and d2 accordingly, solve for v.
3. Mar 26, 2012
### RichardT
Ok, so that means i would have 3 equations:
Equation 1. 50km/v + x/3/5v = 24hours
Equation 2. d2 = 50km + x
Equation 3. d2(with 3 dogs) = 3/5v x 48hours
Correct?
If correct, than:
Equation 3: d2 = (144/5)v
And plug that into Equation 2 which is d2=50km + x
So sub in (144/5)v for d2 and solve for x which means: x = (144/5)v - 50km
And than sub the new equation 2 into equation 1 and solve for v?
So.. 24= ( 144/5v - 50km)/(3/5)v + 50/v
Which turned out to be 1.3888km/h
So than in the first 24 hours he traveled 1.3888 x 24 = 33.333km?
and than in the 48 hours with 3/5 dogs he traveled 1.38888x48 = 39.999
so in total it equals 73.333km??
I know im wrong but i dont know where? Please reply back..
4. Mar 26, 2012
### Staff: Mentor
Well, the results look reasonable to me. Why do you think you're wrong? can you find a contradiction between the results and the given information?
5. Mar 26, 2012
### RichardT
Its just that i have the possible answers and 73.333km isnt one of them, is there anywhere i could have gone wrong??
6. Mar 26, 2012
### Staff: Mentor
I don't think so, your calculations looked okay to me (at first glance at least!). I'll give it some thought...
7. Mar 26, 2012
### Staff: Mentor
Perhaps I've made a misinterpretation of the problem text? When you wrote:
Did you mean "late" or "later"? I had assumed a typo, given the previous sentence In other words, would he have arrived in the next 24 hours, or would he arrive 24 hours AFTER he would have arrived with a full team (24 hours "late")?
8. Mar 26, 2012
### RichardT
Ok thanks!, but can you tell me why i cannot assume the last part as the dogs travelling 50km in 24 hours?
9. Mar 26, 2012
### RichardT
No its meant to be he arrived only 24 hours late rather than the 48 hours he would have been late
So if he had 5 dogs for an additional 50km he would have been ONLY 50km late
Hope that clears up some misinterpretations
10. Mar 26, 2012
### Staff: Mentor
Because it wasn't stated as such All you know is that at one speed it takes a given time, and doing a portion at another speed it takes a different time. You can't assume that the distance was half just because the time was halved.
11. Mar 26, 2012
### Staff: Mentor
Really, that only helps a bit "50km late"?
12. Mar 26, 2012
### RichardT
Oops sorry i meant ONLY 24 hours late... Sorry...
13. Mar 26, 2012
### Staff: Mentor
So, just to be clear, in the first case he is 48 hours late, and in the second case he would be only 24 hours late. This would be based on the expected arrival time of T = D/v where D is the total distance and v the velocity with a full team for the entire trip. Is that the scenario?
14. Mar 26, 2012
### RichardT
Ya thats what i believe the scenario is.
15. Mar 26, 2012
### Staff: Mentor
Okay, then write equations for elapsed times. Let T be the expected time, v be the normal velocity, d1 the first distance using all the dogs, d2 the remaining distance. D is the total distance.
Normal travel would yield an "expected" elapsed time of T = D/v. How would you write equations for the described cases? One elapsed time is T + 48hr, and the other is T + 24hr. What distance and velocity expressions would correspond to them? Hint: dealing with the 50km is the tricky bit
16. Mar 26, 2012
### RichardT
and honestly i have no idea for the 50km but is it d1 + 50km =T??
17. Mar 26, 2012
### PeterO
A picture/graph might help.
With all 5 dogs, you would have a flat v-t graph for the entire trip - ending at some time t.
For the trip with the 2 dogs running away, it would be flat at the original speed for 24 hours, then drop to 3/5 ths of that speed for extra time - finishing at t + 48
Draw those two graphs on the same axes, and you see given a common trip, the area under each graph has to be the same.
The extra 48 hours at 60% of original speed, makes up for the missing section from 24 hours to t - which amounts to 40% [the top bit] of the distance covered if all dogs had stayed.
Now draw in the third possibilty - with the 5 dogs staying for an extra 50km. But that extra 50 k is done at full speed.
The distance covered in 24 hrs = only 40% of 50km.
The
Last edited: Mar 26, 2012
18. Mar 26, 2012
### Staff: Mentor
No, d1 is the distance covered in the first 24 hours. So d1 = v*24hr. You could also say that the time to cover distance d1 is d1/v = 24hr.
You can't equate distance with time...the units don't match.
If the two sections of the trip described in the first scenario are d1 and d2, the first traveled at speed v and the second at (3/5)v, what are the elapsed times for each (symbolically)?
If d1 is made 50km longer, then d2 must be made 50km shorter. What are the new elapsed times for each (symbolically)?
19. Mar 26, 2012
### RichardT
So, would the graph look like the picture i included? and Are my equ ations correct?
20. Mar 26, 2012
### PeterO
In case you are not familiar with solving this type of problem with v-t graphs, the attached file shows you them.
I find them particularly useful.
File size:
78 KB
Views:
95 | 1,990 | 6,941 | {"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} | 4.28125 | 4 | CC-MAIN-2018-51 | latest | en | 0.946376 |
http://ncatlab.org/nlab/show/final+functor | 1,448,780,389,000,000,000 | application/xhtml+xml | crawl-data/CC-MAIN-2015-48/segments/1448398456975.30/warc/CC-MAIN-20151124205416-00251-ip-10-71-132-137.ec2.internal.warc.gz | 161,350,878 | 8,776 | # nLab final functor
### Context
#### Limits and colimits
limits and colimits
# Contents
## Idea
A functor $F : C \to D$ is final (often called cofinal), if we can restrict diagrams on $D$ to diagrams on $C$ along $F$ without changing their colimit.
Dually, a functor is initial (sometimes called co-cofinal) if pulling back diagrams along it does not change the limits of these diagrams.
Beware that this property is pretty much unrelated to that of a functor being an initial object or terminal object in the functor category $[C,D]$. The terminology comes instead from the fact that an object $d\in D$ is initial (resp. terminal) just when the corresponding functor $d:1\to D$ is initial (resp. final).
## Definition
###### Definition
A functor $F : C \to D$ is final if for every object $d \in D$ the comma category $(d/F)$ is non-empty and connected.
A functor $F : C \to D$ is initial if the opposite $F^{op} : C^{op} \to D^{op}$ is final, i.e. if for every object $d \in D$ the comma category $(F/d)$ is non-empty and connected.
## Properties
###### Proposition
Let $F : C \to D$ be a functor
The following conditions are equivalent.
1. $F$ is final.
2. For all functors $G : D \to Set$ the natural function between colimits
$\lim_\to G \circ F \to \lim_{\to} G$
is a bijection.
3. For all categories $E$ and all functors $G : D \to E$ the natural morphism between colimits
$\lim_\to G \circ F \to \lim_{\to} G$
is a isomorphism.
4. For all functors $G : D^{op} \to Set$ the natural function between limits
$\lim_\leftarrow G \to \lim_\leftarrow G \circ F^{op}$
is a bijection.
5. For all categories $E$ and all functors $G : D^{op} \to E$ the natural morphism
$\lim_\leftarrow G \to \lim_\leftarrow G \circ F^{op}$
is an isomorphism.
6. For all $d \in D$
${\lim_\to}_{c \in C} Hom_D(d,F(c)) \simeq * \,.$
###### Proposition
If $F : C \to D$ is final then $C$ is connected precisely if $D$ is.
###### Proposition
If $F_1$ and $F_2$ are final, then so is their composite $F_1 \circ F_2$.
If $F_2$ and the composite $F_1 \circ F_2$ are final, then so is $F_1$.
If $F_1$ is a full and faithful functor and the composite is final, then both functors seperately are final.
## Generalizations
The generalization of the notion of final functor from category theory to (∞,1)-higher category theory is described at
The characterization of final functors is also a special case of the characterization of exact squares.
## Examples
###### Example
If $D$ has a terminal object then the functor $F : {*} \to D$ that picks that terminal object is final: for every $d \in D$ the comma category $d/F$ is equivalent to $*$. The converse is also true: if a functor $*\to D$ is final, then its image is a terminal object.
In this case the statement about preservation of colimits states that the colimit over a category with a terminal object is the value of the diagram at that object. Which is also readily checked directly.
###### Example
Every right adjoint functor is final.
###### Proof
Let $(L \dashv R) : C \to D$ be a pair of adjoint functors.To see that $R$ is final, we may for instance check that for all $d \in D$ the comma category $d / R$ is non-empty and connected:
It is non-empty because it contains the adjunction unit $(L(d), d \to R L (d))$. Similarly, for
$\array{ && d \\ & {}^{\mathllap{f}}\swarrow && \searrow^{\mathrlap{g}} \\ R(a) &&&& R(b) }$
two objects, they are connected by a zig-zag going through the unit, by the universal factorization property of adjunctions
$\array{ && d \\ & \swarrow &\downarrow& \searrow \\ R(a) &\stackrel{R \bar f}{\leftarrow}& R L (d)& \stackrel{R(\bar g)}{\to} & R(b) } \,.$
###### Example
The inclusion $\mathcal{C} \to \tilde \mathcal{C}$ of any category into its idempotent completion is final.
See at idempotent completion in the section on Finality.
###### Example
The inclusion of the cospan diagram into its cocone
$\left( \array{ a \\ \downarrow \\ c \\ \uparrow \\ b } \right) \hookrightarrow \left( \array{ a \\ \downarrow & \searrow \\ c &\longrightarrow & p \\ \uparrow & \nearrow \\ b } \right)$
is initial.
###### Remark
By the characterization (here) of limits in a slice category, this implies that fiber products in a slice category are computed as fiber products in the underlying category, or in other words that dependent sum to the point preserves fiber products.
## References
Section 2.5 of
Section 2.11 of
• Francis Borceux, Handbook of categorical algebra 1, Basic category theory
Notice that this says “final functor” for the version under which limits are invariant.
Section IX.3 of
Revised on November 4, 2014 19:24:28 by Urs Schreiber (141.0.8.155) | 1,323 | 4,693 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 53, "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-2015-48 | latest | en | 0.710792 |
https://docs.blender.org/manual/pt/2.79/modeling/modifiers/modify/weight_mix.html | 1,657,039,088,000,000,000 | text/html | crawl-data/CC-MAIN-2022-27/segments/1656104585887.84/warc/CC-MAIN-20220705144321-20220705174321-00455.warc.gz | 269,588,327 | 6,926 | # Misturar pesos de vértices¶
This modifier mixes a second vertex group (or a simple value) into the affected vertex group, using different operations.
Importante
This modifier does implicit clamping of weight values in the standard (0.0 to 1.0) range. All values below 0.0 will be set to 0.0, and all values above 1.0 will be set to 1.0.
## Opções¶
Grupo de vértices A
O grupo de vértices que será afetado.
Padronização de pesos - grupo A
The default weight to assign to all vertices not in the given vertex group.
Grupo de vértices B
The second vertex group to mix into the affected one. Leave it empty if you only want to mix in a simple value.
Padronização de pesos - grupo B
The default weight to assign to all vertices not in the given second vertex group.
Modo de mistura
How the vertex group weights are affected by the other vertex group’s weights.
Substituir pesos
Replaces affected weights with the second group’s weights.
Adds the values of Group B to Group A.
Subtrai dos pesos de influência
Subtracts the values of Group B from Group A.
Multiplicar pesos
Multiplies the values of Group B with Group A.
Dividir pesos
Divides the values of Group A by Group B.
Diferença
Subtracts the smaller of the two values from the larger.
Média
Adds the values together, then divides by 2.
Definições de mistura
Permite escolher quais vértices serão afetados.
Todos os vértices
Affects all vertices, disregarding the vertex groups content.
Vertices from group A
Affects only vertices belonging to the affected vertex group.
Vertices from group B
Affects only vertices belonging to the second vertex group.
Vertices from one group
Affects only vertices belonging to at least one of the vertex groups.
Vértices em ambos os grupos.
Affects only vertices belonging to both vertex groups.
Importante
When using All vertices, Vertices from group B or Vertices from one group, vertices might be added to the affected vertex group.
### Opções de Influência e máscara¶
Influência global
The overall influence of the modifier (0.0 will leave the vertex group’s weights untouched, 1.0 is standard influence).
Importante
Influence only affects weights, adding/removing of vertices to/from vertex group is not prevented by setting this value to 0.0.
#### Máscara de grupo de vértices¶
Máscara de grupo de vértices
An additional vertex group, the weights of which will be multiplied with the global influence value for each vertex. If a vertex is not in the masking vertex group, its weight will be not be affected.
#### Máscara de textura¶
Máscara de textura
An additional texture, the values of which will be multiplied with the global influence value for each vertex.
This is a standard texture data-block control. When set, it reveals other settings:
How the texture is mapped to the mesh.
Local
Usa as coordenadas locais dos vértices.
Global
Use vertex coordinates in global space.
Objeto
Use vertex coordinates in another object’s space.
Objeto
The object to be used as reference for Object mapping.
UV
Usa as coordenadas definidas no mapa UV.
Mapa UV
O mapa UV que será usado para o mapeamento UV.
Usar canal
Which channel to use as weight factor source.
Red/Green/Blue/Alpha
Um dos valores dos canais de cor.
The average of the RGB channels (if RGB(1.0, 0.0, 0.0) value is 0.33).
Valor
The highest value of the RGB channels (if RGB(1.0, 0.0, 0.0) value is 1.0).
Matiz
Uses the hue value from the standard color wheel (e.g. blue has a higher hue value than yellow).
Saturação
Uses the saturation value (e.g. pure red’s value is 1.0, gray is 0.0).
Nota
All of the channels above are gamma corrected, except for Intensity.
Nota
You can view the modified weights in Weight Paint Mode. This also implies that you will have to disable the Vertex Weight Mix Modifier if you want to see the original weights of the vertex group you are editing.
## Exemplo¶
Using a Texture and the Mapping Curve
Here we are going to create a sort of strange alien wave (yes, another example with the Wave Modifier… but it is a highly visual one; it is easy to see the vertex group effects on it…).
So as above, add a 100×100 grid. This time, add a vertex group, but without assigning any vertex to it – we will do this dynamically.
Add a first Vertex Weight Mix Modifier, set the Vertex Group A field with a Default Weight A of 0.0, and set Default Weight B to 1.0.
Leave the Mix Mode to Replace weights, and select All vertices as Mix Set. This way, all vertices are affected. As none are in the affected vertex group, they all have a default weight of 0.0, which is replaced by the second default weight of 1.0. And all those vertices are also added to the affected vertex group.
Now, select or create a masking texture. The values of this texture will control how much of the «second weight» of 1.0 replaces the «first weight» of 0.0… In other words, they are taken as weight values!
You can then select which texture coordinates and channel to use. Leave the mapping to the default Local option, and play with the various channels…
Usando a intensidade. Usando o vermelho. Usando a saturação.
Do not forget to add a Wave Modifier, and select your vertex group in it!
You can use the weights created this way directly, but if you want to play with the curve mapping, you must add the famous Vertex Weight Edit Modifier, and enable its Custom Curve mapping.
By default, it is a one-to-one linear mapping – in other words, it does nothing! Change it to something like in Fig. Curva de mapeamento personalizada., which maps (0.0, 0.5) to (0.0, 0.25) and (0.5, 1.0) to (0.75, 1.0), thus producing nearly only weights below 0.25, and above 0.75: this creates great «walls» in the waves… | 1,418 | 5,700 | {"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-2022-27 | latest | en | 0.656512 |
https://teachingobjects.net/questions/403148-the-graph-below-shows-the-air-temperature-over-a-10-hour-period-from-noon-until-10-pm-which-is-true.html | 1,621,327,967,000,000,000 | text/html | crawl-data/CC-MAIN-2021-21/segments/1620243989756.81/warc/CC-MAIN-20210518063944-20210518093944-00393.warc.gz | 576,116,077 | 10,145 | dodline56
2017-08-16 14:11:45
The graph below shows the air temperature over a 10 hour period from noon until 10 PM which is true based on the graph? A. The temperature changes greater per hour from noon until 6 PM then from 8 PM until 10 PM B. Temperature change between noon and 6 PM is the same as the temperature change from 8 PM until 10 PM C. The temperature remains constant between noon and 6 PM D. The temperature remains constant between 8 PM and 10 PM | 120 | 462 | {"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-2021-21 | latest | en | 0.935591 |
essentialbiomechanics.com | 1,558,518,509,000,000,000 | text/html | crawl-data/CC-MAIN-2019-22/segments/1558232256778.29/warc/CC-MAIN-20190522083227-20190522105227-00292.warc.gz | 63,301,852 | 15,187 | In our last post (Part 1: Clarifying terms), we explained the Newton’s laws applied to orthodontics, with emphasis on the first law, THE LAW OF INERTIA, by which we showed that ALL orthodontic appliances must be in STATIC EQUILIBRIUM when installed. But do you know exactly what it means to be in balance? Do you know how to assess and recognize this condition? And do you know the clinical applications of this knowledge?
These are the questions that we want to clarify in this post. Being in static equilibrium means not moving, or more specifically, not accelerating. If you install a spring, or elastic, or any other device capable of generating force, certainly this device will not suffer acceleration. The forces generated by the appliances originate from the elastic deformation of its components, which tend to return to their original shape after their interatomic bonds have changed. This elastic deformation, however, does not represent an acceleration. When installing an elastic stretched between two teeth, for example, the elastic will not move to the right, nor to the left, nor up, nor down. That is, the appliance (in this case the elastic) will be in equilibrium. We can easily visualize the forces that hold it in this condition: they are the equal and opposite forces that the brackets exert on the elastic. As we explained in the previous post, these are the activation forces, which will trigger forces of reaction (or deactivation) responsible for tooth movement (Figure 1).
FIGURE 1. A. Elastic shape before force application. B. After applying two equal and opposite activation forces (blue), note lack of motion relative to a fixed reference point (x). C. reaction/deactivation forces (red) acting on the brackets.
And how to evaluate this equilibrium condition? Our only task will be to RECOGNIZE the systems of forces involved in each particular situation. That is, we should be able to visualize the forces and moments necessary to establish the state of equilibrium. In this state, TWO requirements must be met:
1) The sum of all the forces (vertical and / or horizontal) present must be zero.
2) The sum of the moments acting at ANY point must also be zero.
In the example of figure 1, we easily find the equilibrium of the horizontal forces. As they are collinear (have coincident lines of action), the cancel each other naturally without producing any rotation (or moment) in the appliance. In this simple example, the requirements for equilibrium were easily met and recognized.
However, when we apply vertical and / or non-collinear forces in a system, there are rotational forces that are not always easily visualized. Understanding the principle of equilibrium will help us in identifying the forces and moments present in any appliance.
To facilitate its study, we will explain 4 different situations, which may occur between the infinite possibilities of misalignment between two teeth. In our examples, we will use 2 premolars.
Situation 1) Two teeth are rotated in opposite directions, but in the same proportion relative to the interbracket axis. To insert a straight wire between these brackets, you will need to do two equal and opposite moments to elastically deform the wire. These moments (of activation) represent the actions of the brackets on the wire, and are obviously in equilibrium, as stated in Newton’s first law.
Figure 2. Situation 1) A. Two activation couples, in blue, are required to insert a straight wire (wire in solid line has been elastically deformed to the red dashed line) between the brackets. B. Deactivation-reaction forces, in red-that will be perceived by the teeth. This situation represents a class VI geometry.
Situation 2) Two teeth are rotated in opposite directions, one being rotated to half the quantity of the other, in relation to the interbracket axis. In this case, given the equilibrium principle, the forces and moments required to insert a straight wire in these brackets consist of an counterclockwise moment and an intrusive force at the end of the wire on the side of the tooth b, while only one extrusive force is applied to the end of the wire on the side of the tooth a. Note that the moment of side b(counterclockwise) will be counterbalanced by the moment generated by the two forces acting on the ends of the wire. That is, the couple produced by the vertical forces in a and b is clockwise, and thus neutralizes the moment of side b. Remember the second requirement of equilibrium: the sum of the moments at ANY point in the system must be zero. If you choose a point (on tooth a, tooth b, or any other point on the wire) to calculate these values, you will verify this requirement. For practical learning purposes, we suggest that you do not worry about values at this time. Just train your “clinical eye” to visualize the balance of the system.
Figure 3. Situation 2) A. One couple on end B and one couple across the length of the wire, in blue, are required to insert a straight wire (wire in solid line has been elastically deformed to the red dashed line) between the brackets. B. Deactivation-reaction forces, in red-that will be perceived by the teeth. This situation represents a class IV geometry.
Situation 3) Whenever you need to perform opposite moments to insert a wire between two brackets, being one moment longer than the other, there must certainly be vertical forces at the ends of the wire for the principle of equilibrium to be met. This situation occurs, for example, if two teeth are rotated in opposite directions, one being rotated three quarters the quantity of the other in relation to the interbracket axis. Notice again how the equilibrium has been reached: the greatest counterclockwise moment of the side b was counterbalanced by the smallest moment of the side a plus the moment generated by the vertical forces of the extremities (they form a clockwise couple).
Figure 4. Situation 3) A. In this case, three couples are required for equilibrium. Two couples of opposite directions and different magnitudes act at the ends, while one couple along the wire-activation forces, in blue- keeps the system in equilibrium. B. Deactivation/reaction forces, in red, that will be perceived by the teeth. This situation represents a class V geometry.
Situation 4) Finally, there are situations in which two equal moments in the same direction are necessary to insert a wire between two brackets. This occurs, for example, when the two teeth are rotated in the same direction, and in the same proportion with respect to the interbracket axis. In this case, as always, the equilibrium has been reached, since the moments at each end (the two counterclockwise) will be counterbalanced by the moment acting along the length of the wire (ie. the clockwise couple generated by the vertical forces in the ends of the wire). Some variations of this situation occur when the moments of the extremities are in opposite directions and have different intensities. In these cases, these moments will also be counterbalanced by a couple generated by the forces of the extremities, the only difference being in the intensity of these forces, which will be smaller than in the illustrated example of the situation 4.
Figure 5. Situation 4) A. In this case, two couples with the same direction and the same magnitude acting at the ends are balanced by one couple acting across the wire-activation forces, in blue. B. Deactivation/reaction forces, in red, that will be perceived by the teeth. This situation represents a class I geometry.
How to apply this knowledge clinically?
The answer to this question requires a more in-depth study of the subject, but the understanding of the principle of equilibrium represents one of the first steps for the rational and effective application of biomechanical principles in orthodontic clinic.
The beginner may even classify this knowledge as too theoretical and complex, though it forms the basis for understanding how the appliances work. Applying the theory of equilibrium in the day-to-day clinical practice will bring innumerable positive surprises to the professional. You will be able to simulate and predict the desired dental movements in order to select and build the appliances with more consistent force systems. You will notice that sometimes some movements are scientifically impossible to realize with just one device or activation, because we will never be able to disrespect the laws of physics (eg. create an appliance that is not in equilibrium). In addition, you will be able to assess the actual needs of anchorage control in order to minimize undesirable side effects, while potentiating the desired movements.
TIP: The best way to study and apply the principle of equilibrium is by drawing “equilibrium diagrams”, in which you draw the desired force systems and check if it is in equilibrium. Remember that the desired forces and moments (the deactivation ones) are exactly opposite the forces and moments of activation, which ALWAYS must be in equilibrium. Therefore, if your force system is in equilibrium, there will be the possibility of applying it at the clinic. Certainly, your system will fit into one of the four situations described in this post. In the future, we will explain other ways of naming and classifying these situations (the Burstone geometries), and we will describe some of the infinite possibilities of applying this knowledge to the confection of precise and efficient appliances. THE GOOD NEWS is that YOU will be able to create the desired configuration (eg geometry) with simple bends in a great number of appliances.
We conclude by inviting the colleagues to learn more about these biomechanical principles (see recommended reading). For those who haven´t had the time to go deep into complex scientific articles, we also suggest our online course* – focused on teaching the fundamental concepts of bone biology and orthodontic mechanics.
*Enjoy our 40% discount on the Online Course Introduction to Orthodontic Biomechanics and reach this knowledge with updated and truly didactic material! | 2,048 | 10,114 | {"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} | 3.484375 | 3 | CC-MAIN-2019-22 | longest | en | 0.926073 |
https://dr.ntu.edu.sg/handle/10356/87052?mode=simple | 1,701,894,554,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679100603.33/warc/CC-MAIN-20231206194439-20231206224439-00306.warc.gz | 247,877,102 | 9,648 | Please use this identifier to cite or link to this item: `https://hdl.handle.net/10356/87052`
Title: Constructing intrinsic delaunay triangulations from the dual of geodesic voronoi diagrams Authors: Liu, Yong-JinFan, DianXu, Chun-XuHe, Ying Keywords: Intrinsic Delaunay TriangulationGeodesic Voronoi Diagram Issue Date: 2017 Source: Liu, Y.-J., Fan, D., Xu, C.-X., & He, Y. (2017). Constructing intrinsic delaunay triangulations from the dual of geodesic voronoi diagrams. ACM Transactions on Graphics, 36(2), 15-. Series/Report no.: ACM Transactions on Graphics Abstract: Intrinsic Delaunay triangulation (IDT) naturally generalizes Delaunay triangulation from R2 to curved surfaces. Due to many favorable properties, the IDT whose vertex set includes all mesh vertices is of particular interest in polygonal mesh processing. To date, the only way for constructing such IDT is the edge-flipping algorithm, which iteratively flips non-Delaunay edges to become locally Delaunay. Although this algorithm is conceptually simple and guarantees to terminate in finite steps, it has no known time complexity and may also produce triangulations containing faces with only two edges. This article develops a new method to obtain proper IDTs on manifold triangle meshes. We first compute a geodesic Voronoi diagram (GVD) by taking all mesh vertices as generators and then find its dual graph. The sufficient condition for the dual graph to be a proper triangulation is that all Voronoi cells satisfy the so-called closed ball property. To guarantee the closed ball property everywhere, a certain sampling criterion is required. For Voronoi cells that violate the closed ball property, we fix them by computing topologically safe regions, in which auxiliary sites can be added without changing the topology of the Voronoi diagram beyond them. Given a mesh with n vertices, we prove that by adding at most O(n) auxiliary sites, the computed GVD satisfies the closed ball property, and hence its dual graph is a proper IDT. Our method has a theoretical worst-case time complexity O(n2 + tnlog n), where t is the number of obtuse angles in the mesh. Computational results show that it empirically runs in linear time on real-world models. URI: https://hdl.handle.net/10356/87052http://hdl.handle.net/10220/45219 ISSN: 0730-0301 DOI: 10.1145/2999532 Schools: School of Computer Science and Engineering Rights: © 2017 Association for Computing Machinery. This is the author created version of a work that has been peer reviewed and accepted for publication by ACM Transactions on Graphics, Association for Computing Machinery. It incorporates referee’s comments but changes resulting from the publishing process, such as copyediting, structural formatting, may not be reflected in this document. The published version is available at: [http://dx.doi.org/10.1145/2999532]. Fulltext Permission: open Fulltext Availability: With Fulltext Appears in Collections: SCSE Journal Articles
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Updated on Nov 30, 2023 | 785 | 3,334 | {"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-2023-50 | latest | en | 0.884323 |
http://mathbyvemuri.blogspot.com/2011/10/algebra-2-placement-qsgregmat-word.html | 1,508,725,793,000,000,000 | text/html | crawl-data/CC-MAIN-2017-43/segments/1508187825510.59/warc/CC-MAIN-20171023020721-20171023040721-00216.warc.gz | 216,492,820 | 17,343 | ## Saturday, 22 October 2011
### Algebra-3 (Placement Q's)(GRE/GMAT Word problems)
A group of friends went for a dinner and got a bill of Rs 2400. They have decided to contribute equally for the bill. But two of them could not contribute and to compensate that, rest all contributed Rs 100 more. How many are there in the group?
(A) 6 (B)10 (C) 8 (D) 12
Solution follows here:
Solution:
Let there are ‘x’ members in the group.
If all those in the group contribute equally, let the contribution per head be ‘m’.
=> m * x = 2400 ------(1)
But given, two of them could not contribute and to compensate that, rest all contributed Rs 100 more. This means, (x-2) contributed (m+100) each.
=> (m+100) * (x-2) = 2400 ------(2)
Instead of solving the two equations, we check for the given answer options one by one:
Option (A), put x=6 in equation (1), 6m = 2400 => m = 400
put x=6 in equation (2), (m+100)*4 = 2400 => m+100 = 600 => m = 500
both are contradicting each other, hence Option (A) is wrong
Option (B), put x=10 in equation (1), 10m = 2400 => m = 240
put x=10 in equation (2), (m+100)*8 = 2400 => m+100 = 300 => m = 200
both are contradicting each other, hence Option (B) is wrong
Option (C), put x=8 in equation (1), 8m = 2400 => m = 300
put x=8 in equation (2), (m+100)*6 = 2400 => m+100 = 400 => m = 300
yes, both give same result, hence Option (C) is correct. Answer is Option (C) | 462 | 1,438 | {"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} | 4.375 | 4 | CC-MAIN-2017-43 | longest | en | 0.913087 |
https://spatial.engineer/lessons/summarizing-data-and-estimating-population-parameters-using-descriptive-measures/ | 1,597,183,133,000,000,000 | text/html | crawl-data/CC-MAIN-2020-34/segments/1596439738855.80/warc/CC-MAIN-20200811205740-20200811235740-00581.warc.gz | 491,463,566 | 26,169 | Summarizing Data and Estimating Population Parameters Using Descriptive Measures
Overview and learning goals
As we embark on this topic, ask yourself: Do I understand the following concepts and disciplines and how they fit together?
• Do I know what is a descriptive measure?
• Can I name and distinguish between the four categories of descriptive measure, and the kinds we’re going to see of each?
• Can I calculate and interpret the following measures of central tendency?
• Population and sample mean
• Median
• Midrange
• Mode
• Can I calculate and interpret the following measures of variation (or variability or spread or dispersion):
• Population and sample variance
• Population and sample standard deviation
• Range
• Coefficient of variation
• Can I calculate and interpret the following measures of position:
• Percentiles
• Quartiles
• z-scores
• Can I calculate and interpret the following measures of shape:
• Skewness
• Kurtosis
The learning goals above are critical and covered in most courses in statistics. Because it’s so important yet often confused or misunderstood, we’re also going to make sure you:
• Can explain how well some of the key descriptive measures calculated from samples (i.e. sample statistics) represent the corresponding actual and most often unknown population parameters, i.e. how precise our descriptive measures are
• Can calculate and interpret estimates of that precision using equations of the Standard Error
My notes
Here are my lecture notes – the ones I wrote up when I lectured on this topic. They’re not perfect, but if you’re in my class then they should be helpful when you go to create your own “perfect” set of lecture notes.
When you’re ready, proceed by working your way through the self-assessments (under “Lesson Assessments”) below.
Once you’ve clicked through those, use the green button to move on to the next lesson (or to finish up if there are no other lessons).
Lesson Content
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The following schedules are for Alex’s in-class students:
Welcome (back)! | 423 | 2,050 | {"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-2020-34 | latest | en | 0.892978 |
https://www.semesprit.com/1212/solving-polynomial-equations-worksheet-answers/ | 1,720,885,451,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763514510.7/warc/CC-MAIN-20240713150314-20240713180314-00443.warc.gz | 792,488,756 | 18,295 | Solving Polynomial Equations Worksheets answer the most important question that people often have – what can I do now? A Worksheet can be a lifesaver, especially when trying to get your grades on track. It is very helpful to have these sorts of worksheets when you need a solution. Below is a simple example of what is used in this type of worksheet.
Let’s look at what a solvable polynomial equation worksheet might look like. There will be questions that you need to answer in order to create the equation that you need to solve. There are 3 main types of this type of worksheet that you can use.
The first main type of solvable equation worksheet will contain all three of the factors that you will need to put into the equation. The third factor is not included in the worksheet but can be found in your book or online. This worksheet will help you get your calculations to match up with what is being said in the book.
A second type of solvable problem worksheet will not answer the questions that you have already answered in the book. It will not have a formula and instead you will need to go to the internet and find the formula and then enter it yourself. This worksheet is a little more complicated and only works for problem types that require two or more variables.
Finally, a third type of solvable problems worksheet will have only one formula. The other factors that are required to solve the equation will not be included in the worksheet. This worksheet works for those types of equations that you need to calculate for a multiple variable.
Using these worksheets is just as easy as entering the formulas and then answering the question. You will also be able to answer the multiple variable type of problem using this type of worksheet because they will match up with the information found in the book that you are using.
Here is a way to make sure that you know exactly what to do when solving a solvable polynomial equation. Many people find that they know how to solve it and then get stuck. This is why you should always be looking for new solutions to solve new problems.
The best way to learn how to do this is to find a site that has an easy formula and then use that to answer all of your questions. Then once you get a feel for how to do this, then you can go online and find a worksheet that has all of the answers that you need. | 475 | 2,365 | {"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} | 3.40625 | 3 | CC-MAIN-2024-30 | latest | en | 0.969124 |
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1. ## Calculating height of parabola, based on base width and arc length
Thanks bacterius, i aproximated it using taylor series but it only worked for a small arc length to base width ratio, so the good old bisection is what i will settle for Just out of interest, how is the parabola being used? If you're talking about the motion of a projectile under the force of gravity, there are other equations you can use that are more suited to the task.[/quote] I have springs that compress, and i want to keep their length constant so i bend them accordingly when they compress.
2. ## Calculating height of parabola, based on base width and arc length
So if I understand you correctly, you need to keep the length of the parabolic arc constant, while modifying its base width, so you need to obtain the correct height for it to have the same length?[/quote] exactly
3. ## Calculating height of parabola, based on base width and arc length
I have no idea how to do any of those things you mentioned, i just finished high school my knowledge of math is limited.. Is there some software that does these approximations or do i have to try and do it myself?
4. ## Calculating height of parabola, based on base width and arc length
the base width of my parabola varies (the distance between x1 and x2), between some value q and 0, the thing is that i need the arc length to always be equal to q, I am modeling a spring that when compressed bends like a parabola, so when the spring compresses to a smaller length than its rest length q, i must maintain the length by bending it. and in order to bend it to a certain arc length (q), i must calculate the height every time the base width changes.
5. ## Calculating height of parabola, based on base width and arc length
this is the formula for the arc length of a parabola 0.5?16h²+w² + [w²/(8h)][Ln(4h + ?16h²+w²) - Ln(w)], from http://www.had2know.com/academics/parabola-segment-arc-length-area.html ., if i know the arc length and the base width, how can i find the height? I've tried solving for h, using wolfram alpha and mathematica, both failed... said it cant be solved, But there must be a way? It's mathematics, everything is possible, right?
6. ## How to add source tree to visual C++ 2010?
I don't want to use VS filters. Is there a way to add all source files from one folder that is the root of a source tree? And to access that structure in the solution explorer? In other words i want my source structure in windows explorer to be the same as in Visual studio. Thanks..
7. ## length of a 2D quadratic bezier curve?
i figured it out from the code.. no need to explain, thanks again.
8. ## length of a 2D quadratic bezier curve?
Wow, i tried it and it works, thanks, but i have a question, what is the D in the b = 2P1 - 2DP0? And why is there no line above P0? I need to understand this so that i could simplify this equation, because i have a very simple case of a bezier curve.
9. ## Game Development
If you never made games before, try making some 2D games first, if you already know C++, this is a good place to start http://lazyfoo.net/SDL_tutorials/index.php simple tutorials teaching you how to use a 2D graphics library called SDL
10. ## How to find a size of variable
SDL_Surface has a member format which is of type SDL_PixelFormat http://sdl.beuc.net/sdl.wiki/SDL_PixelFormat, it tells you all you need to know about how pixels are represented in a surface. It has a member BytesPerPixel, which is what you need to figure out the size of your Surface, given the number of pixels.
11. ## length of a 2D quadratic bezier curve?
Is there a formula? Or must i approximate it by dividing the curve into line segments and summing them up?
12. ## How to learn Visual Studio for C++ game programming?
I don't expect to find a book "visual studio for game programming" i just want to learn about all the compiler options, there has to bee some resources about it? There are great books on GCC, are there any similar resources for MSVC?
13. ## How to learn Visual Studio for C++ game programming?
I have been programming small openGL/SDL games in Visual Studio for some time now, and i know how to use it, but i still get confused with the overwhelming number of compiler options and various tools in the IDE, sometimes when an error occurs, for example in the debug config everything compiles fine and in release all hell brakes loose, and i dont know why? That is i dont undestand how the MSVC works.. Where can i learn more about the Visual Studio IDE for C++, i dont care about CLI or .NET or MFC, or Win32, just the compiler and IDE? btw, im using the 2010 express edition..
14. ## Stencil buffer soft(blurry) edges
No its not dynamic, i just have to uncover parts of the map with player movement. Anyway I'm looking into FBO's and generally need to learn OpenGL more to implement these effects... Thanks...
15. ## Stencil buffer soft(blurry) edges
Ok then, i suppose i have to have a texture the size of my map, and than make holes in it, holes being blurred circles. But i'm not quite sure how i would do this, maybe if i had a 32 bit texture with a alpha hole in it and than if i could put the alpha values of that texture to the alpha values of the texture that i want to make holes in... And then as my character moves i could make holes in the big texture by changing the original alpha with my hole texture.. But again i don't know how to do this? | 1,319 | 5,466 | {"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-2018-51 | longest | en | 0.914196 |
http://python-tutorials.in/category/python-programs/ | 1,585,396,486,000,000,000 | text/html | crawl-data/CC-MAIN-2020-16/segments/1585370491857.4/warc/CC-MAIN-20200328104722-20200328134722-00335.warc.gz | 147,049,394 | 64,332 | # Category: Python Programs
python tutorials and learn python
### Python program to search an element in a doubly linked list.
Python program to search an element in a doubly linked list. In this program, we need to search a given node in a doubly linked list. To solve this problem, we will traverse through the list using a node current. Current points to head and start comparing searched node data with current node data. If…
### Python program to rotate doubly linked list by N nodes.
Python program to rotate doubly linked list by N nodes. In this program, we need to create a doubly linked list and rotate it by n node. This can be achieved by maintaining a pointer that starts from the head node and traverses the list until current points to the nth node. Move the list…
### Python program to remove duplicate elements from a Doubly Linked List.
Python program to remove duplicate elements from a Doubly Linked List. In this program, we will create a doubly linked list and remove the duplicate, if present, by traversing through the list. List after removing duplicates: In the above list, node2 is repeated thrice, and node 3 is repeated twice. Current will point to head,…
### Python program to insert a new node at the middle of the Doubly Linked List.
Python program to insert a new node at the middle of the Doubly Linked List. In this program, we create a doubly linked list and insert a new node in the middle of the list. If the list is empty, both head and tail will point to the new node. If the list is not…
### Python program to insert a new node at the end of the Doubly Linked List.
Python program to insert a new node at the end of the Doubly Linked List. In this program, we will create a doubly linked list and insert every new node at the end of the list. If the list is empty, then head and tail will point to the newly added node. If the list…
### Python program to insert a new node at the beginning of the Doubly Linked list.
Python program to insert a new node at the beginning of the Doubly Linked list. In this program, we will create a doubly linked list and insert every new node at the beginning of the list. If the list is empty, then head and tail will point to the newly added node. If the list…
### Python program to find the maximum and minimum value node from a doubly linked list.
Python program to find the maximum and minimum value node from a doubly linked list. In this program, we will create a doubly linked list then, iterate through the list to find out the minimum and maximum node. We will maintain two variables min and max. Min will hold the minimum value node, and max…
### Python program to delete a new node from the middle of the doubly linked list.
Python program to delete a new node from the middle of the doubly linked list. In this program, we will create a doubly linked list and delete a node from the middle of the list. If the list is empty, display the message “List is empty”. If the list is not empty, we will calculate… | 644 | 3,010 | {"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 | latest | en | 0.837939 |
https://arinjayacademy.com/category/maths-class-9/ | 1,620,393,382,000,000,000 | text/html | crawl-data/CC-MAIN-2021-21/segments/1620243988793.99/warc/CC-MAIN-20210507120655-20210507150655-00594.warc.gz | 129,508,863 | 10,504 | Category: Maths Class 9
NCERT Solutions for Class 9 Maths Chapter 7 Exercise 7.4 – Triangles
Download NCERT Solutions for Class 9 Maths Chapter 7 Exercise 7.4 – Triangles. This Exercise contains 6 questions, for which detailed answers have been provided
NCERT Solutions for Class 9 Maths Chapter 7 Exercise 7.3 – Triangles
Download NCERT Solutions for Class 9 Maths Chapter 7 Exercise 7.3 – Triangles. This Exercise contains 5 questions, for which detailed answers have been provided
NCERT Solutions for Class 9 Maths Chapter 7 Exercise 7.2 – Triangles
Download NCERT Solutions for Class 9 Maths Chapter 7 Exercise 7.2 – Triangles. This Exercise contains 8 questions, for which detailed answers have been provided
NCERT Solutions for Class 9 Maths Chapter 7 Exercise 7.1 – Triangles
Download NCERT Solutions for Class 9 Maths Chapter 7 Exercise 7.1 – Triangles. This Exercise contains 8 questions, for which detailed answers have been provided
NCERT Solutions for Class 9 Maths Chapter 10 Exercise 10.5 – Circles
Download NCERT Solutions for Class 9 Maths Chapter 10 Exercise 10.5 – Circles. This Exercise contains 12 questions, for which detailed answers have been provided
NCERT Solutions for Class 9 Maths Chapter 10 Exercise 10.4 – Circles
Download NCERT Solutions for Class 9 Maths Chapter 10 Exercise 10.4 – Circles. This Exercise contains 6 questions, for which detailed answers have been provided
NCERT Solutions for Class 9 Maths Chapter 10 Exercise 10.3 – Circles
Download NCERT Solutions for Class 9 Maths Chapter 10 Exercise 10.3 – Circles. This Exercise contains 3 questions, for which detailed answers have been provided
NCERT Solutions for Class 9 Maths Chapter 10 Exercise 10.2 – Circles
Download NCERT Solutions for Class 9 Maths Chapter 10 Exercise 10.2 – Circles. This Exercise contains 2 questions, for which detailed answers have been provided
NCERT Solutions for Class 9 Maths Chapter 10 Exercise 10.1 – Circles
Download NCERT Solutions for Class 9 Maths Chapter 10 Exercise 10.1 – Circles. This Exercise contains 2 questions, for which detailed answers have been provided
NCERT Solutions for Class 9 Maths
NCERT Solutions for Class 9 Maths comprises of 15 Chapters for Class 9, which contains 39 Exercises. These Solutions are provided where each of these | 557 | 2,302 | {"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} | 3.09375 | 3 | CC-MAIN-2021-21 | latest | en | 0.876041 |
https://explainxkcd.com/wiki/index.php?title=Talk:2403:_Wrapping_Paper&oldid=305039 | 1,686,179,193,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224654016.91/warc/CC-MAIN-20230607211505-20230608001505-00100.warc.gz | 278,960,221 | 8,583 | # Talk:2403: Wrapping Paper
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
I was reminded of the old http://bjornsmaths.blogspot.com/2005/11/how-to-catch-lion-in-sahara-desert.html
``` The method of inverse geometry: We place a spherical cage in the desert and enter it. We then perform an inverse operation with respect to the cage. The lion is then inside the cage and we are outside.
```
Bmwiedemann (talk) 02:41, 26 December 2020 (UTC)
An engineer, a physicist, and a mathematician are shown a pasture with a herd of sheep, and told to put them inside the smallest possible amount of fence.
The engineer is first. He herds the sheep into a circle and then puts the fence around them, declaring, "A circle will use the least fence for a given area, so this is the best solution."
The physicist is next. He creates a circular fence of infinite radius around the sheep, and then draws the fence tight around the herd, declaring, "This will give the smallest circular fence around the herd."
The mathematician is last. After giving the problem a little thought, he puts a small fence around himself and then declares, "I define myself to be on the outside."
(for example here) -- Hkmaly (talk) 05:05, 26 December 2020 (UTC)
Note: In some countries, presents are opened already on Christmas Eve. Svízel přítula (talk) 08:04, 26 December 2020 (UTC)
Sorry but this immediately brings Jevil (Deltarune) to mind. 108.162.216.198 09:17, 27 December 2020 (UTC)
Maybe we could make Klein bottle-shaped wrapping paper, it can: (1) let everything in the universe be the gift, including what is inside (well, I know it's unreasonable to say something is “inside” a Klein bottle) the gift box; (2) reduce the cost of printing to zero. Lamda05 (talk) 05:35, 28 December 2020 (UTC)
"Wow, rude of you to regift literally every gift that you or anyone else has ever received." - except, perhaps, the headphones. Jordan Brown (talk) 20:31, 19 January 2023 (UTC)
## My hobby
Prank Randall by selling him wrapping paper that is printed on both sides so he can't turn it inside out 172.69.33.220 02:46, 26 December 2020 (UTC) | 561 | 2,146 | {"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-2023-23 | latest | en | 0.974327 |
https://www.teachoo.com/4367/1253/Ex-6.3--8---Find-a-point-on-y--(x-2)2--tangent-is-parallel/category/Finding-point-when-tangent-is-parallel--perpendicular/ | 1,656,904,882,000,000,000 | text/html | crawl-data/CC-MAIN-2022-27/segments/1656104293758.72/warc/CC-MAIN-20220704015700-20220704045700-00600.warc.gz | 1,080,689,540 | 31,331 | Finding point when tangent is parallel/ perpendicular
Chapter 6 Class 12 Application of Derivatives
Concept wise
Introducing your new favourite teacher - Teachoo Black, at only βΉ83 per month
### Transcript
Ex 6.3, 8 Find a point on the curve π¦=(π₯β2)^2 at which the tangent is parallel to the chord joining the points (2, 0) and (4, 4).Given Curves is π¦=(π₯β2)^2 Let AB be the chord joining the Point (2 , 0) & (4 ,4) & CD be the tangent to the Curve π¦=(π₯β2)^2 Given that tangent is Parallel to the chord i.e. CD β₯ AB β΄ Slope of CD = Slope of AB If two lines are parallel, then their slopes are equal Slope of tangent CD Slope of tangent CD = ππ¦/ππ₯ =(π(π₯ β 2)^2)/ππ₯ = 2(π₯β2) (π (π₯ β 2))/ππ₯ = 2(π₯β2) (1β0) = 2(π₯β2) Slope of AB As AB is chord joining Points (2 , 0) & (4 , 4) Slope of AB =(4 β 0)/(4 β 2) =4/2 As slope of line joining point (π₯ , π¦) & (π₯2 , π¦2) ππ (π¦2 β π¦1)/(π₯2 β π₯1) =2 Now, Slope of CD = Slope of AB 2(π₯β2)=2 π₯β2=2/2 π₯β2=1 π₯=3 Finding y when π₯=3 π¦=(π₯β2)^2 π¦=(3β2)^2 π¦=(1)^2 π¦=1 Hence, Point is (π , π) Thus, the tangent is parallel to the chord at (3 ,1) | 598 | 1,243 | {"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-2022-27 | latest | en | 0.72179 |
https://www.slideshare.net/Turbomach2010/wind-turbine-2554710 | 1,513,631,475,000,000,000 | text/html | crawl-data/CC-MAIN-2017-51/segments/1512948623785.97/warc/CC-MAIN-20171218200208-20171218222208-00151.warc.gz | 769,725,642 | 39,387 | Successfully reported this slideshow.
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# Wind Turbine
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• Such a detailed presentation! It's clear and highly informative. Thanks for this set!
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• Nice presentation. The information was introduced in a very detailed manner. There were calculations shown which is effective since you are giving a specific detail about the topic. It was explained further to the benefit of many. With this, many will be influenced to use wind turbines because of its many benefits.
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### Wind Turbine
1. 1. Wind Turbines<br />By: Ahmed Yehya Mohamed MohamedSameh MohamedMohamed MahmoudMoustafaMina FaragAdlyMohamed Anwar<br />
2. 2. wind<br />
3. 3. Wind power calculation<br />Power= work / time<br /> = Kinetic Energy / t<br /> = ½mV2 / t<br /> = ½(ρAd)V2/t<br /> = ½ρAV2(d/t)<br /> = ½ρAV3<br />Power in the Wind = ½ρAV3<br />
4. 4. Inside a Wind Turbine<br />
5. 5.
6. 6. Types of wind turbines according to power<br />Small (10 kW)<br /><ul><li>Homes
7. 7. Farms
8. 8. Remote Applications</li></ul>(e.g. water pumping, telecom sites, icemaking)<br />Intermediate<br /> (10-250 kW)<br /><ul><li>Village Power
9. 9. Hybrid Systems
10. 10. Distributed Power</li></ul>Large (250 kW - 2+MW)<br /><ul><li>Central Station Wind Farms
11. 11. Distributed Power</li></li></ul><li>Types of wind turbinesaccording to design <br />
12. 12. Horizontal axis turbines<br />advantages<br />Variable blade pitch, which gives the turbine blades the optimum angle of attack<br />The tall tower base allows access to stronger wind in sites with wind shear.<br />High efficiency, since the blades always move perpendicularly to the wind, receiving power through the whole rotation.<br />disadvantages<br />Tall towers and blades up to 90 meters long are difficult to transport. Transportation can now cost 20% of equipment costs.<br />Tall HAWTs are difficult to install, needing very tall and expensive cranes and skilled operators<br />Massive tower construction is required to support the heavy blades, gearbox, and generator<br />
13. 13. Vertical Axis Turbines<br />Advantages<br />Omnidirectional<br />Accepts wind from any angle<br />Components can be mounted at ground level<br />Ease of service<br />Lighter weight towers<br />Can theoretically use less materials to capture the same amount of wind<br />Disadvantages<br />Rotors generally near ground where wind poorer<br />Centrifugal force stresses blades<br />Poor self-starting capabilities<br />Requires support at top of turbine rotor<br />Requires entire rotor to be removed to replace bearings<br />Overall poor performance and reliability<br />Have never been commercially successful<br />
14. 14. Vertical Axis Turbines<br />advantages<br />Omnidirectional<br />Accepts wind from any angle<br />Components can be mounted at ground level<br />Ease of service<br />Lighter weight towers<br />Can theoretically use less materials to capture the same amount of wind<br />Disadvantages<br />Rotors generally near ground where wind poorer<br />Centrifugal force stresses blades<br />Poor self-starting capabilities<br />Requires support at top of turbine rotor<br />Requires entire rotor to be removed to replace bearings<br />Overall poor performance and reliability<br />Have never been commercially successful<br />
15. 15. Classification according to number of blades<br />
16. 16. Number of Blades – One<br />Rotor must move more rapidly to capture same amount of wind<br />Gearbox ratio reduced<br />Added weight of counterbalance negates some benefits of lighter design<br />Higher speed means more noise, visual, and wildlife impacts<br />Blades easier to install because entire rotor can be assembled on ground<br />Captures 10% less energy than two blade design<br />Ultimately provide no cost savings<br />
17. 17. Number of Blades - Two<br />Advantages & disadvantages similar to one blade<br />Need teetering hub and or shock absorbers because of gyroscopic imbalances<br />Capture 5% less energy than three blade designs<br />
18. 18. Number of Blades - Three<br />Balance of gyroscopic forces<br />Slower rotation<br />increases gearbox & transmission costs<br />More aesthetic, less noise, fewer bird strikes<br />
19. 19. Airfoil Nomenclaturewind turbines use the same aerodynamic principals as aircraft<br />
20. 20. Lift & Drag Forces<br />The Lift Force is perpendicular to the direction of motion. We want to make this force BIG.<br />The Drag Force is parallel to the direction of motion. We want to make this force small.<br />α = low<br />α = medium<br /><10 degrees<br />α = High<br />Stall!!<br />
21. 21. ΩR<br />Ωr<br />α<br />V<br />V<br />VR = Relative Wind<br />Apparent Wind & Angle of Attack<br />α = angle of attack = angle between the chord line and the direction of the relative wind, VR .<br />VR = wind speed seen by the airfoil – vector sum of V (free stream wind) and ΩR (tip speed).<br />
22. 22. Twist & Taper<br />Speed through the air of a point on the blade changes with distance from hub<br />Therefore, tip speed ratio varies as well<br />To optimize angle of attack all along blade, it must twist from root to tip<br />Fastest<br />Faster<br />Fast<br />
23. 23. Wind turbines sites<br />
24. 24.
25. 25. “The rotor is the single most critical element of any wind turbine… How a wind turbine controls the forces acting on the rotor, particularly in high winds, is of the utmost importance to the long-term, reliable function of any wind turbine.” Paul Gipe<br />Rotor Controls<br />Micro Turbines<br />May not have any controls<br />Blade flutter<br />Small Turbines<br />Furling (upwind) – rotor moves to reduce frontal area facing wind<br />Coning (downwind) – rotor blades come to a sharper cone<br />Passive pitch governors – blades pitch out of wind<br />Medium Turbines<br />Aerodynamic Stall<br />Mechanical Brakes<br />Aerodynamic Brakes<br />
26. 26. Turbine Power Limited By <br /><ul><li>Power in the wind
27. 27. Betz limit (air can not be slowed to zero)
28. 28. Low speed losses - wake rotation
29. 29. Drag losses – aerodynamics and blade geometry
30. 30. Generator and drivetrain inefficiencies</li></li></ul><li>Thank you<br /> | 1,595 | 6,413 | {"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-2017-51 | latest | en | 0.819242 |
http://www.onlinemathlearning.com/reflection-transformation.html | 1,510,947,343,000,000,000 | text/html | crawl-data/CC-MAIN-2017-47/segments/1510934803906.12/warc/CC-MAIN-20171117185611-20171117205611-00361.warc.gz | 490,072,604 | 10,889 | # Reflection Transformation
Related Topics: More Lessons on Transformation and Geometry
In these lessons, we will learn
• what is reflection?
• how to draw the reflected image of an object (drawn on grid lines) given the line of reflection.
• how to draw the reflected image of an object (using a compass or ruler) given the line of reflection.
• how to reflect points and shapes on the coordinate plane using the Coordinate Rules.
• how to reflect an object using a transformation matrix.
### What is Reflection?
In a reflection transformation, all the points of an object are reflected or flipped on a line called the axis of reflection or line of reflection.
Example:
A reflection is defined by the axis of symmetry or mirror line. In the above diagram, the mirror line is x = 3.
Under reflection, the shape and size of an image is exactly the same as the original figure. This type of transformation is called isometric transformation.
The orientation is laterally inverted, that is they are facing opposite directions.
The line of reflection is the perpendicular bisector of the line joining any point and its image (e.g. PP ’ in the above figure).
All the points on the mirror line are not changed. These points are said to be invariant.(R is an invariant point in the above.)
### Drawing The Image on Grid Lines
If the axis of reflection is on one of the grid lines, we just count the number of squares from a point on the object to the axis and the image is the same distance from the axis.
Example:
In the diagram, the figure A is reflected in the line XY. Draw the image of A in the diagram.
Solution:
Note that the point O remained unchanged under reflection because it is on the axis of reflection. Any point on the line of reflection is unchanged – such points are described as invariant.
How to reflect a shape on squared paper without using tracing paper
This video shows how to reflect a shape on squared paper without using tracing paper. Just count the distance of each corner to the mirror line and count the same distance away from the mirror line. Once all the points have been reflected them, join the points up neatly using your ruler.
### Draw the image using a compass
If the axis of reflection is not on the grid lines, we will need to use a compass to construct the image.
Example:
In the diagram below, the triangle ABC is reflected in the line XY. Draw the image of the triangle in the diagram.
Solution:
Step1: Place the sharp point of a compass at A and draw two arcs intersecting the line XY
Step 2: Place the sharp point of the compass on the first intersecting point and mark an arc on the opposite side of XY. Place the sharp point of the compass on the second intersecting point and mark an arc to intersect with the first arc. The intersection is the image of A’ .
Step 3: Repeat steps 1 and 2 to get the points B ’ and C ’ . Join the points A ’ , B ’ and C ’ to get the image A ’ B ’ C ’ .
Construct Reflection by Hand
How to reflect a figure over a line by hand using a ruler. How to construct a Line of Reflection?
Construct a line of reflection given the object and the image.
### Reflection on the Coordinate Plane
We will now look at how points and shapes are reflected on the coordinate plane. It will be helpful to note the patterns of the coordinates when the points are reflected over different lines of reflection.
Coordinate Rules for Reflection
If (a, b) is reflected on the x-axis, its image is the point (a, -b)
If (a, b) is reflected on the y-axis, its image is the point (-a, b)
If (a, b) is reflected on the line y = x, its image is the point (b, a)
If (a, b) is reflected on the line y = -x, its image is the point (-b, a)
Geometry Reflection
A reflection is an isometry, which means the original and image are congruent, that can be described as a "flip". To perform a geometry reflection, a line of reflection is needed; the resulting orientation of the two figures are opposite. Corresponding parts of the figures are the same distance from the line of reflection. Ordered pair rules reflect over the x-axis: (x, -y), y-axis: (-x, y), line y = x: (y, x).
This video shows reflection over the x-axis, y-axis, x = 2, y = −2 This video shows reflection over y = x, y = x. A reflection that results in an overlapping shape. This video shows reflection over the x-axis, y-axis, x = −3, y = 5, y = x, and y = x.
### Reflections using Matrices
This lesson involves reflections in the coordinate plane. We use coordinate rules as well as matrix multiplication to reflect a polygon (or polygon matrix) about the x-axis, y-axis, the line y = x or the line y = -x. Matrices and Reflections
Performing reflections with matrices over the y-axis and x-axis. Matrices for Reflections over the y-axis and x-axis. Matrices for Reflections over the line y = x.
Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.
You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations. | 1,167 | 5,235 | {"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} | 4.625 | 5 | CC-MAIN-2017-47 | latest | en | 0.89441 |
thisishowyouplay.org | 1,544,455,267,000,000,000 | text/html | crawl-data/CC-MAIN-2018-51/segments/1544376823348.23/warc/CC-MAIN-20181210144632-20181210170132-00203.warc.gz | 292,199,379 | 7,395 | # Egg physics
Egg physics
Group Size medium (6-20)
Setting indoors, outdoors
Setup Time medium (6-30 min)
Duration medium (11-30 min)
Subjects physics
Materials cooking oil, boiled eggs (3-4), a 225 ml glass bottle with mouth big enough for egg to half rest on, a strip of paper 4 inches, matches
Alias egg in a bottle
Presentation Style demonstration
## Brief Description
Students will demonstrate how air contracts and expands with temperature. They will attempt to fit an egg threw a small opening in the top of a bottle without damaging the egg.
## Objective
Demonstrate how air contracts and expands with temperature. Pressure changes as temperature changes.
## This Is How You Play
Before the activity:
Challenge a friend to push a shelled hard-boiled egg into a narrow-necked bottle without damaging the egg. Ask a grown-up to stand by during your performance because you have to drop a burning piece of paper into the bottle
The activity:
1. Put some cooking oil, butter of margarine around the mouth of the bottle.
2. Place the egg on the mouth of the bottle and challenge your friend to push it inside without breaking it.
3. When he gives up, it’s time to act as the magician. Fold the paper to form an accordion. Light one end with a match and drop it into the bottle.
4. Now quickly place the egg over the mouth of the bottle. It will be sucked into the bottle. (The burning paper has heated the air inside the bottle so that the air has expanded. When the paper stops burning, the air cools and contracts again. This creates a vacuum that will suck the egg into the bottle.)
5. Challenge your friend to get the egg out. When he’s given up, invert the bottle so that the egg drops down into the neck. Hold the bottle to your lips and blow a fast, hard blast of air into the bottle. The egg will zoom out, so get ready to catch it. ( The egg acts as a valve that opens while you’re blowing air into the bottle and then closes when you stop. The extra air is trapped inside, behind the egg, when the valve suddenly closes. That pressure forces the egg out.) | 462 | 2,078 | {"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-2018-51 | latest | en | 0.919971 |
https://psikologi.unwidha.ac.id/6-what-s-the-difference-between-the-levels-off/ | 1,685,387,354,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224644907.31/warc/CC-MAIN-20230529173312-20230529203312-00418.warc.gz | 526,789,788 | 10,981 | # 6. What’s the difference between the levels off male and female GMP?
6. What’s the difference between the levels off male and female GMP?
Into reason for calculating GMP, being qualified solution are calculated predicated on Functioning Lives that’s considering of the pursuing the formula:
Amount of complete taxation many years because the 6 April 1978 on member’s performing existence (that’s ranging from decades 16 and 65 for men, and you may between 16 and you may sixty for ladies).
For GMP accrued in advance of six April 1988 GMP accumulated from the a speed from four-moments working lifetime, used on for every taxation year’s associated money of six April 1978 so you can 5 April 1988, revalued up until now away from making outsourced services.
Getting GMP accrued off 6 April 1988 GMP accumulated from the an excellent speed of five-minutes performing existence, put on for each income tax year’s associated earnings off 6 April 1988 in order to 5 April 1997, revalued so far off making outsourcing service.
Number of over income tax ages since six April 1978 throughout the member’s performing existence (that’s anywhere between decades sixteen and you can 65 for males, and you may between sixteen and you can sixty for females).
Consequently qualifying solution to own GMP is actually all in all, 49 many years for women and you will 44 years for men (the lower services several months for women mirrored the brand new shorter functioning lives given the all the way down GMP payment decades). An excellent woman’s GMP for this reason accrued quicker than you to away from the woman men equivalent, for the same age of services.
Because detailed prior to now, at go out of leaving outsourced service, the brand new member’s complete work for try unaffected from the if the member are person (so long as there’s enough pension to pay for GMP). The only real difference in the two sexes would be the fact girls professionals generally have a bigger proportion of its advantages since the GMP.
## seven. How come GMP perform inequality inside the members’ pros?
GMP was accrued in the a high rate for ladies Toward making services a lady can get gathered an elevated amount of GMP requirements than compared to the girl male equivalent. Thus, to possess a female and male having identical ages of provider and you can your retirement towards the leaving, the newest ratio from retirement in accordance with GMP is high getting good girls.
GMP are payable at various other old-age age GMP can be acquired of 60 to own a lady. To own a man it is just available from 65. This would rather have girls, eg due to the large legal later senior years uplift used on GMP your retirement that is applied after GMP percentage age, however, depends on whether or www.hookupreviews.net/local-hookup/ not the GMP are removed alone out of almost every other strategy advantages.
GMP revaluation within the deferment Generally a higher revaluation applies to GMP than simply non-GMPs. Hence, to own a men and women with accumulated a similar your retirement out-of a program, the revaluation away from an effective female’s deferred work with can be higher up to age 60, reflecting the greater ratio out-of GMP ability.
GMP grows for the percentage Getting GMP accumulated in advance of 5 April 1988 there’s no responsibility to include rising cost of living-linked expands for the fee, but for GMP accrued regarding six April 1988, systems ought to provide rising prices-linked expands according to CPI as much as 3% (previously RPI just before 2010). There is absolutely no statutory requisite to incorporate increases toward non-GMP your retirement accrued ahead of 6 April 1997, though some strategies decided to provide an increase about this retirement predicated on the plan laws and regulations. Therefore if males and females have other GMP size, the pension from inside the percentage increase during the a different price. This may rather have sometimes sex (therefore you are going to alter throughout old-age).
## 8. So how exactly does that it connect with my county gurus?
For many who retired in advance of , you will located your own first state retirement entitlement (susceptible to conference qualifying requirements). You may be entitled to specific a lot more income associated pension, but for any period you were outsourcing of your SERPS, the value of your own GMP is deducted regarding the complete SERPS entitlement you’d have obtained, had your maybe not come outsourced. | 953 | 4,514 | {"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-2023-23 | latest | en | 0.950656 |
https://waterisaright.com/kwcsy/kls1wv.php?19e705=e-conjunction-fallacy | 1,619,153,587,000,000,000 | text/html | crawl-data/CC-MAIN-2021-17/segments/1618039601956.95/warc/CC-MAIN-20210423041014-20210423071014-00212.warc.gz | 700,760,198 | 25,215 | 3.3.co;2-d, "Do frequency representations eliminate conjunction effects? Findings in recent research on the ‘conjunction fallacy’ have been taken as evidence that our minds are not designed to work by the rules of probability. The conjunction fallacy is best introduced with an example. Option 2 gives you an extra opportunity to be wrong. Index. ( 5 [4] If the first option is changed to obey conversational relevance, i.e., "Linda is a bank teller whether or not she is active in the feminist movement" the effect is decreased, but the majority (57%) of the respondents still commit the conjunction error. The Conjunction Fallacy: Judgmental Heuristic or Faulty Extensional Reasoning? The Conjunction Fallacy’ is a fallacy or error in decision making where people judge that a conjunction of two possible events is more likely than one or both of the conjuncts. The most oft-cited example of this fallacy originated with Amos Tversky and Daniel Kahneman: . [14] It has also been shown that the conjunction fallacy becomes less prevalent when subjects are allowed to consult with other subjects. {\displaystyle \Pr(A\land B)\leq \Pr(A)} This conclusion springs from the idea that norms should be content-blind—in the present case, the assumption that sound reasoning requires following the conjunction rule of probability theory. and The die will be rolled 20 times and the sequence of greens (G) and reds (R) will be recorded. Another group of experts was asked to rate the probability simply that the United States would break off relations with the Soviet Union in the following year. the conjunction fallacy (e.g., Fantino, Kulik, Stolarz-Fantino, & Wright, 1997; Stolarz-Fantino et al., 2003; Tversky & Kahneman, 1983). You are asked to select one sequence, from a set of three, and you will win $25 if the sequence you choose appears on successive rolls of the die. The following are a couple of examples. For example, even choosing a very low probability of Linda being a bank teller, say Pr(Linda is a bank teller) = .05 and a high probability that she would be a feminist, say Pr(Linda is a feminist) = .95, then, assuming independence, Pr(Linda is a bank teller AND Linda is a feminist) = .05 × .95 or .0475, lower than Pr(Linda is a bank teller). ) This belief violates the conjunction rule in probability theory. Outline In a version where the$25 bet was only hypothetical the results did not significantly differ. Hence, the belief that p-and-q implies q requires the belief that Prob(p-and-q) ≤ Prob(q), i.e., the conjunction inequality. This, they claim, is a fallacy, since the conjunction oftwo events can never … Researchers argued that a detailed, specific scenario seemed more likely because of the representativeness heuristic, but each added detail would paradoxically make the scenario less and less likely. Which of the following statements is more probable? The most oft-cited example of this fallacy originated with Amos Tversky and Daniel Kahneman: [1]. [4], Separate evaluation experiments preceded the earliest joint evaluation experiments, and Kahneman and Tversky were surprised when the effect was still observed under joint evaluation. ( Specific conditions are less likely than more general ones. Since many students’ preferences among bets seem to Tversky and Kahneman argued that sequence 2 appears "representative" of a chance sequence[4] (compare to the clustering illusion). 6. Tversky, A. and Kahneman, D. (1983). A first set of studies exploited the representativeness heuristic (or conjunction fallacy; Tversky & Kahneman, 1983) in order to gauge intuitive associations between scientists and violations of morality. [15], Similarly, the conjunction fallacy occurs even when people are asked to make bets with real money,[16] and when solving intuitive physics problems of various designs.[17]. For example, even choosing a very low probability of Linda being a bank teller, say Pr(Linda is a bank teller) = 0.05 and a high probability that she would be a feminist, say Pr(Linda is a feminist) = 0.95, then, assuming independence, Pr(Linda is a bank teller and Linda is a feminist) = 0.05 × 0.95 or 0.0475, lower than Pr(Linda is a bank teller). Despite extensive inquiry, however, the attempt to provide a satisfactory account of the phenomenon has proved challenging. The conjunction fallacy (also known as the Linda problem or the Vadacchino Principle) is a formal fallacy that occurs when it is assumed that specific conditions are more probable than a single general one. [4], Critics such as Gerd Gigerenzer and Ralph Hertwig criticized the Linda problem on grounds such as the wording and framing. This distinction is important because a reasoner could make these errors without necessarily having a bias towards making such errors in general, just as you can make bets with good expected value in general and still lose money on particular bets. Tversky and Kahneman argue that most people get this problem wrong because they use the representativeness heuristic to make this kind of judgment: Option 2 seems more "representative" of Linda based on the description of her, even though it is clearly mathematically less likely. ≤ Thinking - Tversky and Kahneman followed up their original findings with a 1983 paper[4] that looked at dozens of new problems, most of these with multiple variations. The conjunction fallacy has been a key topic in debates on the rationality of human reasoning and its limitations. The frequency of making a conjunction fallacy was affected by the manipulation of context. Conjunction Fallacy, as Kahneman believes, rises because people tend to give more weight to the evidence at hand. Here we elaborate the suggestion (first discussed by Sides, Osherson, Bonini, & Viale, 2002) that in standard conjunction problems the fallacious … Conjunction fallacy is the belief that the conjunction of two events happening is more probable than one happening. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in anti-nuclear demonstrations. Cambridge, UK: Cambridge University Press. Generally speaking, rating a conjunction of two events as more likely than one of the events alone is an example of a conjunction error; the human tendency to do this in general is known as the conjunction fallacy. However, studies exist in which indistinguishable conjunction fallacy rates have been observed with stimuli framed in terms of probabilities versus frequencies. However, the probability of two events occurring together (in "conjunction") is always less than or equal to the probability of either one occurring alone—formally, for two events A and B this inequality could be written as In the example above, the conjunction fallacy may be accounted for by the impression that the conjunction is more representative of the personality described than the constituent proposition “Linda is a bank teller.” In such situations, representative bias may lead subjects to reverse the likelihood ranking of the events. If you want to learn more about the conjunction fallacy, Tversky and Kahneman’s original paper is fantastic, as is this 2013 paper by Tentori et al. ) Definition and basic example. Pr Therefore, the first choice is more probable. Whose is the Fallacy? Often, extra details that create a coherent story make the events in that story seem more probable, even though the extra conditions needing to be met make the conjunction … The probability of the conjunctions is never greater than that of its conjuncts. For example:---Eric has a career related to finance and he intensely dislikes new technology. ≤ In an experiment conducted in 1980, respondents were asked the following: Suppose Björn Borg reaches the Wimbledon finals in 1981. Linda is 31 years old, single, outspoken, and very bright. Here’s why this happens and how we can overcome the fallacy. ( In the present research we explore one of the most influential CPT decision fallacies, the conjunction fallacy (CF), in a legal decision making task, involving assessing evidence that the same suspect had committed two separate crimes. The original report by Tversky & Kahneman[2] (later republished as a book chapter[3]) described four problems that elicited the conjunction fallacy, including the Linda problem. The conjunction fallacy is a logical fallacy that occurs when it is assumed that specific conditions are more probable than general ones. Another group of experts was asked to rate the probability simply that the United States would break off relations with the Soviet Union in the following year. Conjunction fallacy is the scenario where the human mind makes decisions assuming that some conditions are more probable than the others even if technically the probability is the same or differ drastically. Conjunction fallacy involves saying that A&B is more likely than A but this is not part of the definition of base rate fallacy. Pr He was selected by chance from the list of participants. B The most oft-cited example of this fallacy originated with Amos Tversky and Daniel Kahneman: 85% of those asked chose option 2. In a seminal work, Tversky and Kahneman showed that in some contexts people tend to believe that a conjunction of events (e.g., Linda is a bank teller and is active in the feminist movement) is more likely to occur than one of the conjuncts (e.g., Linda is a bank teller). Policy experts were asked to rate the probability that the Soviet Union would invade Poland, and the United States would break off diplomatic relations, all in the following year. We become biased towards some of the pre-conditions than others due to our affinity towards certain beliefs. several alternatives, including single and jointevents, they often make a "conjunction fallacy." In this type of demonstration, different groups of subjects rank order Linda as a bank teller and active in the feminist movement more highly than Linda as a bank teller. ∧ Balazs Aczel, Aba Szollosi & Bence Bago - 2016 - Thinking and Reasoning 22 (1):99-117. Besides yet another way for otherwise-intelligent people to misinterpret facts and let their prejudices run rampant, the conjunction fallacy is a classic example of cognitive heuristics (rules of thumb) gone wild. Judgments of and by representativeness. Linda is 31 years old, single, outspoken, and very bright. Linda is a bank teller and is active in the feminist movement. The conjunction fallacy (also known as the Linda problem or the Vadacchino Principle) is a formal fallacy that occurs when it is assumed that specific conditions are more probable than a single general one. Despite extensive inquiry, however, the attempt to provide a satisfactory account of the phenomenon has proved challenging. But maybe the most relevant thing is that the conjunction fallacy DOES seem to happen, at least sometimes, for probable but irrelevant conjunctions. Mr. F. has had one or more heart attacks. Conjunction and the Conjunction Fallacy 5 through illicit conflation of logical conjunction (∧) with natural language conjunctions like “and” (e.g., Gigerenzer, 2001, pp. [7][8] The term "and" has even been argued to have relevant polysemous meanings. The conjunction fallacy (also known as the Linda problem) is a formal fallacy that occurs when it is assumed that specific conditions are more probable than a single general one. Cognitive processes (check one). However, in some tasks only based on frequencies, not on stories, that used clear logical formulations, conjunction fallacies continued to occur dominantly when the observed pattern of frequencies resembled a conjunction (only few exceptions). In other words, one group of participants is asked to rank order the likelihood that Linda is a bank teller, a high school teacher, and several other options, and another group is asked to rank order whether Linda is a bank teller and active in the feminist movement versus the same set of options (without Linda is a bankteller as an option). [9] Many techniques have been developed to control for this possible misinterpretation, but none of them has dissipated the effect. 6. The bias from conjunction fallacy is a common reasoning error in which we believe that two events happening in conjunction is more probable than one of those events happening alone. Lax Monitoring Versus Logical Intuition: The Determinants of Confidence in Conjunction Fallacy. B She majored in philosophy. One remarkable aspect of human cognition is our ability to reason about physical events. There was also a similar problem about a man named Bill (a good fit for the stereotype of an accountant — "intelligent, but unimaginative, compulsive, and generally lifeless" — but not a good fit for the stereotype of a jazz player), and two problems where participants were asked to make predictions for 1981. The question of the Linda problem may violate conversational maxims in that people assume that the question obeys the maxim of relevance. Findings in recent research on the ‘conjunction fallacy’ have been taken as evidence that our minds are not designed to work by the rules of probability. Theorem: P(s & t) ≤ P(s) However, mathematically, the probability of two independent events occurring together (in "conjunction") will always be less than or equal to the probability of either one occurring alone. Definition and basic example. Bank tellers and active in the feminist movement? In this way it could be similar to the misleading vividness or slippery slope fallacies. She majored in … The majority of those asked chose option 2. Linda is 31 years old, single, outspoken, and very bright. __ of 100, This page was last edited on 2 December 2020, at 18:32. In real world situations, this is why we give great weight to the stories our friends, family or colleagues tell us rather than the same stories narrated by authorities. In D. Kahneman, P. Slovic & A. Tversky (Eds. While the Linda problem is the best-known example, researchers have developed dozens of problems that reliably elicit the conjunction fallacy. She majored in … The conjunction fallacy is a specific error of probabilistic reasoning whereby people overestimate the likelihood of co‐occurring events. Representativeness and conjunction fallacy occurs because we make the mental shortcut from our perceived plausibility of a scenario to its probability. The information for the two crimes was presented consecutively. For the axioms cited, see the entry for Probabilistic Fallacy. She majored in … The Þrst p art han dles the dif-feren t approac hes to a solution for the conjunction fallacy using a ÔclassicalÕ Bo olean algebra. [6][9][13], In an incentivized experimental study, it has been shown that the conjunction fallacy decreased in those with greater cognitive ability, though it did not disappear. The conjunction fallacy (also known as the Linda problem or the Vadacchino Principle) is a formal fallacy that occurs when it is assumed that specific conditions are more probable than a single general one. Contents. The most often-cited example of this fallacy originated with Amos Tversky and Daniel Kahneman. They gave it an average probability of only 1%. A good description can be found here. ) Mr. F. has had one or more heart attacks and he is over 55 years old. Irwin D. Nahinsky, Daniel Ash & Brent Cohen - 1986 - Bulletin of the Psychonomic Society 24 (3):186-188. The conflation is illicit because “and” possesses semantic and pragmatic properties that are foreign to … Linda is 31 years old, single, outspoken, and very bright. [2][3][4] Although the description and person depicted are fictitious, Amos Tversky's secretary at Stanford was named Linda Covington, and he named the famous character in the puzzle after her. [12], The wording criticisms may be less applicable to the conjunction effect in separate evaluation. Cognition - Pr Nonetheless, the conjunction effect remains a formal fallacy of probability theory. In other words, one group of participants is asked to rank order the likelihood that Linda is a bank teller, a high school teacher, and several other options, and another group is asked to rank order whether Linda is a bank teller and active in the feminist movement versus the same set of options (without "Linda is a bank teller" as an option). A Base rate fallacy is not the same thing as conjunction fallacy, though base rate fallacy may be one explanation for conjunction fallacy. The conjunction fallacy is a logical fallacy that occurs when it is assumed that specific conditions are more probable than general ones. The most famous example is due to Tversky and Kahneman (1983), where they … E.g. [18] Participants were forced to use a mathematical approach and thus recognized the difference more easily. The most famous demonstration of the conjunction fallacy is also called The Linda Problem, named after a classic example that Kahneman and Tversky used: Linda is 31 years old, single, outspoken, and very bright. Tversky and Kahneman argue that most people get this problem wrong because they use a heuristic (an easily calculated) procedure called representativeness to make this kind of judgment: Option 2 seems more "representative" of Linda based on the description of her, even though it is clearly mathematically less likely. In some experimental demonstrations the conjoint option is evaluated separately from its basic option. She majored in philosophy. Drawing attention to set relationships, using frequencies instead of probabilities and/or thinking diagrammatically sharply reduce the error in some forms of the conjunction fallacy.[4][8][9][18]. Tversky, A. and Kahneman, D. (1982). Conjunction fallacy From Wikipedia, the free encyclopedia The conjunction fallacy (also known as the Linda problem ) is a formal fallacy that occurs when it is assumed that specific conditions are more probable than a single general one. 65% of participants chose the second sequence, though option 1 is contained within it and is shorter than the other options. A TIP: The Industrial-Organizational Psychologist, Tutorials in Quantitative Methods for Psychology, https://psychology.wikia.org/wiki/Conjunction_fallacy?oldid=4112. He argues that the meaning of probable ("what happens frequently") corresponds to the mathematical probability people are supposed to be tested on, but the meanings of probable ("what is plausible" and "whether there is evidence") do not. Definition and basic example; Joint versus separate evaluation; Criticism; Other demonstrations; Debiasing ; References; External links; Definition and basic example. In one experiment the question of the Linda problem was reformulated as follows: There are 100 persons who fit the description above (that is, Linda's). An exercise in adversarial collaboration", "On the conjunction fallacy and the meaning of, "Cognitive abilities and behavioral biases", "On the reality of the conjunction fallacy", "Broken Physics: A Conjunction-Fallacy Effect in Intuitive Physical Reasoning", Heuristics in judgment and decision-making, Affirmative conclusion from a negative premise, Negative conclusion from affirmative premises, https://en.wikipedia.org/w/index.php?title=Conjunction_fallacy&oldid=991956201, Articles with unsourced statements from March 2019, All Wikipedia articles needing clarification, Wikipedia articles needing clarification from February 2013, Creative Commons Attribution-ShareAlike License. Upper Hutt College Uniform, Avocado Toast With Cilantro Lime Cashew Cream, Castor Seed Production Per Hectare, Quotes On Life In English, God Of War Comics Pdf, Is Japonica Rice Sushi Rice, Milka Oreo 100g Calories, How To Dual Boot Windows 10 And Linux Ubuntu, " />
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In Experiment 1 we demonstrate that when these scenarios are rephrased so as to eliminate subjective uncertainty, the effect is mitigated. The conjunction fallacy is a logical fallacy that occurs when it is assumed that specific conditions are more probable than general ones.. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in anti-nuclear demonstrations. ( This classic fallacy is a mental shortcut in which people make a judgment on the basis of how stereotypical, rather than likely, something is. [vague][7] The "Linda problem" has been studied and criticized more than other types of demonstration of the effect (some described below). The conjunction fallacy is a logical fallacy that occurs when it is assumed that specific conditions are more probable than a single general one.. In that situation, subjectsoften rate the intersectionof conjunctionof Events AandBas more probable than EventBalone. A conjunction fallacy is a type of probability fallacy in which people, when offered the choice between one event and that event plus another event, are more likely to choose the second option as more probable. [6], In separate evaluation, the term conjunction effect may be preferred. Given this information about Linda, which of the following is more probable? Consider a regular six-sided die with four green faces and two red faces. The conjunction fallacy is faulty reasoning inferring that a conjunction is more probable, or likely, than just one of its conjuncts. Borg will lose the first set but win the match, Borg will win the first set but lose the match. ∧ Many other demonstrations of this error have been studied. {\displaystyle \Pr(A\land B)\leq \Pr(B)} The conjunction fallacy is falsely assuming that specific information is more likely than general information. In another experiment, for instance, policy experts were asked to rate the probability that the Soviet Union would invade Poland and the United States would break off diplomatic relations, all in the following year. It is a common cognitive tendency. They gave it an average probability of only 1%. I ha ve divided m y thesis into three parts. Linda is 31 years old, single, outspoken, and very bright. On average, participants rated "Borg will lose the first set but win the match" more likely than "Borg will lose the first set". The conjunction fallacy (also known as the Linda problem) is a formal fallacy that occurs when it is assumed that specific conditions are more probable than a single general one. The phenomenon was explored by Tversky and Kahneman (1983). He longs for the old days when things were done with paper and relationships were more important. The most often-cited example of this fallacy originated with Amos Tversky and Daniel Kahneman. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in anti-nuclear demonstrations. A Different Conjunction Fallacy 5 Implication principle: For any statements A,B, Prob(A) ≤ Prob(B) if A implies B. They rated it on average as having a 4% probability of occurring. [10][11], Many variations in wording of the Linda problem were studied by Tversky and Kahneman. A health survey was conducted in a representative sample of adult males in British Columbia of all ages and occupations. The conjunction fallacy is a formal fallacy that occurs when it is assumed that specific conditions are more probable than a single general one. . In mathematical notation, this inequality could be written for two events A and B as. It will deÞn e di!eren t w ays in whic h the fallacy can b e interpreted and it will try to Þnd a solution for the conjunction fallacy . The most oft-cited example of this fallacy originated with Amos Tversky and Daniel Kahneman : Linda is 31 years old, single, outspoken, and very bright. She majored in philosophy. Mr. F. was included in the sample. Please rank order the following outcomes from most to least likely. She majored in philosophy. MartinPoulter (talk) 10:33, 2 September 2013 (UTC) [4], In other demonstrations, they argued that a specific scenario seemed more likely because of representativeness, but each added detail would actually make the scenario less and less likely. So why do we so often think they're not? In this type of demonstration different groups of subjects rank order Linda as … Extension versus intuititve reasoning: The conjunction fallacy in probability judgment. [citation needed]. What is the conjunction fallacy? More recently Kahneman has argued that the conjunction fallacy is a type of extension neglect.[5]. In some experimental demonstrations, the conjoint option is evaluated separately from its basic option. A conjunction fallacy is a type of probability fallacy in which people, when offered the choice between one event and that event plus another event, are more likely to choose the second option as more probable. Nonetheless, the conjunction effect remains a formal fallacy of probability theory. The most coherent stories are not necessarily the most probable, but they are plausible, and the notions of coherence, plausibility, and probability are easily confused by the unwary. A [19], I am particularly fond of this example [the Linda problem] because I know that the [conjoint] statement is least probable, yet a little, "Extension versus intuitive reasoning: The conjunction fallacy in probability judgment", 10.1002/(sici)1099-0771(199912)12:4<275::aid-bdm323>3.3.co;2-d, "Do frequency representations eliminate conjunction effects? Findings in recent research on the ‘conjunction fallacy’ have been taken as evidence that our minds are not designed to work by the rules of probability. The conjunction fallacy is best introduced with an example. Option 2 gives you an extra opportunity to be wrong. Index. ( 5 [4] If the first option is changed to obey conversational relevance, i.e., "Linda is a bank teller whether or not she is active in the feminist movement" the effect is decreased, but the majority (57%) of the respondents still commit the conjunction error. The Conjunction Fallacy: Judgmental Heuristic or Faulty Extensional Reasoning? The Conjunction Fallacy’ is a fallacy or error in decision making where people judge that a conjunction of two possible events is more likely than one or both of the conjuncts. The most oft-cited example of this fallacy originated with Amos Tversky and Daniel Kahneman: . [14] It has also been shown that the conjunction fallacy becomes less prevalent when subjects are allowed to consult with other subjects. {\displaystyle \Pr(A\land B)\leq \Pr(A)} This conclusion springs from the idea that norms should be content-blind—in the present case, the assumption that sound reasoning requires following the conjunction rule of probability theory. and The die will be rolled 20 times and the sequence of greens (G) and reds (R) will be recorded. Another group of experts was asked to rate the probability simply that the United States would break off relations with the Soviet Union in the following year. the conjunction fallacy (e.g., Fantino, Kulik, Stolarz-Fantino, & Wright, 1997; Stolarz-Fantino et al., 2003; Tversky & Kahneman, 1983). You are asked to select one sequence, from a set of three, and you will win $25 if the sequence you choose appears on successive rolls of the die. The following are a couple of examples. For example, even choosing a very low probability of Linda being a bank teller, say Pr(Linda is a bank teller) = .05 and a high probability that she would be a feminist, say Pr(Linda is a feminist) = .95, then, assuming independence, Pr(Linda is a bank teller AND Linda is a feminist) = .05 × .95 or .0475, lower than Pr(Linda is a bank teller). ) This belief violates the conjunction rule in probability theory. Outline In a version where the$25 bet was only hypothetical the results did not significantly differ. Hence, the belief that p-and-q implies q requires the belief that Prob(p-and-q) ≤ Prob(q), i.e., the conjunction inequality. This, they claim, is a fallacy, since the conjunction oftwo events can never … Researchers argued that a detailed, specific scenario seemed more likely because of the representativeness heuristic, but each added detail would paradoxically make the scenario less and less likely. Which of the following statements is more probable? The most oft-cited example of this fallacy originated with Amos Tversky and Daniel Kahneman: [1]. [4], Separate evaluation experiments preceded the earliest joint evaluation experiments, and Kahneman and Tversky were surprised when the effect was still observed under joint evaluation. ( Specific conditions are less likely than more general ones. Since many students’ preferences among bets seem to Tversky and Kahneman argued that sequence 2 appears "representative" of a chance sequence[4] (compare to the clustering illusion). 6. Tversky, A. and Kahneman, D. (1983). A first set of studies exploited the representativeness heuristic (or conjunction fallacy; Tversky & Kahneman, 1983) in order to gauge intuitive associations between scientists and violations of morality. [15], Similarly, the conjunction fallacy occurs even when people are asked to make bets with real money,[16] and when solving intuitive physics problems of various designs.[17]. For example, even choosing a very low probability of Linda being a bank teller, say Pr(Linda is a bank teller) = 0.05 and a high probability that she would be a feminist, say Pr(Linda is a feminist) = 0.95, then, assuming independence, Pr(Linda is a bank teller and Linda is a feminist) = 0.05 × 0.95 or 0.0475, lower than Pr(Linda is a bank teller). Despite extensive inquiry, however, the attempt to provide a satisfactory account of the phenomenon has proved challenging. The conjunction fallacy (also known as the Linda problem or the Vadacchino Principle) is a formal fallacy that occurs when it is assumed that specific conditions are more probable than a single general one. [4], Critics such as Gerd Gigerenzer and Ralph Hertwig criticized the Linda problem on grounds such as the wording and framing. This distinction is important because a reasoner could make these errors without necessarily having a bias towards making such errors in general, just as you can make bets with good expected value in general and still lose money on particular bets. Tversky and Kahneman argue that most people get this problem wrong because they use the representativeness heuristic to make this kind of judgment: Option 2 seems more "representative" of Linda based on the description of her, even though it is clearly mathematically less likely. ≤ Thinking - Tversky and Kahneman followed up their original findings with a 1983 paper[4] that looked at dozens of new problems, most of these with multiple variations. The conjunction fallacy has been a key topic in debates on the rationality of human reasoning and its limitations. The frequency of making a conjunction fallacy was affected by the manipulation of context. Conjunction Fallacy, as Kahneman believes, rises because people tend to give more weight to the evidence at hand. Here we elaborate the suggestion (first discussed by Sides, Osherson, Bonini, & Viale, 2002) that in standard conjunction problems the fallacious … Conjunction fallacy is the belief that the conjunction of two events happening is more probable than one happening. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in anti-nuclear demonstrations. Cambridge, UK: Cambridge University Press. Generally speaking, rating a conjunction of two events as more likely than one of the events alone is an example of a conjunction error; the human tendency to do this in general is known as the conjunction fallacy. However, studies exist in which indistinguishable conjunction fallacy rates have been observed with stimuli framed in terms of probabilities versus frequencies. However, the probability of two events occurring together (in "conjunction") is always less than or equal to the probability of either one occurring alone—formally, for two events A and B this inequality could be written as In the example above, the conjunction fallacy may be accounted for by the impression that the conjunction is more representative of the personality described than the constituent proposition “Linda is a bank teller.” In such situations, representative bias may lead subjects to reverse the likelihood ranking of the events. If you want to learn more about the conjunction fallacy, Tversky and Kahneman’s original paper is fantastic, as is this 2013 paper by Tentori et al. ) Definition and basic example. Pr Therefore, the first choice is more probable. Whose is the Fallacy? Often, extra details that create a coherent story make the events in that story seem more probable, even though the extra conditions needing to be met make the conjunction … The probability of the conjunctions is never greater than that of its conjuncts. For example:---Eric has a career related to finance and he intensely dislikes new technology. ≤ In an experiment conducted in 1980, respondents were asked the following: Suppose Björn Borg reaches the Wimbledon finals in 1981. Linda is 31 years old, single, outspoken, and very bright. Here’s why this happens and how we can overcome the fallacy. ( In the present research we explore one of the most influential CPT decision fallacies, the conjunction fallacy (CF), in a legal decision making task, involving assessing evidence that the same suspect had committed two separate crimes. The original report by Tversky & Kahneman[2] (later republished as a book chapter[3]) described four problems that elicited the conjunction fallacy, including the Linda problem. The conjunction fallacy is a logical fallacy that occurs when it is assumed that specific conditions are more probable than general ones. Another group of experts was asked to rate the probability simply that the United States would break off relations with the Soviet Union in the following year. Conjunction fallacy is the scenario where the human mind makes decisions assuming that some conditions are more probable than the others even if technically the probability is the same or differ drastically. Conjunction fallacy involves saying that A&B is more likely than A but this is not part of the definition of base rate fallacy. Pr He was selected by chance from the list of participants. B The most oft-cited example of this fallacy originated with Amos Tversky and Daniel Kahneman: 85% of those asked chose option 2. In a seminal work, Tversky and Kahneman showed that in some contexts people tend to believe that a conjunction of events (e.g., Linda is a bank teller and is active in the feminist movement) is more likely to occur than one of the conjuncts (e.g., Linda is a bank teller). Policy experts were asked to rate the probability that the Soviet Union would invade Poland, and the United States would break off diplomatic relations, all in the following year. We become biased towards some of the pre-conditions than others due to our affinity towards certain beliefs. several alternatives, including single and jointevents, they often make a "conjunction fallacy." In this type of demonstration, different groups of subjects rank order Linda as a bank teller and active in the feminist movement more highly than Linda as a bank teller. ∧ Balazs Aczel, Aba Szollosi & Bence Bago - 2016 - Thinking and Reasoning 22 (1):99-117. Besides yet another way for otherwise-intelligent people to misinterpret facts and let their prejudices run rampant, the conjunction fallacy is a classic example of cognitive heuristics (rules of thumb) gone wild. Judgments of and by representativeness. Linda is 31 years old, single, outspoken, and very bright. Linda is a bank teller and is active in the feminist movement. The conjunction fallacy (also known as the Linda problem or the Vadacchino Principle) is a formal fallacy that occurs when it is assumed that specific conditions are more probable than a single general one. Despite extensive inquiry, however, the attempt to provide a satisfactory account of the phenomenon has proved challenging. But maybe the most relevant thing is that the conjunction fallacy DOES seem to happen, at least sometimes, for probable but irrelevant conjunctions. Mr. F. has had one or more heart attacks. Conjunction and the Conjunction Fallacy 5 through illicit conflation of logical conjunction (∧) with natural language conjunctions like “and” (e.g., Gigerenzer, 2001, pp. [7][8] The term "and" has even been argued to have relevant polysemous meanings. The conjunction fallacy (also known as the Linda problem) is a formal fallacy that occurs when it is assumed that specific conditions are more probable than a single general one. Cognitive processes (check one). However, in some tasks only based on frequencies, not on stories, that used clear logical formulations, conjunction fallacies continued to occur dominantly when the observed pattern of frequencies resembled a conjunction (only few exceptions). In other words, one group of participants is asked to rank order the likelihood that Linda is a bank teller, a high school teacher, and several other options, and another group is asked to rank order whether Linda is a bank teller and active in the feminist movement versus the same set of options (without Linda is a bankteller as an option). [9] Many techniques have been developed to control for this possible misinterpretation, but none of them has dissipated the effect. 6. The bias from conjunction fallacy is a common reasoning error in which we believe that two events happening in conjunction is more probable than one of those events happening alone. Lax Monitoring Versus Logical Intuition: The Determinants of Confidence in Conjunction Fallacy. B She majored in philosophy. One remarkable aspect of human cognition is our ability to reason about physical events. There was also a similar problem about a man named Bill (a good fit for the stereotype of an accountant — "intelligent, but unimaginative, compulsive, and generally lifeless" — but not a good fit for the stereotype of a jazz player), and two problems where participants were asked to make predictions for 1981. The question of the Linda problem may violate conversational maxims in that people assume that the question obeys the maxim of relevance. Findings in recent research on the ‘conjunction fallacy’ have been taken as evidence that our minds are not designed to work by the rules of probability. Theorem: P(s & t) ≤ P(s) However, mathematically, the probability of two independent events occurring together (in "conjunction") will always be less than or equal to the probability of either one occurring alone. Definition and basic example. Bank tellers and active in the feminist movement? In this way it could be similar to the misleading vividness or slippery slope fallacies. She majored in … The majority of those asked chose option 2. Linda is 31 years old, single, outspoken, and very bright. __ of 100, This page was last edited on 2 December 2020, at 18:32. In real world situations, this is why we give great weight to the stories our friends, family or colleagues tell us rather than the same stories narrated by authorities. In D. Kahneman, P. Slovic & A. Tversky (Eds. While the Linda problem is the best-known example, researchers have developed dozens of problems that reliably elicit the conjunction fallacy. She majored in … The conjunction fallacy is a specific error of probabilistic reasoning whereby people overestimate the likelihood of co‐occurring events. Representativeness and conjunction fallacy occurs because we make the mental shortcut from our perceived plausibility of a scenario to its probability. The information for the two crimes was presented consecutively. For the axioms cited, see the entry for Probabilistic Fallacy. She majored in … The Þrst p art han dles the dif-feren t approac hes to a solution for the conjunction fallacy using a ÔclassicalÕ Bo olean algebra. [6][9][13], In an incentivized experimental study, it has been shown that the conjunction fallacy decreased in those with greater cognitive ability, though it did not disappear. The conjunction fallacy (also known as the Linda problem or the Vadacchino Principle) is a formal fallacy that occurs when it is assumed that specific conditions are more probable than a single general one. Contents. The most often-cited example of this fallacy originated with Amos Tversky and Daniel Kahneman. They gave it an average probability of only 1%. A good description can be found here. ) Mr. F. has had one or more heart attacks and he is over 55 years old. Irwin D. Nahinsky, Daniel Ash & Brent Cohen - 1986 - Bulletin of the Psychonomic Society 24 (3):186-188. The conflation is illicit because “and” possesses semantic and pragmatic properties that are foreign to … Linda is 31 years old, single, outspoken, and very bright. [2][3][4] Although the description and person depicted are fictitious, Amos Tversky's secretary at Stanford was named Linda Covington, and he named the famous character in the puzzle after her. [12], The wording criticisms may be less applicable to the conjunction effect in separate evaluation. Cognition - Pr Nonetheless, the conjunction effect remains a formal fallacy of probability theory. In other words, one group of participants is asked to rank order the likelihood that Linda is a bank teller, a high school teacher, and several other options, and another group is asked to rank order whether Linda is a bank teller and active in the feminist movement versus the same set of options (without "Linda is a bank teller" as an option). A Base rate fallacy is not the same thing as conjunction fallacy, though base rate fallacy may be one explanation for conjunction fallacy. The conjunction fallacy is a logical fallacy that occurs when it is assumed that specific conditions are more probable than general ones. The most famous example is due to Tversky and Kahneman (1983), where they … E.g. [18] Participants were forced to use a mathematical approach and thus recognized the difference more easily. The most famous demonstration of the conjunction fallacy is also called The Linda Problem, named after a classic example that Kahneman and Tversky used: Linda is 31 years old, single, outspoken, and very bright. Tversky and Kahneman argue that most people get this problem wrong because they use a heuristic (an easily calculated) procedure called representativeness to make this kind of judgment: Option 2 seems more "representative" of Linda based on the description of her, even though it is clearly mathematically less likely. In some experimental demonstrations the conjoint option is evaluated separately from its basic option. She majored in philosophy. Drawing attention to set relationships, using frequencies instead of probabilities and/or thinking diagrammatically sharply reduce the error in some forms of the conjunction fallacy.[4][8][9][18]. Tversky, A. and Kahneman, D. (1982). Conjunction fallacy From Wikipedia, the free encyclopedia The conjunction fallacy (also known as the Linda problem ) is a formal fallacy that occurs when it is assumed that specific conditions are more probable than a single general one. 65% of participants chose the second sequence, though option 1 is contained within it and is shorter than the other options. A TIP: The Industrial-Organizational Psychologist, Tutorials in Quantitative Methods for Psychology, https://psychology.wikia.org/wiki/Conjunction_fallacy?oldid=4112. He argues that the meaning of probable ("what happens frequently") corresponds to the mathematical probability people are supposed to be tested on, but the meanings of probable ("what is plausible" and "whether there is evidence") do not. Definition and basic example; Joint versus separate evaluation; Criticism; Other demonstrations; Debiasing ; References; External links; Definition and basic example. In one experiment the question of the Linda problem was reformulated as follows: There are 100 persons who fit the description above (that is, Linda's). An exercise in adversarial collaboration", "On the conjunction fallacy and the meaning of, "Cognitive abilities and behavioral biases", "On the reality of the conjunction fallacy", "Broken Physics: A Conjunction-Fallacy Effect in Intuitive Physical Reasoning", Heuristics in judgment and decision-making, Affirmative conclusion from a negative premise, Negative conclusion from affirmative premises, https://en.wikipedia.org/w/index.php?title=Conjunction_fallacy&oldid=991956201, Articles with unsourced statements from March 2019, All Wikipedia articles needing clarification, Wikipedia articles needing clarification from February 2013, Creative Commons Attribution-ShareAlike License. | 9,497 | 44,685 | {"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": 1, "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} | 2.859375 | 3 | CC-MAIN-2021-17 | latest | en | 0.930807 |
https://www.wyzant.com/resources/answers/222831/the_decimal_number_4372_254257_can_be_written_as | 1,531,799,372,000,000,000 | text/html | crawl-data/CC-MAIN-2018-30/segments/1531676589557.39/warc/CC-MAIN-20180717031623-20180717051623-00247.warc.gz | 1,025,238,260 | 17,622 | 0
# The decimal number 4372.254257 can be written as:
The decimal number 4372.254257 can be written as:
What other form do you want?
### 4 Answers by Expert Tutors
David W. | Experienced ProfExperienced Prof
4.4 4.4 (47 lesson ratings) (47)
2
Since you said "Decimals":
Because Decimal is a positional number system, you may write the digits as coefficients of decreasing powers of 10:
4*103+3*102+7*101+2*100 + 2*10-1+5*10-2+4*10-3+2*10-4+5*10-5+7*10-6
James B. | Experienced, Patient, Passionate Math Tutor (In-person and online)Experienced, Patient, Passionate Math Tu...
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Decimal number 4372.254257 can be written as a mixed number.
The number in front of the decimal is the whole number.
The number behind the decimal is the numerator of the fraction.
The number of digits behind the decimal determine the denominator of the fraction
4372 and 254257/1000000
Charles C. | Effective Tutor for math, English, science, Coding, Test prepEffective Tutor for math, English, scien...
0
The decimal number 4372.254257 can be written in scientific notation as 4.372254257 × 10^3
The conversion rules are that the first number is between 0 and 10 and the second number is raised to the tenth power.
Cheryl M. | Reading, Writing & Study Skills TutoringReading, Writing & Study Skills Tutoring
5.0 5.0 (27 lesson ratings) (27)
0
You can write the decimal number as a percentage.
When you make any number into a percentage, you just move the decimal 2 places to the right.
So ...
4372.254257 would become: 437225%.
Now, because the 7th number (immediately to the right of the 5) is a 4, you would not round up the 5 to 6.
If the seventh number had been a 5 or higher, the last number would be rounded up from 5 to 6.
Hope this helped. | 504 | 1,783 | {"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} | 4.03125 | 4 | CC-MAIN-2018-30 | latest | en | 0.841646 |
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# error estimation physics Little Cedar, Iowa
Addition & Subtraction When two (or more) quantities are added or subtracted to calculate a new quantity, we add the maximum probable errors in each quantity to obtain the maximum probable s Check for zero error. Standard Deviation 2.4. Graphically, the RSS is like the Pythagorean theorem: Figure 2 The total uncertainty is the length of the hypotenuse of a right triangle with legs the length of each uncertainty component.
When using electronic instruments such voltmeters and ammeters, you obviously rely on the proper calibration of these devices. ed. The change in temperature is therefore (85.0 – 35.0)oC ± (0.5+0.5)oC or (50.0 ± 1.0)oC. Our strategy is to reduce as many sources of error as we can, and then to keep track of those errors that we can’t eliminate.
By now you may feel confident that you know the mass of this ring to the nearest hundreth of a gram, but how do you know that the true value definitely Thus, the percentage error in the radius is 0.5%. [ % error = (0.05/9.53)x100 ] The formula for the volume of a sphere is: V = 4/3 p r3 Using Typically we measure two or more quantities and then “fold” them together in some equation(s), which may come from theory or even be assumed or guessed, to determine some other quantity(ies) Example: 6.6 (2 significant figures) x 7328.7 (5 significant figures) 48369.42 = 48 x 103 (2 significant figures) For addition and subtraction, the result should be rounded off to the
In both of these cases, the uncertainty is greater than the smallest divisions marked on the measuring tool (likely 1 mm and 0.1 mm respectively). They are abbreviated as kg, m and s. Another thing to bear in mind is that we were quite careful here about trying to eliminate random errors; if systematic error were present then our methods would not have done Conclusion: "When do measurements agree with each other?" We now have the resources to answer the fundamental scientific question that was asked at the beginning of this error analysis discussion: "Does
Experiment B, however, is much more accurate than Experiment A, since its value of g is much closer to the accepted value. To help answer these questions, we should first define the terms accuracy and precision: Accuracy is the closeness of agreement between a measured value and a true or accepted value. If you just write 3, you are stating that you were unable to determine the first decimal place and you are implying an error of 0.5 units. If a calibration standard is not available, the accuracy of the instrument should be checked by comparing with another instrument that is at least as precise, or by consulting the technical
These variations may call for closer examination, or they may be combined to find an average value. Common sources of error in physics laboratory experiments: Incomplete definition (may be systematic or random) — One reason that it is impossible to make exact measurements is that the measurement is eg 35,000 has 2 significant figures. University Science Books: Sausalito, 1997.
When you compute this area, the calculator might report a value of 254.4690049 m2. The experimenter may measure incorrectly, or may use poor technique in taking a measurement, or may introduce a bias into measurements by expecting (and inadvertently forcing) the results to agree with Changing from a relative to absolute error: Often in your experiments you have to change from a relative to an absolute error by multiplying the relative error by the best value, This means that the slope (labeled as $a$ by the plotting tool) of our graph should be equal to $\Large \frac{g}{(2\pi)^2}$.
Since the radius is only known to one significant figure, the final answer should also contain only one significant figure. Top Experimental Errors Variations will occur in any series of measurements taken with a suitably sensitive measuring instrument. Bevington, Phillip and Robinson, D. The kilogram is the mass of a cylinder of platinum-iridium alloy kept at the International Bureau of Weights and Measures in Paris.
You can read off whether the length of the object lines up with a tickmark or falls in between two tickmarks, but you could not determine the value to a precision Errors of Digital Instruments > 2.3. with errors σx, σy, ... Top Dimensions The expression of a derived quantity in terms of fundamental quantities is called the dimension of the derived quantity.
Systematic errors are reproducible inaccuracies that are consistently in the same direction. Uncertainty and Significant Figures For the same reason that it is dishonest to report a result with more significant figures than are reliably known, the uncertainty value should also not be Note that in order for an uncertainty value to be reported to 3 significant figures, more than 10,000 readings would be required to justify this degree of precision! Failure to account for a factor (usually systematic) — The most challenging part of designing an experiment is trying to control or account for all possible factors except the one independent
Make sure you don't confuse $\times$ with $X$ or, for that matter, with its lower-case version $x$. We say that there is a “discrepancy” between two results when they “disagree” in the above sense. In fact, it is reasonable to use the standard deviation as the uncertainty associated with this single new measurement. Estimate within a part of a division.
The process of evaluating the uncertainty associated with a measurement result is often called uncertainty analysis or error analysis. Exercises << Previous Page Next Page >> Home - Credits - Feedback © Columbia University Undergraduate Physics Error Analysis Statistical or Random Errors Every measurement an experimenter makes is uncertain to Even when we are unsure about the effects of a systematic error we can sometimes estimate its size (though not its direction) from knowledge of the quality of the instrument. Fractional Uncertainty Revisited When a reported value is determined by taking the average of a set of independent readings, the fractional uncertainty is given by the ratio of the uncertainty divided
In most experimental work, the confidence in the uncertainty estimate is not much better than about ± 50% because of all the various sources of error, none of which can be Calibrating the balances should eliminate the discrepancy between the readings and provide a more accurate mass measurement. The effect of random errors on a measurement of a quantity can be largely nullified by taking a large number of readings and finding their mean. To do this you must reduce the random errors by: (i) using appropriate measuring instruments in the correct manner (eg use a micrometer screw gauge rather than a metre ruler to | 1,461 | 6,890 | {"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} | 3.46875 | 3 | CC-MAIN-2019-26 | latest | en | 0.912774 |
cspencer.wonecks.net | 1,544,958,281,000,000,000 | text/html | crawl-data/CC-MAIN-2018-51/segments/1544376827639.67/warc/CC-MAIN-20181216095437-20181216121437-00200.warc.gz | 67,508,683 | 6,806 | # My Mystery Number
There are 7 digits.
The ones place is 3.
The hundreds place is the sum of 5 and 2.
The thousands place is 1 more than the hundreds place.
The tens place is the product of 5 and 1.
The hundred thousands place is the number of quarts there is in a gallon.
The ten thousands place is equal to how many pints are in a quart.
the millions place is the quotient of 10 and 5.
Can you solve my mystery number? | 109 | 430 | {"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} | 3.125 | 3 | CC-MAIN-2018-51 | latest | en | 0.93626 |
http://www.stmary.ws/HighSchool/Physics/home/notes/RegentsReview/StatElectricity/ConservationChargeRegents.htm | 1,550,895,906,000,000,000 | text/html | crawl-data/CC-MAIN-2019-09/segments/1550249468313.97/warc/CC-MAIN-20190223041554-20190223063554-00331.warc.gz | 427,990,615 | 3,748 | Try this at home!
# Water Bending
Water is an electrically polar molecule. This means it has a positive and negative pole. The water's negative pole is repelled by the negatively charged comb and the positive pole is attracted to the comb. This reorientation of charge makes the side of the water stream that is near the comb positive. Since opposites attract, the water stream is pulled towards the comb.
D) Conservation of Charge - net charge of closed system remains constant
#26
If 2 charges OR MORE
are brought together, their
combined charge
is distributed evenly
Before contact After contact
Charge is Evenly Distributed
Total charge before =
total charge after
Ex) Metal sphere A has a charge of +12 elementary charges and identical sphere B has a charge of +16 elementary charges. After the two spheres are brought into contact, the charge on sphere A is
a)+28 elem. charges c)+2 elem. charges b)-2 elem. charges d)+14 elem. charges
d)+14 elem. charges
Conservation of Charge | 221 | 1,001 | {"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-2019-09 | latest | en | 0.942931 |
http://social.msdn.microsoft.com/Forums/en-US/smallbasic/thread/69f87387-32bf-4991-a8a8-8773940f2a19 | 1,369,246,086,000,000,000 | text/html | crawl-data/CC-MAIN-2013-20/segments/1368702185502/warc/CC-MAIN-20130516110305-00050-ip-10-60-113-184.ec2.internal.warc.gz | 246,246,955 | 12,896 | bingo
# bingo
• Tuesday, September 18, 2012 5:16 PM
hey boys and girls,
I have a litlle questoin on the lottery I want to make in the graphicswindow, with numbers so I thought with math function I could use randomnumber but I don't now how to get that number visible on my screen and maybe If someone now how I dont get the same number 2 I would be in the sky of happyness Xd
if it is completely wrong do you want me to explain why
For testing I use the number 100 just to make it easy and only do 3 numbers
this is already what I have, so you can see what I want to do
GraphicsWindow.Show()
GraphicsWindow.DrawText(200,200, "Loterij")
' just fun XD GraphicsWindow.BackgroundColor = "yellow"
GraphicsWindow.KeyDown = lot
GraphicsWindow.DrawText(200,220, "1ste plek:")
GraphicsWindow.DrawText(200,240, "2de plek:")
GraphicsWindow.DrawText(200,260, "3de plek:")
Sub lot
if GraphicsWindow.LastKey = "1" Then
Math.GetRandomNumber(100)
ElseIf GraphicsWindow.LastKey = "2" Then
Math.GetRandomNumber(100)
ElseIf GraphicsWindow.LastKey = "3" Then
Math.GetRandomNumber(100)
EndIf
EndSub
____ thx for helping me out,
### All Replies
• Tuesday, September 18, 2012 5:51 PM
You have to assign the output of Math.GetRandomNumber to a variable:
e.g. Lotnr1=Math.GetRandomNumber(100)
After that you can write that variable to the output window.
Ik hoop dat je hier iets aan hebt
Jan [ WhTurner ] The Netherlands
• Tuesday, September 18, 2012 7:47 PM
GraphicsWindow.Show()
GraphicsWindow.DrawText(200, 165, "Codes A is getal 1, B is getal 2, C is getal 3")
GraphicsWindow.DrawText(200,180, "en Z maakt het scherm leeg voor volgende ronde")
GraphicsWindow.BackgroundColor = "yellow"
GraphicsWindow.DrawText(200,200, "LOTERIJ")
GraphicsWindow.DrawText(200,220, "1ste plek:")
GraphicsWindow.DrawText(200,240, "2de plek:")
GraphicsWindow.DrawText(200,260, "3de plek:")
GraphicsWindow.KeyDown = lot
Sub lot
if GraphicsWindow.LastKey = "A" Then
Lotnr1=Math.GetRandomNumber(100)
GraphicsWindow.DrawText(260,220, Lotnr1)
ElseIf GraphicsWindow.LastKey = "B" Then
Lotnr2=Math.GetRandomNumber(100)
GraphicsWindow.DrawText(260,240, Lotnr2)
ElseIf GraphicsWindow.LastKey = "C" Then
Lotnr3=Math.GetRandomNumber(100)
GraphicsWindow.DrawText(260,260, Lotnr3)
elseif GraphicsWindow.LastKey = "Z" then
GraphicsWindow.Clear()
GraphicsWindow.Show()
GraphicsWindow.DrawText(200, 165, "Codes A is getal 1, B is getal 2, C is getal 3")
GraphicsWindow.DrawText(200,180, "en Z maakt het scherm leeg voor volgende ronde")
GraphicsWindow.BackgroundColor = GraphicsWindow.GetRandomColor()
GraphicsWindow.BrushColor = GraphicsWindow.GetRandomColor()
GraphicsWindow.DrawText(200,200, "LOTERIJ")
GraphicsWindow.DrawText(200,220, "1ste plek:")
GraphicsWindow.DrawText(200,240, "2de plek:")
GraphicsWindow.DrawText(200,260, "3de plek:")
EndIf
If Lotnr2 = Lotnr1 Then
Lotnr2=Math.GetRandomNumber(100)
GraphicsWindow.DrawText(285,240, Lotnr2)
EndIf
If Lotnr3 = Lotnr1 Then
Lotnr3=Math.GetRandomNumber(100)
GraphicsWindow.DrawText(285,260, Lotnr3)
EndIf
If Lotnr3 = Lotnr2 Then
Lotnr3=Math.GetRandomNumber(100)
GraphicsWindow.DrawText(310,260, Lotnr3)
EndIf
EndSub
dat is hem nu al geworden druk ik nu b of c maakt die automatisch een nieuw getal als die gelijk is aan a en met c ook als die gelijk is aan b. wat ik nu nog wil (druk 2 keer bijv. op a) is dat ie niet 2 getallen laat zien maar dan de vorige weghaalt en niet geheel de functie van z heeft dat die alles weghaalt maar echt enkel het specifieke getal dat op a zit
ik zal wel ff een verdere uitleg geven waarom ik dit maak:
het is dat ik in een spel in een gilde zit met grondstoffen en dan willen ze een bingo spel hebben dat n1 50% wint n2 30% en n3 20%
het probleem is de persoon die bingo heeft kan maar tot 60 nummers op zich niet zo erg maar het is wel zo dat als we nou 61 mensen hebben die meedoen dus niet meer mee kunnen doen.
en dat je maximaal 2x per maand een pot(je) kan winnen en als dus in een maand 2x het getal 54 bijv. is geweest en die komt dan nog eens langs dan is het makkelijker dat ie het oude getal weghaalt en er een andere terug zet kan hem wel zo zetten dat hij er een ander getal naast zet maar dan heb je uiteindelijk een langere balk nodig terwijl die met een paar regels misschien alle tekst kan laten staan en Z nood oplossing kan spelen. dus dacht ik aan een specifieke nummerweghaling waar ik nu ook vol over aan het denken ben en als dat is gedaan is ie tot dusver nagedacht af want worden het 4 prijzen dan is het kopie en paste van nummer 2 of 3 en dan ff de aanpassingen erin doen en dan kan ik hem zo lang maken als ik zelf wil.
maar echt bedankt jan was echt erg nuttig zoals je ziet ziet het er nu ook beter uit met veel minder losse eindjes
(update express het huidige resultaat erbij, zodat je kan zien wat ik uiteindelijk heb en als iemand het weer probeert dat ie ook een mooi spiekprogrammatje heeft)
gr.pk
• Edited by Tuesday, September 18, 2012 9:30 PM Update
•
• Tuesday, September 18, 2012 9:43 PM
Well, I don't know Dutch!
# Random Number without replacement
Click on "Propose As Answer" if some post solves your problem or "Vote As Helpful" if some post has been useful to you! (^_^)
• Tuesday, September 18, 2012 10:45 PM
Translation:
that's him already become busy I b or c that automatically creates a new number as equal to a and c as equal to b. I still want (eg press 2 times to a) that he is not 2 digits show but then removes the last and not the whole function of z has that removes everything but really only the specific number that is a
I'll ff further explain why I do this:
it is that I am in a game in a guild sits with raw materials and then they want a bingo game that wins 50% n1 n2 n3 30% and 20%
the problem is the person who can only have up to 60 bingo numbers are not so bad but it is true that if we now have 61 people who participate can no longer participate.
and that you are up to 2x per month a pot (you) can win, and if so in a month 2x the number 54 for example has been and is then further along than it is easier that he take away the old number and another back can put him up so that he has a different number next move but then you eventually need a longer bar, while those with a few lines of text can perhaps all leave and Z stopgap can play. So I thought of a specific nummerweghaling where I now am full of thinking and if that is done he is so far considered to be off because the 4 prizes then the copy and paste of number 2 or 3, then ff the adjustments it and then I can do it for as long as I want.
but really thank January was really useful as you can see it looks better now with much less loose ends
(Update express the current result there, so you can see what I finally did, and if someone tries again that he also has a nice cheat program manages)
gr.pk
-Noah J. Buscher "Nothing is Impossible Until Proven Impossible."
• Wednesday, September 19, 2012 2:28 PM
You could store the number to a variable. (or an array(this may be more easy))
Than you start a "If ... Then" commando and control if this number is already used. If yes, restart the getting number part with your subroutine.
And if the number is ok, show it on the display, and do whatever you want with it. :)
Ask, if you don't understand anything we all write/wrote here.
Greetings
Timo
Ich bin Neu | 2,057 | 7,328 | {"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-2013-20 | latest | en | 0.610373 |
https://www.tutorialspoint.com/python-extend-consecutive-tuples | 1,702,241,649,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679102637.84/warc/CC-MAIN-20231210190744-20231210220744-00746.warc.gz | 1,122,305,239 | 21,017 | # Python – Extend consecutive tuples
When it is required to extend consecutive tuples, a simple iteration is used.
## Example
Below is a demonstration of the same −
my_list = [(13, 526, 73), (23, 67, 0, 72, 24, 13), (94, 42), (11, 62, 23, 12), (93, ), (83, 61)]
print("The list is :")
print(my_list)
my_list.sort(reverse=True)
print("The list after sorting in reverse is :")
print(my_list)
my_result = []
for index in range(len(my_list) - 1):
my_result.append(my_list[index] + my_list[index + 1])
print("The result is :")
print(my_result)
## Output
The list is :
[(13, 526, 73), (23, 67, 0, 72, 24, 13), (94, 42), (11, 62, 23, 12), (93,), (83, 61)]
The list after sorting in reverse is :
[(94, 42), (93,), (83, 61), (23, 67, 0, 72, 24, 13), (13, 526, 73), (11, 62, 23, 12)]
The result is :
[(94, 42, 93), (93, 83, 61), (83, 61, 23, 67, 0, 72, 24, 13), (23, 67, 0, 72, 24, 13, 13, 526, 73), (13,
526, 73, 11, 62, 23, 12)]
## Explanation
• A list of tuples is defined and is displayed on the console.
• It is sorted in reverse using ‘sorted’ method and displayed on the console.
• An empty list is created.
• The list is iterated over, consecutive elements are added and appended to the empty list.
• This is the output that is displayed on the console.
Updated on: 13-Sep-2021
79 Views | 468 | 1,304 | {"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} | 2.859375 | 3 | CC-MAIN-2023-50 | latest | en | 0.758804 |
https://www.fmaths.com/square-root/question-how-to-find-square-root-of-5.html | 1,620,744,608,000,000,000 | text/html | crawl-data/CC-MAIN-2021-21/segments/1620243989614.9/warc/CC-MAIN-20210511122905-20210511152905-00614.warc.gz | 782,912,117 | 10,703 | # Question: How To Find Square Root Of 5?
## How do you find the fifth root without a calculator?
You can find 2.55=97.65625 so you need the fifth power to be 10897.65625≈1.106 times larger. Now we can use (1+x)n≈1+nx for x≪1 so we want the root to be about 1.02 times larger, giving 2.5⋅1.02≈2.55. You can then find 2.555≈107.82 and call that good enough.
## What is the square root of 5 simplified?
The numerical value of the square root of 5, which has been shortened to 50 decimal places is as follows: 2.23606797749978969640917366873127623544061835961152… This is the simplified value of square root of 5.
## How do I find square root of a number?
How to find the square root of a number and calculate it by hand
1. STEP 1: Separate The Digits Into Pairs. To begin, let’s organize the workspace.
2. STEP 2: Find The Largest Integer.
3. STEP 3: Now Subtract That Integer.
4. STEP 4: Let’s Move To The Next Pair.
5. STEP 5: Find The Right Match.
6. STEP 6: Subtract Again.
## How do you find the 5th root of 32?
Direct link to David Severin’s post “Go to the MATH button, the first screen under MATH” Go to the MATH button, the first screen under MATH has the cubed root as 4:, and any root as 5:. So the fifth root of 32, put try 5 MATH 5: 32.
You might be interested: Often asked: How To Compute Square Root Easily?
## What is the square of 5?
List of Perfect Squares
NUMBER SQUARE SQUARE ROOT
2 4 1.414
3 9 1.732
4 16 2.000
5 25 2.236
## What is the value of 5 Root 5?
Therefore, the value of root 5 is, √ 5 = 2.2360… You can find the value of the square root of all the non-perfect square number with the help of the long division method. This is the old method which gives the exact value of the root of numbers.
## Is 5 a perfect square?
In mathematics, a square is a product of a whole number with itself. For instance, the product of a number 2 by itself is 4. In this case, 4 is termed as a perfect square. Example 1.
Integer Perfect square
2 x 2 4
3 x 3 9
4 x 4 16
5 x 5 25
## How do you find the root value?
The product property of square roots states that for any given numbers a and b, Sqrt (a × b) = Sqrt (a) × Sqrt (b). Because of this property, we can now take the square roots of our perfect square factors and multiply them together to get our answer. In our example, we would take the square roots of 25 and 16.
## What is 3125 to the 5th root?
Example of 5th Root of Numbers
5th Root of 1 = 1 Fifth root of 7,776 = 6
Fifth root of 32 = 2 Fifth root of 7,776 = 7
Fifth root of 243 = 3 Fifth root of 32,768 = 8
Fifth root of 1,024 = 4 Fifth root of 59,049 = 9
Fifth root of 3,125 = 5 Fifth root of 100,000 = 10
## What are the roots of 4 √ 256?
The 4th root of 256 is 4. | 854 | 2,717 | {"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} | 4.59375 | 5 | CC-MAIN-2021-21 | latest | en | 0.852998 |
https://www.cemnet.com/Forum/thread/107805/angle-of-repose.html | 1,502,996,973,000,000,000 | text/html | crawl-data/CC-MAIN-2017-34/segments/1502886103910.54/warc/CC-MAIN-20170817185948-20170817205948-00575.warc.gz | 869,841,611 | 8,006 | 4 posts
TimePosted 22/08/2007 20:38:52
Tanbaig says
angle of repose
hi every body can any body answer
1. What is angle of repose and how it can be calculated?
2. What is the formulae to calculate retension time of kiln feed?
Reply
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4 posts
TimePosted 10/01/2008 17:43:41
SIMEQ says
Re: angle of repose
The angle of repose is simply the angle between horizontal and the material after the material is put on a horizontal surfuce from one point. For many raw material its about 40 deg. Angle of drawoff is the angle between horizontal and the material if you remove material from the buttom. Normally a few degrees higher. Wet sand can get fully up to 90 deg (and higher). Water has angle of repose and drawoff equal to 0 deg. The term is commonly used when dealing with bridge reclaimers.
FLS uses the following formula for the kiln retention time:
RetentionTime=23*Length/(Rpm*Diameter*SlopePct);
best regards
best regards
Reply
108 posts
TimePosted 03/03/2009 13:58:17
Dastgir says
Re: angle of repose
Dear SIMEQ,
What does slope Pct is here. Pl elaboate?
Regards
Gualm dastgir
Reply
4 posts
TimePosted 06/03/2009 11:04:41
SIMEQ says
Re: angle of repose
The kiln slope pct is 4% when the kiln drops 4cm each meter.
Reply | 386 | 1,353 | {"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} | 2.75 | 3 | CC-MAIN-2017-34 | latest | en | 0.881052 |
http://math.stackexchange.com/questions/80174/derivative-of-this-function-quadratic-over-quadratic | 1,467,211,351,000,000,000 | text/html | crawl-data/CC-MAIN-2016-26/segments/1466783397748.48/warc/CC-MAIN-20160624154957-00141-ip-10-164-35-72.ec2.internal.warc.gz | 193,946,332 | 18,748 | $$K = \frac{-(\sigma^2 + 3\sigma + 2)}{\sigma^2 - 8\sigma +15}$$
How is this differentiated with respect to $\sigma$?
$$\dfrac{dK}{d\sigma} = \frac{11\sigma^2 - 26\sigma -61}{(\sigma^2 - 8\sigma + 15)^2}$$
And the quotient rule is a very long process, I get the feeling there was a short method.
-
It's just the quotient rule. $(f/g)'={f'g-g'f\over g^2}$. Your comment about partial fractions leads me to say "the derivative, not the indefinite integral"... – David Mitra Nov 8 '11 at 12:58
That would be the quotient rule... partial fractions is an integration technique, not differentiation. – process91 Nov 8 '11 at 12:58
Er I meant quotient, I was tired – Supernovah Nov 8 '11 at 12:59
Oh thanks, I didn't know that rule – Supernovah Nov 8 '11 at 13:06
The three comments below are not really shortcuts. More like longcuts. Because $x$ is easier to type than $\sigma$, the variable has been changed. We show how to differentiate $\frac{x^2+3x+2}{x^2-8x+15}$ and leave it to someone else to change the sign at the end.
$1$) We are being asked to divide $x^2+3x+2$ by $x^2-8x+15$. So divide. We get $$\frac{x^2+3x+2}{x^2-8x+15}=1+\frac{11x-13}{x^2-8x+15}.$$ The derivative of $1$ is $0$, so we want the derivative of $$\frac{11x-13}{x^2-8x+15}.$$ The algebra of the Quotient Rule is definitely easier with a linear polynomial on top than if we use the Rule on the original expression.
$2$) If we want to practice partial fractions before they are needed for integration, we can simplify further. Note that $x^2-8x+15=(x-3)(x-5)$. The partial fractions process shows that $$\frac{11x-13}{x^2-8x+15}=-\frac{10}{x-3}+\frac{21}{x-5}.$$ Now differentiation is genuinely easy.
$3$) Logarithmic differentiation can be useful. We will be deliberately sloppy, and not worry about the fact that $\log u$ is not defined when $u \le 0$. One can show that negative $u$ in fact give no problem. The derivative of $\log|u|$ with respect to $u$ is $\frac{1}{u}$. Breaking up the interval so that we can deal with $\log$ properly gives the same derivative as the one we get if we just heedlessly calculate. Let $f(x)=\frac{x^2+3x+2}{x^2-8x+15}$. Then $$\log f(x)=\log(x^2+3x+2)-\log(x^2-8x+15).$$ Differentiate. We get more or less instantly $$\frac{f'(x)}{f(x)}=\frac{2x+3}{x^2+3x+2}-\frac{2x-8}{x^2-8x+15}.\qquad (\ast)$$ If we have to "simplify" $(\ast)$ to the form $\frac{P(x)}{Q(x)}$ where $P(x)$ and $Q(x)$ are polynomials, the simplification will not be much fun. But the expression $(\ast)$ is certainly pleasant enough if we just want to evaluate the derivative at a particular numerical value of $x$.
For complicated products/quotients, "logarithmic differentiation" can be, for certain purposes, much more efficient than conventional differentiation. However, if we want to find where the derivative vanishes, the advantage tends to evaporate.
-
The quotient rule is not too long...
\begin{align*}\frac {dK}{d\sigma} =& \frac {(-2\sigma-3)(\sigma^2-8\sigma+15)-(2\sigma-8)(-\sigma^2-3\sigma-2)}{(\sigma^2-8\sigma+15)^2}\\ =& \frac{-(2\sigma^3-13\sigma^2+14\sigma+45)+(2\sigma^3-2\sigma^2-12\sigma-16)}{(\sigma^2-8\sigma+15)^2}\\ =& \frac{11\sigma^2-26\sigma-61}{(\sigma^2-8\sigma+15)^2}\end{align*} The squared denominator is a good clue that the book (or whatever reference you are using for the answer) used the quotient rule.
I don't see any shortcuts to this question, so if you are being asked to differentiate it you should be familiar with the quotient rule at this point. http://en.wikipedia.org/wiki/Quotient_rule
-
He could use so-called ''logarithmic differentiation''; but I don't think this would qualify as a ''shortcut''. – David Mitra Nov 8 '11 at 13:26
Actually, OP could've used a combination of the product rule and chain rule if he didn't remember how to differentiate a quotient... – J. M. Nov 8 '11 at 13:35
Definitely true, although neither seems to be much of a "shortcut" (as you mentioned). Perhaps it's worth mentioning that the quotient rule is simply an application of the product rule and the chain rule? Although that's probably in the Wikipedia entry... – process91 Nov 8 '11 at 13:37 | 1,292 | 4,127 | {"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": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.25 | 4 | CC-MAIN-2016-26 | latest | en | 0.87909 |
http://www.numbersaplenty.com/1221111221221 | 1,585,850,280,000,000,000 | text/html | crawl-data/CC-MAIN-2020-16/segments/1585370507738.45/warc/CC-MAIN-20200402173940-20200402203940-00126.warc.gz | 286,237,867 | 3,596 | Search a number
1221111221221 = 2353091792227
BaseRepresentation
bin10001110001001111111…
…001101000101111100101
311022201220100012021011201
4101301033321220233211
5130001313433034341
62332545403202501
7154136163056653
oct21611771505745
94281810167151
101221111221221
114309634a5061
121787ab816431
138b1c5271998
144316022ddd3
1521b6d2a7331
hex11c4fe68be5
1221111221221 has 4 divisors (see below), whose sum is σ = 1274203013472. Its totient is φ = 1168019428972.
The previous prime is 1221111221219. The next prime is 1221111221273. The reversal of 1221111221221 is 1221221111221.
Adding to 1221111221221 its reverse (1221221111221), we get a palindrome (2442332332442).
It is a happy number.
It is a semiprime because it is the product of two primes, and also a Blum integer, because the two primes are equal to 3 mod 4.
It is a cyclic number.
It is not a de Polignac number, because 1221111221221 - 21 = 1221111221219 is a prime.
It is a super-2 number, since 2×12211112212212 (a number of 25 digits) contains 22 as substring.
It is a Duffinian number.
It is a congruent number.
It is not an unprimeable number, because it can be changed into a prime (1221111221021) by changing a digit.
It is a pernicious number, because its binary representation contains a prime number (23) of ones.
It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 26545896091 + ... + 26545896136.
It is an arithmetic number, because the mean of its divisors is an integer number (318550753368).
Almost surely, 21221111221221 is an apocalyptic number.
It is an amenable number.
1221111221221 is a deficient number, since it is larger than the sum of its proper divisors (53091792251).
1221111221221 is an equidigital number, since it uses as much as digits as its factorization.
1221111221221 is an odious number, because the sum of its binary digits is odd.
The sum of its prime factors is 53091792250.
The product of its digits is 64, while the sum is 19.
The spelling of 1221111221221 in words is "one trillion, two hundred twenty-one billion, one hundred eleven million, two hundred twenty-one thousand, two hundred twenty-one".
Divisors: 1 23 53091792227 1221111221221 | 671 | 2,224 | {"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} | 3.171875 | 3 | CC-MAIN-2020-16 | latest | en | 0.847053 |
http://search.cpan.org/~smueller/Math-SZaru/lib/Math/SZaru/QuantileEstimator.pm | 1,498,482,735,000,000,000 | text/html | crawl-data/CC-MAIN-2017-26/segments/1498128320736.82/warc/CC-MAIN-20170626115614-20170626135614-00422.warc.gz | 345,351,993 | 5,010 | Steffen Müller > Math-SZaru > Math::SZaru::QuantileEstimator
# NAME
Math::SZaru::QuantileEstimator - Quantile estimation based on Munro-Paterson algorithm
# SYNOPSIS
``` use Math::SZaru::QuantileEstimator;
my \$ue = Math::SZaru::QuantileEstimator->new(\$maxelems);
# add many more elems using add_elem ...
my \$inserted_elems_count = \$ue->tot_elems;
my \$estimated_unique_count = \$ue->estimate();```
# DESCRIPTION
`Math::SZaru::QuantileEstimator` provides a statistical estimate of quantiles in a large data set (or stream). It uses the algorithm published by Munro and Paterson: Munro & Paterson, "Selection and Sorting with Limited Storage", Theoretical Computer Science, Vol 12, p 315-323, 1980.
# METHODS
## new
Constructor. Expects an integer indicating the number of quantiles to calculate. In a nutshell, passing 101 will mean that the return value of the `estimate` call (see below) will return a list of min, 1st-percentile, 2nd-percentile, ..., 99th-percentile, max (min + 100 = 101). Other values cause the space between min and max to be differently divided. Asking for only two quantiles will just yield min/max to be tracked. Asking for three quantiles will add the median (50th percentile).
Given a floating point number, adds the number to the QuantileEstimator.
Same as `add_elem`, but accepts an arbitrary list of numbers to insert into the estimator at once.
## tot_elems
Returns the total count of the number of elements that were added to the estimator.
## estimate
Returns the estimated quantiles in a raference to an array as described in the `new` documentation above.
Math::SZaru
# AUTHOR
Steffen Mueller, <smueller@cpan.org>
` http://www.apache.org/licenses/LICENSE-2.0` | 432 | 1,719 | {"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-2017-26 | longest | en | 0.671071 |
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