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https://fr.mathworks.com/matlabcentral/profile/authors/7688782?detail=answers&page=2 | 1,652,801,535,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662517485.8/warc/CC-MAIN-20220517130706-20220517160706-00780.warc.gz | 345,215,897 | 4,992 | Matlab code for solving 2D Laplace pde
Sparse linear solvers are already available in Matlab, the backslash operator per default uses the Umfpack direct solver y...
plus de 4 ans ago | 0
3D diffusion equation in cylinder
Modelling and simulation of convection and diffusion for a 3D cylindrical (and other) domains is possible with the <https://www....
plus de 4 ans ago | 0
| accepted
How to solve fick's 2nd law of diffusion equation?
<http://www.featool.com/doc/physics.html#phys_cd Modeling and simulation of convection and diffusion> is certainly possible to s...
plus de 4 ans ago | 1
| accepted
How to find the maximum length in a structure of vectors?
If by "maximum length" you mean the number of struct entries, then you can just use one of the standard *length*, *numel*, or *s...
plus de 4 ans ago | 1
Mesh Plotting in Matlab
The following will plot quadrilaterals from your grid (if you prefer triangles you can use the *patch* command) x = 0 : 0...
plus de 4 ans ago | 0
Information about meshgrid in pdetool. How can I define specific mesh?
If you prefer to set up and solve heat transfer plate and other PDE problems with a structured quadrilateral mesh, it is possibl...
plus de 4 ans ago | 0
Assembling global matrix from element matrices based on location.
Normally you would have a list of integer pointers between local and global degrees of freedom constructed from the mesh connect...
plus de 4 ans ago | 0
How can I solve the equation of curvature on PDE Toolbox?
∥∇f∥ should typically be *sqrt(fx^2+fy^2+eps)* where eps is a small constant to avoid divisions by zeros (since ∥∇f∥ is in the d...
plus de 4 ans ago | 0
Create laplacian smoothing matlab
You can get something quite similar with the following code, and tune it by playing around with the <http://www.featool.com/doc/...
plus de 4 ans ago | 0
Did anyone developed a code/function to create Stiffness matrix of 8-Node Brick (Hexahedral) in Finite Element Analysis ?
For a single element you can just create a grid with one cell, for example using grid = blockgrid(1); in the example ab...
plus de 4 ans ago | 0
Did anyone developed a code/function to create Stiffness matrix of 8-Node Brick (Hexahedral) in Finite Element Analysis ?
Q1 hexahedral elements are available and pre-defined with the <www.featool.com FEA Toolbox>. Once installed, the following code ...
plus de 4 ans ago | 0
You can use the Matlab <https://www.mathworks.com/products/pde.html PDE Toolbox> or <https://www.featool.com FEATool FEM Toolbox...
plus de 4 ans ago | 2
| accepted
delaunaytriangulation function: How to associate triangles with edges?
With the <https://www.featool.com/doc/gridedge_8m.html gridedge> function included with the <https://www.featool.com Matlab FEA ...
plus de 4 ans ago | 0
Is there any way to solve an advection heat equation in pdetool box?
This <http://www.featool.com/doc/quickstart.html#ex_he1 coupled fluid flow heat transfer model> might be a good starting point. ...
plus de 4 ans ago | 2
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PDE Toolbox Structural mechanics Static bending of a beam with material properties varying inside the beam
Perhaps you can modify this <http://www.featool.com/tutorial/2017/05/30/Euler-Bernoulli-Beam-Matlab-Simulation-in-FEATool-Multip...
plus de 4 ans ago | 0
hello every one , I have a 3d cylinderical shape with temperature distributed in this cylinder in a given function. the question is , can this be ploted by matlab??
Another option if you for example want to <http://www.featool.com/tutorial/2017/09/06/Matlab-Plotly-3D-Unstructured-Visualizatio...
plus de 4 ans ago | 2
PDE Thermal Model with heat produced as a function
If you are using the FEATool Multiphysics Toolbox it is possible enter PDE coefficients as regular string expressions, for examp...
plus de 4 ans ago | 0
magnetic fiel simulator tools ?
FEATool <https://www.featool.com/multiphysics Multiphysics> has built-in physics modes for Electrostatics simulations, you can f...
plus de 4 ans ago | 0
how i can program the following function of (convection-convection) in matlab??
With the <https://www.featool.com FEATool Multiphysics Matlab FEM Toolbox> you can enter your own <http://www.featool.com/tutori...
plus de 4 ans ago | 1
| accepted
How to plot solid tetrahedrons in MATLAB?
With the coordinates and connectivities in your example, and the <https://www.featool.com Matlab FEM Toolbox>, you can create a ...
plus de 4 ans ago | 0
Matlab: 2d linear elasticity PDE
2D linear elasticity (plane stress, plane strain, and axisymmetric stress-strain) for small displacements are available as pre-d...
plus de 4 ans ago | 0
How can I solve PDE with boundary condition?
Alternatively, if you still prefer to solve it as a PDE, you can quite easily input and solve it with the <https://www.featool.c...
plus de 4 ans ago | 0
PDE solver without PDE solver toolpack
Depending on your problem the FEATool FEM Toolbox could possibly work for your case as both modeling and simulation of <http://w...
plus de 4 ans ago | 0
How to plot temperature distribution T(X,Y) over a 2D rectangular plate in Matlab?
You can use the <https://www.featool.com/ FEATool FEM toolbox> and postprocessing function to <https://www.featool.com/tutorial/...
presque 5 ans ago | 0
Coupling transport of a species to surface reactions
The <https://www.featool.com FEATool Multiphysics Matlab FEM toolbox> allows for easy coupling and <https://www.featool.com/matl...
presque 5 ans ago | 0
How does MATLAB build the mass matrix for 6-node triangle meshes?
In the FEATool Multiphysics FEM toolbox the finite element shape functions are defined quite easily and available in the <http:/...
presque 5 ans ago | 0
Sparse FEM Matrix build inefficiency
Although looping over all element, finite element forms, and quadrature points is the typical fem assembly approach, even with t...
presque 5 ans ago | 0 | 1,526 | 5,900 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.03125 | 3 | CC-MAIN-2022-21 | latest | en | 0.844951 |
https://woodworking.stackexchange.com/questions/9845/how-can-i-bevel-the-edge-of-a-large-disc | 1,660,006,897,000,000,000 | text/html | crawl-data/CC-MAIN-2022-33/segments/1659882570879.37/warc/CC-MAIN-20220809003642-20220809033642-00072.warc.gz | 579,708,107 | 67,102 | # How can I bevel the edge of a large disc?
I'm cutting a 900mm circle out of a 35mm thick hardwood panel using a router jig that I've built and a straight cut bit. That works very well for 90° degree sides, but I would also like to be able to bevel the edge, so that it has a ~15-30° angle to it all the way around. The exact angle isn't so important, though it would need to be less than 45°.
I have a 45° chamfer bit for my router, but the depth is only about 18mm, so that won't work on its own.
My current thinking is to cut the 45° using the chamfer bit, and then mount the circle on a pivot (probably using the same pivot the cutting jig uses), and use a belt sander to smooth out the transition from straight to 45° to an even ~30° all the way around - I can spin the circle and hold the sander fixed that way. I'm somewhat concerned that this won't be even enough though. A more geometrically precise method would be better, I think.
My other thought is to adapt the jig so that it can hold a jigsaw at an angle and trim the edge that way. It seems tricky, though, and I don't know if I trust my jigsaw enough.
Any other ideas?
• Do you have a band saw? You could use a circle cutting jig for a band saw, with the table tilted to obtain the angle. Or, do you have a router table? I can imagine a ramped jig that would accomplish this task. Jul 31, 2019 at 2:38
• No band saw, I'm afraid. I have a home-made router "table", well, a big flat sheet with places to mount the router and a fence - but it's fairly basic and I don't know that it would cope with the weight of the circle (probably 20kg or so). Jul 31, 2019 at 3:50
• Could you explain the ramped jig for a router table a little? Would you cut the circle with a straight bit first, and then apply the taper via the ramp? It's making me wonder if I can achieve the same thing by somehow angling the router on my circle jig with an adapter. Jul 31, 2019 at 3:53
belt sander
A belt sander is certainly one way this could be done and it's one of the methods I was just about to suggest1 after reading the first part of your Question.
I'm somewhat concerned that this won't be even enough though. A more geometrically precise method would be better, I think.
If the belt sander is fixed in place, has a hard platen and the pivot point doesn't shift there's no reason this couldn't be accurate enough. Circle-shaping is now often done via sanding, using jigs that allow the workpiece to rotate against a disk or belt sander.
Tip: start coarse! You don't want to try to remove this much wood with a 100-grit belt, for bulk material removal you want to begin at 60 or even coarser and work up from there. I know some users would start at 36 grit for something like this as extreme as that sounds (if doing this entirely by sanding).
My other thought is to adapt the jig so that it can hold a jigsaw at an angle and trim the edge that way. It seems tricky, though, and I don't know if I trust my jigsaw enough
You could remove the majority of the waste with your jigsaw. You'd want to cut well on the waste side of the line because of the expected wobble in the cut at certain areas along the perimeter (as the grain orientation relative to the cut changes).
But even if you could get the cut really neat you should expect to have to refine the sawn surface a lot afterwards. This doesn't argue against using the jigsaw — you'd have a very similar amount of cleanup to do if the cut were done on a bandsaw, which is the saw many would recommend most highly for this cut.
Hand sanding to finish
Regardless of whether you do this entirely by sanding or not, expect to have to do a fair amount of hand sanding to complete the job. Use a block to back the paper2. The two portions of the circle that are towards to ends of the boards will be tougher to sand than the sides as end grain is always harder than long-grain surfaces, so you'll need to concentrate more effort there.
In general there's no need to sand beyond about 180-220 grit, but for the end grain it's worth taking the time to go up higher, to 400 grit or a bit finer. End grain sanded to higher grits looks better anyway but it finishes better too (helping to avoid the usual tendency it has for going much darker than the rest of the wood when finish is applied).
Remember to slightly soften the top arris. Leaving it sharp would make the table surprisingly uncomfortable or even hazardous to sit at, press against or bump into3, plus finishes can creep away from sharp edges, so it's necessary to round them over slightly. I find a quick sand, just 2-3 swipes, with very worn 250 is often enough for arrises to stay looking sharp but be comfortable to handle. But you can give the edge a definite rounding if you prefer, it's entirely a matter of personal taste.
1 My main suggestion was going to be to do it using hand tools but I'm presuming you don't want to go there so I'm leaving that out :-)
2 If you don't own one make one now from a piece of scrap. You may find, as many have before you, that this 'temporary' sanding block will stick around in the workshop for many years! I still have the first sanding block I made, it's just a length of 1x2 with cork glued to one face that I had no expectation would last more than a couple of months and it's now over six years old.
3 I've cut myself a couple of times on 90° edges in harder woods like oak and this angle you're creating is more acute than that.
• Thank you for this comprehensive answer! You're right about hand-tools: I don't have the luxury of unlimited time to spend on the project and am a novice in their use. Do you mind quickly outlining how you would do it by hand? I've worked on this today, and used the chamfer bit, then a power plane and belt sander mounted on an angle to refine the edge. It's not finished, but is looking promising! Good call on the end-grain and the top arris. My plan is to make a tiny bevel on the top edge, then soften those angles with sandpaper, which will hopefully protect against chipping somewhat, too. Jul 31, 2019 at 12:30
• There are a number of different ways you could do this by hand. A drawknife or spokeshave could be used similarly to peel or shave off wood working 'downhill' (towards the end grain in both directions). One or more planes could be used to plane the wood away although that could be very slow if one doesn't have a plane set up to take off lots of wood. Re. time, shockingly and somewhat surprisingly this might actually be done faster using hand tools, not just because of the lack of setup time but also because some of the methods are inherently very efficient (esp. the drawknife if super sharp). Jul 31, 2019 at 18:16
• That's really helpful. I did eye my spokeshave when thinking about how to approach this, but I have really only used it for trivial things (shaving spokes, basically!). I don't doubt that hand-tools could be very efficient - the time for me would be learning and practice! In any case, I finished the bevel today with a flap disc on the angle-grinder: I found an angle and pressure that both steadily spun the disc and removed material quickly and evenly. I'll finish with a disc sander and then hand sanding - it's looking better than I expected. Thank you again for your knowledge and advice. Aug 1, 2019 at 11:07
• "flap disc on the angle-grinder: I found an angle and pressure that both steadily spun the disc and removed material quickly and evenly." Nice one! Good to figure out little tricks like this that get the job done. Aug 1, 2019 at 16:12 | 1,805 | 7,553 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.875 | 3 | CC-MAIN-2022-33 | longest | en | 0.966386 |
http://www.jiskha.com/search/index.cgi?query=7th+grade+Pre+algebra(+math+honors0 | 1,496,079,552,000,000,000 | text/html | crawl-data/CC-MAIN-2017-22/segments/1495463612502.45/warc/CC-MAIN-20170529165246-20170529185246-00037.warc.gz | 661,178,361 | 10,223 | # 7th grade Pre algebra( math honors0
181,154 results
7th grade Pre algebra( math honors0
triangle ABC is smilar to triangle FED Ab= 12 Ac=15 De=4 df=5 1. write three equal ratios to show correspnding sides are prosportional. 2. find the value of bc 3. find the value of ef.
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At Jefferson School, both 6th grade & 7th grade classes take a math test. The average score for the 6th grade is 80 and for the 7th grade is 90. If there are twice as many students, in the 7th grade as there is in the 6th grade, what is the average test score for both grades ...
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How many 7th grade students are expected to move by the end of the year? If 12 students actually moved, did more or fewer 7th-grade students move than expected? Justify your answer. 6th-grade # of students: 250 % moves: 2% 7th-grade # of students 200 % moves: 4% 8th-grade # of...
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This website is so helpful!!!! Thanks to everyone you posts lessons and answers! I will be posting both soon!
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How do you solve this equation; There are 128 7th graders at Mark's school, if there are 16 more girls than boys, how many 7th grade boys are there?
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A fertilizer covers 5/8 square foot in 1/4 hour. i don't understand how to work out this math problem. By the way i'm in 6th grade but technically doing advanced math so i'm doing 7th grade math. I don't know how to do this
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explain the usefulness of algebra in modern mathematics.
what is -8(700-3)= (using distributive property)
what is -8(700-3)= (using distributive property)
what is -8(700-3)= (using distributive property)
Physical Science
Hi... well anyways so I am in 7th grade but I'm taking 8th grade science...I think...I know for sure that I am in Accelerated 7th grade science so if that helps at all, there you go:) Back to the subject I'm really confused with acceleration calculation and velocity, time, ...
math
Can i have the answers to the Algebra workbook 7th grade with the link to a pdf document with all the answers. Thank you
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What does 20 divided by 4 minus 5 plus 12 equal? I'm trying to understand the order of operation. I think the answer might be -12. Is this correct?
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english
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Find the area of the circle with the given circumference C Use 3.14 for pi C=37.68
algebra honors
I was placed into algebra honors instead of advanced math.. I am in 7th grade.. I have to maintain an 80% for the entire year or go to virtual school all summer.. My question is: Is there a special technique, formula, or very useful site that might help me grasp the concepts ...
Math
use the digits 1,2,3, and 4 to write a number in scientific notation that is close to .001 this was in a 7th grade algebra book... what? is this even possible without the use of 0?
? reads,"7th place driver had a time that was 18.5 min slower thatn the driver ahead of him(2hr 43min 7sec), what was his time in hrs, min & sec.? What was the diff. btwn 1st and 7th? Calculate the winner's time in hrs. only(answer correct to 3 decimal places). Winners time: ...
7th grade Algebra 1 Honors 5-2 textbook help
How do you solve this for example g(t)-4 and the function is g(x)=x squared +1 . . . . . . .. . .I NEED THIS DONE BY TOMORROW HELP!
My teacher has me working on something he calls "tinging fractions". What is this? What does it mean? How does it work?
I need help putting this problem into slope intercept form please. (3,4)m=2 Thank you.
I need help putting this problem into slope intercept form please. (3,4) m=2 Thank you.
I need to see a completed example of input/output patterns at the 7th grade level. Thanks,
geometry
Suppose line AB is parallel to line MN.Name all angles congruent to angle 8. In the figure at the right, x is parallel to y.List all angles that are congruent to angle 1. If the measure of angle 5 is 45 degrees, what are the measures of the other angles. This is on page 472 in...
Algebra
pre- algebra(MATH)
I need help with pre-algebra solving equations by multiplying or dividing. Can you help me with this homework for free?
the sum of the weights of twin brothers if one weighs four more pounds than the other
pre alg
How do u find the GCF with exponets in a 7th gr. pre alg. class?
y3-2y2- + 3y-4 for y+5
I am supposed to match the function with its possible range. y=2x-1 is the probrem The ranges include -7,-4,-1,2,5,8 or -5,-3,-1,1,3 or 11,6,1,-4,-9,-14 or 4,3,2,1,0 Can you teach me how to figure this out???
I am supposed to match the function with its possible range. y=2x-1 is the probrem The ranges include -7,-4,-1,2,5,8 or -5,-3,-1,1,3 or 11,6,1,-4,-9,-14 or 4,3,2,1,0 Can you teach me how to figure this out???
pre-algebra
kk my teach told me to describe and draw things that are about pre-algebra and she told me to write what pre-algebra is... so can anyone help me??
Pre-algebra 7th NEED HELP
This is a question my teacher gave me and there are no parenthesis or whatever you might think it needs. It's 20 divided by 4 minus 5 plus 12. I think the answer is -12, but I'm not sure. PLEASE HELP!!!
7.5*8.4
34/6=(2x+1)/3
1. 36/7= _ _ 2. -8-m>-19
12 - 5 3/10
6 11/12 - 4 5/12
40/n = 28/22 what is n?
2x+7=4x+3 ? 3x+6=5x+1 ? 2n+6=8N+3 ? 6N+9=9n+6 ?
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Post a New Question | 4,180 | 14,386 | {"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-2017-22 | latest | en | 0.950969 |
https://mscampicchio.com/DAR_04.php | 1,679,440,019,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296943747.51/warc/CC-MAIN-20230321225117-20230322015117-00568.warc.gz | 470,948,213 | 263,979 | # Aim of the Unit
This Unit aims to Write user-defined functions
# Define a new function
A new function is defined with the following synthax:
function_name <- function(x) { ... }
where:
• function_name is the name of the function
• function() function call
• x is the argument
• {...} space for typing the function
For instance, let’s define a new function that calculate the coeffient of variation or “CV”. This is determined as:
$CV=\frac{\text{standard deviation}}{\text{mean}}$
This algorithm $CV=\frac{s}{\overline{x}}$$CV = \dfrac{s}{\bar{x}}$ can be implemented in a user-defined function in the following way:
CV = function(x) {sd(x)/mean(x)}
Now, having defined the following vector:
A <- c(5,4,6,4,5,4,6,3)
Let’apply the function CV:
CV(A)
## [1] 0.2293319 | 215 | 781 | {"found_math": true, "script_math_tex": 1, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 2, "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} | 2.828125 | 3 | CC-MAIN-2023-14 | longest | en | 0.686767 |
https://electricalvoice.com/digital-frequency-meter-block-diagram-working/ | 1,722,869,732,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722640451031.21/warc/CC-MAIN-20240805144950-20240805174950-00668.warc.gz | 179,603,489 | 24,159 | # Digital Frequency Meter – Block Diagram & Working
Functional Block diagram of Digital Frequency Meter
Contents
## Working principle of Digital frequency meter
1. The unknown frequency signal is fed to the Schmitt trigger. The signal may be amplified before being applied to Schmitt trigger.
2. In a Schmitt trigger, the signal is converted into a square wave with very fast rise and fall times, then differentiated and clipped.
3. As a result, the output from a Schmitt trigger is a train of pulses, one pulse, for each cycle of the signal.
4. The output pulses from the Schmitt trigger are fed to a start/stop gate when this gate opens (start), the input pulses pass through this gate and are fed to an electronic counter which starts registering the input pulses.
5. When the gate is closed (stop), the input of pulses to counter ceases and it stops counting.
6. The counter displays the number of pulses that have passed through it in the time interval between the start and stop. If this interval is known, the pulse rate and hence the frequency of the input signal can be known. The frequency (f) of an unknown signal is given by
f = N / t
where
f = frequency of an unknown signal
N = number of counts displayed by the counter
t = time interval between the start and stop of the gate
The range of modern digital frequency meter is between the range from 104 to 109 Hz.
## Applications of Digital frequency meter
1. It is used for testing radio equipment.
2. It is used for measuring temperature, pressure, and other physical values.
3. It is used for measuring vibration, strain
Q. The unknown input signal of 2 V square wave is 3.5 kHz. Determine the display indication if the gate enable time is (a) 0.1 seconds (b) 1 second and (c) 10 seconds.
Frequency of the signal, f = 3.5 kHz = 3500 Hz
Assuming 5 digit display
(a) t = 0.1 sec
f = N/t
N = ft = 3500 x 0.1 = 350
display = 00350
(b) t = 1 sec
f = N/t
N = ft = 3500 x 1 = 3500
display = 03500
(c) t = 10 sec
f = N/t
N = ft = 3500 x 10 = 35000
display = 35000
### 1 thought on “Digital Frequency Meter – Block Diagram & Working”
1. Nice explanation. | 545 | 2,144 | {"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} | 4.09375 | 4 | CC-MAIN-2024-33 | latest | en | 0.881484 |
https://code.research.uts.edu.au/bigprint/twins-controller/-/commit/42fa6bb843650e2fe01fe81d1a8c556f09177e45?view=parallel | 1,653,197,376,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662543797.61/warc/CC-MAIN-20220522032543-20220522062543-00785.warc.gz | 234,631,868 | 25,930 | Commit 42fa6bb8 by Jayant Khatkar
### fix logic error for when only one arm has trajs left, cleanup (#5)
parent e56bc51e
... @@ -45,24 +45,32 @@ def execute_plan(plan, ... @@ -45,24 +45,32 @@ def execute_plan(plan, delays = [0,0] # measure delays of each arm delays = [0,0] # measure delays of each arm relative_delay = 0 # how far arm 0 is behind arm 2 relative_delay = 0 # how far arm 0 is behind arm 2 i_r = [0,0] # index of which traj we're up to for each arm i_r = [0,0] # index of which traj we're up to for each arm arm_complete= None while time.time() < expected_end_time + max(delays): while time.time() < expected_end_time + max(delays): print("----------") print("----------") # Find which arm and which trajectory is next to be executed # Find which arm and which trajectory is next to be executed arm = np.argmin([plan.cumul_time[0][i_r[0]], plan.cumul_time[1][i_r[1]]]) if arm_complete is not None: next_time = min(plan.cumul_time[0][i_r[0]], plan.cumul_time[1][i_r[1]])/move_speed arm = 1 - arm_complete # if one arm complete, only need to do other else: arm = np.argmin([plan.cumul_time[0][i_r[0]], plan.cumul_time[1][i_r[1]]]) next_time = plan.cumul_time[arm][i_r[arm]]/move_speed i_r[arm] += 1 i_r[arm] += 1 # if last trajectory has already been sent # if the last trajectory for this arm has already been sent if i_r[arm] == len(plan.trajs[arm]): if i_r[arm] == len(plan.trajs[arm]): print("Last Trajectory sent, wait for completion") print("Last Trajectory for this arm has been sent") time.sleep(expected_end_time - time.time()) if arm_complete is None: print("Complete") arm_complete = arm # mark this arm as complete break continue else: print("All arms done (unless Logic error), leaving main loop") break t = plan.trajs[arm][i_r[arm]] t = plan.trajs[arm][i_r[arm]] # wait till time to execute next trajectory # wait till it's time to execute the next trajectory rel_delay_arm = max(0, -relative_delay * (-1)**arm) rel_delay_arm = max(0, -relative_delay * (-1)**arm) sleep_time = next_time - (time.time() - s ) + rel_delay_arm sleep_time = next_time - (time.time() - s ) + rel_delay_arm if sleep_time > 0: if sleep_time > 0: ... @@ -70,7 +78,7 @@ def execute_plan(plan, ... @@ -70,7 +78,7 @@ def execute_plan(plan, sleep_time)) sleep_time)) time.sleep(sleep_time) time.sleep(sleep_time) # Execute next Trajectory # Execute next trajectory print("Printing {}th trajectory of arm {}, which is contour {}".format( print("Printing {}th trajectory of arm {}, which is contour {}".format( i_r[arm], arm, t.contour i_r[arm], arm, t.contour )) )) ... @@ -96,7 +104,7 @@ def execute_plan(plan, ... @@ -96,7 +104,7 @@ def execute_plan(plan, # Traj started now, measure delay # Traj started now, measure delay delays[arm] = (time.time() - s ) - next_time delays[arm] = (time.time() - s ) - next_time print("Arm {} is behind by {} when executing {}th Traj".format( print("Arm {} is behind by {}s when executing {}th Traj".format( arm, arm, delays[arm], delays[arm], i_r[arm])) i_r[arm])) ... ...
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Finish editing this message first! | 910 | 3,146 | {"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} | 2.640625 | 3 | CC-MAIN-2022-21 | latest | en | 0.706752 |
http://www.phy.ntnu.edu.tw/ntnujava/msg.php?id=1990 | 1,558,927,951,000,000,000 | text/html | crawl-data/CC-MAIN-2019-22/segments/1558232260658.98/warc/CC-MAIN-20190527025527-20190527051527-00245.warc.gz | 316,023,773 | 1,527 | Here is a link to a series of animated photo's of the farthest throw ever thrown. The throw was over 104 meters and an East German by the name of Uwe Hohn threw it.
http://www.geocities.com/jabalina_2y/UweHon104.80.gif
There is a very good paper written on the physics of javelin throwing located here:
http://www.leshatton.org/Documents/jav2007a_paper.pdf
The author states in it that "The javelin is not so much a throw as a long pull" this is his analysis but other techniques challenge
this statement. The world record holder of the current javelin, Jan Zelezny, has a best toss of 98 meters. He also has the shortest
pull of the current crop of throwers but he stops his momentum the best. The number one factor of distance in the javelin is
speed of javelin at the release. Jan has hit upwards of 33 meters per second in this factor.
The author of the web page also has a windows application for download that simulates many different factors on the javelin thrown
today and this javelin page and application can be found here:
http://www.leshatton.org/javelin_2005.html
There is a very clear and well graphed paper of the 11th World championships located here:
http://www.iaaf.org/newsfiles/38220.pdf
The simulation that I would like to see is how much force can be created on the javelin by stopping your momentum quickly. In this
event, all throwers try to relax their arms and use the reaction to the stop as the main power for the javelin, if they anticipate the
stop and try to use their arm, it results in slowing the javelin down. This may not sound correct for someone who has never thrown
but the arm just cant move faster then the reaction force on the javelin when a thrower stops.
Thank you agin Fu-Kwun for considering this simulation.
Sean Elkinton | 428 | 1,787 | {"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-2019-22 | latest | en | 0.952337 |
https://www.dollartimes.com/calculate/time/days/hours | 1,695,619,208,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233506686.80/warc/CC-MAIN-20230925051501-20230925081501-00879.warc.gz | 812,355,040 | 5,655 | # Convert Days to Hours
Metric conversions between days and hours. Just enter the number to convert and hit the Calculate button.
Time
From
To
Result
15 Days =
360 Hours
(exact result)
How many? Days to Hours. Conversion chart from day to hr
Note: results are rounded
1 day = 24 hr 51 day = 1,224 hr 101 day = 2,424 hr 151 day = 3,624 hr 2 day = 48 hr 52 day = 1,248 hr 102 day = 2,448 hr 152 day = 3,648 hr 3 day = 72 hr 53 day = 1,272 hr 103 day = 2,472 hr 153 day = 3,672 hr 4 day = 96 hr 54 day = 1,296 hr 104 day = 2,496 hr 154 day = 3,696 hr 5 day = 120 hr 55 day = 1,320 hr 105 day = 2,520 hr 155 day = 3,720 hr 6 day = 144 hr 56 day = 1,344 hr 106 day = 2,544 hr 156 day = 3,744 hr 7 day = 168 hr 57 day = 1,368 hr 107 day = 2,568 hr 157 day = 3,768 hr 8 day = 192 hr 58 day = 1,392 hr 108 day = 2,592 hr 158 day = 3,792 hr 9 day = 216 hr 59 day = 1,416 hr 109 day = 2,616 hr 159 day = 3,816 hr 10 day = 240 hr 60 day = 1,440 hr 110 day = 2,640 hr 160 day = 3,840 hr 11 day = 264 hr 61 day = 1,464 hr 111 day = 2,664 hr 161 day = 3,864 hr 12 day = 288 hr 62 day = 1,488 hr 112 day = 2,688 hr 162 day = 3,888 hr 13 day = 312 hr 63 day = 1,512 hr 113 day = 2,712 hr 163 day = 3,912 hr 14 day = 336 hr 64 day = 1,536 hr 114 day = 2,736 hr 164 day = 3,936 hr 15 day = 360 hr 65 day = 1,560 hr 115 day = 2,760 hr 165 day = 3,960 hr 16 day = 384 hr 66 day = 1,584 hr 116 day = 2,784 hr 166 day = 3,984 hr 17 day = 408 hr 67 day = 1,608 hr 117 day = 2,808 hr 167 day = 4,008 hr 18 day = 432 hr 68 day = 1,632 hr 118 day = 2,832 hr 168 day = 4,032 hr 19 day = 456 hr 69 day = 1,656 hr 119 day = 2,856 hr 169 day = 4,056 hr 20 day = 480 hr 70 day = 1,680 hr 120 day = 2,880 hr 170 day = 4,080 hr 21 day = 504 hr 71 day = 1,704 hr 121 day = 2,904 hr 171 day = 4,104 hr 22 day = 528 hr 72 day = 1,728 hr 122 day = 2,928 hr 172 day = 4,128 hr 23 day = 552 hr 73 day = 1,752 hr 123 day = 2,952 hr 173 day = 4,152 hr 24 day = 576 hr 74 day = 1,776 hr 124 day = 2,976 hr 174 day = 4,176 hr 25 day = 600 hr 75 day = 1,800 hr 125 day = 3,000 hr 175 day = 4,200 hr 26 day = 624 hr 76 day = 1,824 hr 126 day = 3,024 hr 176 day = 4,224 hr 27 day = 648 hr 77 day = 1,848 hr 127 day = 3,048 hr 177 day = 4,248 hr 28 day = 672 hr 78 day = 1,872 hr 128 day = 3,072 hr 178 day = 4,272 hr 29 day = 696 hr 79 day = 1,896 hr 129 day = 3,096 hr 179 day = 4,296 hr 30 day = 720 hr 80 day = 1,920 hr 130 day = 3,120 hr 180 day = 4,320 hr 31 day = 744 hr 81 day = 1,944 hr 131 day = 3,144 hr 181 day = 4,344 hr 32 day = 768 hr 82 day = 1,968 hr 132 day = 3,168 hr 182 day = 4,368 hr 33 day = 792 hr 83 day = 1,992 hr 133 day = 3,192 hr 183 day = 4,392 hr 34 day = 816 hr 84 day = 2,016 hr 134 day = 3,216 hr 184 day = 4,416 hr 35 day = 840 hr 85 day = 2,040 hr 135 day = 3,240 hr 185 day = 4,440 hr 36 day = 864 hr 86 day = 2,064 hr 136 day = 3,264 hr 186 day = 4,464 hr 37 day = 888 hr 87 day = 2,088 hr 137 day = 3,288 hr 187 day = 4,488 hr 38 day = 912 hr 88 day = 2,112 hr 138 day = 3,312 hr 188 day = 4,512 hr 39 day = 936 hr 89 day = 2,136 hr 139 day = 3,336 hr 189 day = 4,536 hr 40 day = 960 hr 90 day = 2,160 hr 140 day = 3,360 hr 190 day = 4,560 hr 41 day = 984 hr 91 day = 2,184 hr 141 day = 3,384 hr 191 day = 4,584 hr 42 day = 1,008 hr 92 day = 2,208 hr 142 day = 3,408 hr 192 day = 4,608 hr 43 day = 1,032 hr 93 day = 2,232 hr 143 day = 3,432 hr 193 day = 4,632 hr 44 day = 1,056 hr 94 day = 2,256 hr 144 day = 3,456 hr 194 day = 4,656 hr 45 day = 1,080 hr 95 day = 2,280 hr 145 day = 3,480 hr 195 day = 4,680 hr 46 day = 1,104 hr 96 day = 2,304 hr 146 day = 3,504 hr 196 day = 4,704 hr 47 day = 1,128 hr 97 day = 2,328 hr 147 day = 3,528 hr 197 day = 4,728 hr 48 day = 1,152 hr 98 day = 2,352 hr 148 day = 3,552 hr 198 day = 4,752 hr 49 day = 1,176 hr 99 day = 2,376 hr 149 day = 3,576 hr 199 day = 4,776 hr 50 day = 1,200 hr 100 day = 2,400 hr 150 day = 3,600 hr 200 day = 4,800 hr
How much? Days to Hours. Conversion chart from day to hr
Note: results are rounded
300 day = 7,200 hr 2,800 day = 67,200 hr 5,300 day = 127,200 hr 7,800 day = 187,200 hr 400 day = 9,600 hr 2,900 day = 69,600 hr 5,400 day = 129,600 hr 7,900 day = 189,600 hr 500 day = 12,000 hr 3,000 day = 72,000 hr 5,500 day = 132,000 hr 8,000 day = 192,000 hr 600 day = 14,400 hr 3,100 day = 74,400 hr 5,600 day = 134,400 hr 8,100 day = 194,400 hr 700 day = 16,800 hr 3,200 day = 76,800 hr 5,700 day = 136,800 hr 8,200 day = 196,800 hr 800 day = 19,200 hr 3,300 day = 79,200 hr 5,800 day = 139,200 hr 8,300 day = 199,200 hr 900 day = 21,600 hr 3,400 day = 81,600 hr 5,900 day = 141,600 hr 8,400 day = 201,600 hr 1,000 day = 24,000 hr 3,500 day = 84,000 hr 6,000 day = 144,000 hr 8,500 day = 204,000 hr 1,100 day = 26,400 hr 3,600 day = 86,400 hr 6,100 day = 146,400 hr 8,600 day = 206,400 hr 1,200 day = 28,800 hr 3,700 day = 88,800 hr 6,200 day = 148,800 hr 8,700 day = 208,800 hr 1,300 day = 31,200 hr 3,800 day = 91,200 hr 6,300 day = 151,200 hr 8,800 day = 211,200 hr 1,400 day = 33,600 hr 3,900 day = 93,600 hr 6,400 day = 153,600 hr 8,900 day = 213,600 hr 1,500 day = 36,000 hr 4,000 day = 96,000 hr 6,500 day = 156,000 hr 9,000 day = 216,000 hr 1,600 day = 38,400 hr 4,100 day = 98,400 hr 6,600 day = 158,400 hr 9,100 day = 218,400 hr 1,700 day = 40,800 hr 4,200 day = 100,800 hr 6,700 day = 160,800 hr 9,200 day = 220,800 hr 1,800 day = 43,200 hr 4,300 day = 103,200 hr 6,800 day = 163,200 hr 9,300 day = 223,200 hr 1,900 day = 45,600 hr 4,400 day = 105,600 hr 6,900 day = 165,600 hr 9,400 day = 225,600 hr 2,000 day = 48,000 hr 4,500 day = 108,000 hr 7,000 day = 168,000 hr 9,500 day = 228,000 hr 2,100 day = 50,400 hr 4,600 day = 110,400 hr 7,100 day = 170,400 hr 9,600 day = 230,400 hr 2,200 day = 52,800 hr 4,700 day = 112,800 hr 7,200 day = 172,800 hr 9,700 day = 232,800 hr 2,300 day = 55,200 hr 4,800 day = 115,200 hr 7,300 day = 175,200 hr 9,800 day = 235,200 hr 2,400 day = 57,600 hr 4,900 day = 117,600 hr 7,400 day = 177,600 hr 9,900 day = 237,600 hr 2,500 day = 60,000 hr 5,000 day = 120,000 hr 7,500 day = 180,000 hr 10,000 day = 240,000 hr 2,600 day = 62,400 hr 5,100 day = 122,400 hr 7,600 day = 182,400 hr 2,700 day = 64,800 hr 5,200 day = 124,800 hr 7,700 day = 184,800 hr | 2,867 | 6,159 | {"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} | 2.78125 | 3 | CC-MAIN-2023-40 | latest | en | 0.431895 |
https://brainmass.com/business/upper-and-lower-bounds-of-options/assessing-control-risk-and-upper-deviation-155448 | 1,540,110,065,000,000,000 | text/html | crawl-data/CC-MAIN-2018-43/segments/1539583513804.32/warc/CC-MAIN-20181021073314-20181021094814-00346.warc.gz | 662,518,763 | 21,094 | Explore BrainMass
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# Assessing Control Risk and Upper Deviation
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6.Based on a 5% risk of assessing control risk too low, how would an auditor interpret a computed upper deviation rate of 7%?
A)The auditor is willing to live with a deviation rate of 7% before deciding not to rely on the control.
B)There is a 5% chance that the deviation rate in the population is less than 7%.
C)There is a 5% chance that the deviation rate in the population exceeds 7%.
D)There is a 95% chance that the deviation rate in the population equals 7%.
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https://brainmass.com/business/upper-and-lower-bounds-of-options/assessing-control-risk-and-upper-deviation-155448
#### Solution Preview
C.
Tolerable rate. The maximum population deviation rate the auditor is willing to accept without altering the planned assessed level of control risk. For example, a low (3-7%) rate might be used if substantial reliance on the control is planned. The tolerable rate is inversely related to sample size.
Risk of assessing control risk too low (RACRTL). The maximum risk the auditor is willing to accept of incorrectly concluding that the population deviation rate is less than or equal to the ...
#### Solution Summary
This solution identifies the correct answer and justifies why by defining and explaining the concepts of tolerable rate, risk of assessing control risk too low, and expected population deviation rate. References used are included.
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## Auditing Practice Exam Questions: Audit Risk; audit reports; sampling
1. Control risk is the probability that a material misstatement (error or fraud) could occur and not be prevented or detected on a timely basis by the auditors' substantive procedures.
a. True
b. False
c. True if control risk is set a maximum
d. False because you don't know the inherent risk level
2. What is the audit risk model?
Audit risk: AR
Control risk: CR
Inherent risk: IR
Detection risk: DR
Risk of material misstatement: ROMM
a. AR = CR x IR x DR
b. DR = CR x IR x AR
c. ROMM = CR x IR x DR
d. AR = ROMM x CR x IR x DR
3. An unqualified opinion indicates that the financial statements present the entity's financial condition, results of operations, and cash flows in conformity with GAAP.
a. True
b. False
4. For the copy of the purchase order that goes to the receiving department, it is best to:
a. leave off the description of the goods
b. leave off the quantity of the goods ordered
c. leave off the name of the vendor
d. provide duplicates, one to keep and one to forward to accounting
5. The auditors' report should either contain an expression of opinion on the financial statements taken as a whole or an assertion to the effect that an opinion cannot be expressed.
a. True
b. False
6. Which of the following types of auditors' reports requires an explanatory paragraph to support the opinion?
a. adverse opinion
b. qualified opinion
c. disclaimer of opinion
d. all of the above
7. Statistical sampling plans ensure that samples are selected randomly from the population by removing auditor judgment from the sampling process.
a. True
b. False, you can never remove judgment completely as results are always interpreted
c. False, statistical sampling only permits a computation of sampling risk
d. False, there is no way to ensure random sampling
8. The risks of incorrect acceptance in variables sampling and of assessing control risk too low in attributes sampling both relate to
a. effectiveness of an audit
b. efficiency of an audit
c. assessment of control risk during planning phase
d. amount of substantive testing needed
9. The audit team will choose to reduce the reliance on controls if the ________ is greater than the ________.
a. tolerable rate of deviation; upper limit rate of deviation
b. upper limit rate of deviation; tolerable rate of deviation
c. expected rate of deviation; tolerable rate of deviation
d. tolerable rate of deviation; expected rate of deviation
10. Which of these is characteristic of the sampling process?
a. sampling identifies what belongs in the population
b. sampling requires judgments on the part of the auditor
c. sampling is normally more effective than looking at all the items in the population
d. sampling is not influenced by the definition of the population
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# Comparing Ruby and C# Performance
, 8 Nov 2012 CPOL
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A quick test of Ruby performance vs. C#
## Introduction
As I'm in the middle of learning Ruby and Ruby on Rails, I wanted to do a quick comparison of Ruby vs C#, knowing quite well that C# will outperform Ruby, but I wanted to get some idea by how much. This site indicates that Ruby is about 25 times slower on average, but I wanted to see for myself. As it turns out, Ashraff Ali Wahab had a couple days ago posted the article Eratosthenes/Sundaram/Atkins Sieve Implementation in C#, and I figured this would be a quick way to write some tests.
This is obviously not conclusive - it's a bit like comparing apples and oranges at the code level, especially since I tried to leverage the syntax of Ruby to my current level of understanding. Also, I decided to give IronRuby a try as well, however the tests were inconclusive as the program failed to complete.
## Source Code
### C#
Please refer to Ashraff Ali Wahab article for the C# source code.
### Ruby
#### Brute Force Algorithm
```def BruteForce(topCandidate)
totalCount = 1
isPrime = true
3.step(topCandidate, 2) do |i|
j=3
while j*j <= i && isPrime
isPrime = false if i%j==0
j += 2
end
isPrime ? totalCount += 1 : isPrime = true
end
totalCount
end```
#### Sieve of Eratosthenes Algorithm
```def SieveOfEratosthenes(topCandidate)
myBA1 = Array.new(topCandidate + 1) {true}
myBA1[0] = myBA1[1] = false
thisFactor = 2
while thisFactor * thisFactor <= topCandidate do
mark = thisFactor + thisFactor
mark.step(topCandidate+1, thisFactor) {|n| myBA1[n] = false}
thisFactor += 1
while !myBA1[thisFactor] do
thisFactor += 1
end
end
myBA1.count(true)
end```
#### Sieve of Sundaram Algorithm
```def SieveOfSundaram(topCandidate)
k = topCandidate / 2
myBA1 = Array.new(k + 1) {true}
myBA1[0] = myBA1[k] = false
for i in 1..k do
denominator = (i << 1) + 1
maxVal = (k - i) / denominator
i.step(maxVal+1, 1) {|n| myBA1[i + n * denominator] = false}
# this version takes .20 seconds longer to run 1M iterations!
# for n in i..maxVal+1 do
# myBA1[i + n * denominator] = false
# end
end
myBA1.count(true) + 1
end```
#### "Main"
```def main
max = 1000000
startTime = Time.now()
primes = BruteForce(max)
endTime = Time.now()
elapsed = endTime - startTime
printf("Elapsed time for Brute Force : %f Primes = %d\n", elapsed, primes)
startTime = Time.now()
primes = SieveOfEratosthenes(max)
endTime = Time.now()
elapsed = endTime - startTime
printf("Elapsed time for Sieve of Eratosthenes: %f Primes = %d\n", elapsed, primes)
startTime = Time.now()
primes = SieveOfSundaram(max)
endTime = Time.now()
elapsed = endTime - startTime
printf("Elapsed time for Sieve of Sundaram : %f Primes = %d\n", elapsed, primes)
end```
## The Results
As you can see from these screenshots:
Ruby is:
• about 5 times slower for the brute force algorithm
• about 19 times slower for the Eratosthenes and Sundaram algorithms
For my purposes, that's essentially inline with the shootout website I mentioned in the Introduction.
Sadly, the IronRuby program did not complete:
Dying on this line:
`myBA1.count(true)`
But the brute force algorithm was consistently almost twice as slow.
## Running on a Virtual Box
I'm also running Ubuntu on Virtual Box (2GB RAM, 3 processors) and was pleased with the results:
## Conclusion
While not conclusive, it was a useful exercise to go through. Note particularly the commented out Ruby code:
```i.step(maxVal+1, 1) {|n| myBA1[i + n * denominator] = false}
# this version takes .20 seconds longer to run 1M iterations!
# for n in i..maxVal+1 do
# myBA1[i + n * denominator] = false
# end
```
The "for" loop version takes almost 50% longer! That is a significant and worthwhile discovery, and it essentially makes sense -- the `step` function is a library implementation (and I would assume therefore compiled) whereas the `for` loop I would imagine is constantly being interpreted. Still, it's a significant difference, especially considering that the block `{|n| myBA1[i + n * denominator] = false}` theoretically is implemented as a function call.
Also, it was disappointing that the IronRuby code failed. I was hoping that something this "simple" would not have issues.
Lastly, please do not take this as a detraction to Ruby! This is an amazing language and for many purposes, performance is not the most important concern - interactions with a database and network latency (if you're thinking of Ruby on Rails) will often contribute more to the perception of performance than the language performance.
Also, there appear to be some compilers available, for example Rubinius as well as The Ludicrous JIT Compiler. The former looked much too complicated to try, and the latter, Ludicrous, I did try but was not successful with the installation. Given that the creator claims "Though still in the experimental stage, its performance is roughly on par with YARV", it doesn't seem that helpful, given that: "Probably the most exciting and visible change in Ruby 1.9 is the addition of a bytecode interpreter for Ruby. The YARV (Yet Another Ruby VM) interpreter was integrated into the Ruby project, replacing the interpreter created by Matz (aka MRI, Matz's Ruby Interpreter)." (read here).
## Share
United States
Marc is the creator of two open source projects, MyXaml, a declarative (XML) instantiation engine and the Advanced Unit Testing framework, and Interacx, a commercial n-tier RAD application suite. Visit his website, www.marcclifton.com, where you will find many of his articles and his blog.
Marc lives in Philmont, NY.
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# Relational Algebra – Part 2 - PowerPoint PPT Presentation
Relational Algebra – Part 2. Much of the material presented in these slides was developed by Dr. Ramon Lawrence at the University of Iowa. Relational Algebra Operators. Relational Operators: Selection σ Projection Π Cartesian product x Join Union Difference - Intersection ∩
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## Relational Algebra – Part 2
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Presentation Transcript
1. Relational Algebra – Part 2 Much of the material presented in these slides was developed by Dr. Ramon Lawrence at the University of Iowa
2. Relational Algebra Operators • Relational Operators: • Selection σ • Projection Π • Cartesian product x • Join • Union • Difference - • Intersection ∩ • Division • Summarize • Note that relational algebra is the foundation of ALL relational database systems. SQL gets translated into relational algebra.
3. Relational Algebra Operators
4. Cartesian Product • The Cartesian product of two relations R (of degree k1) and S (of degree k2) is: R x S = {t | t [A1,…,Ak1] R and t [Ak1+1,…,Ak1+k2] S} • The result of R x S is a relation of degree (k1 + k2) and consists of all (k1 + k2)-tuples where each tuple is a concatenation of one tuple of R with one tuple of S. • The cardinality of R x S is |R| * |S|. • The Cartesian product is also known as cross product.
5. Cartesian Product Example
6. θ -Join • Theta (θ) join is a derivative of the Cartesian product. Instead of taking all combinations of tuples from R and S, we only take a subset of those tuples that match a given condition F: R FS = {t | t [A1,…,Ak1] R and t [Ak1+1 ,…,Ak1+k2] S and F(t) is true} where • R, S are relations, t is any tuple • F(t) is a formula defined as that of selection. • Note that R F S = σF(R × S).
7. θ -Join Example
8. Types of Joins • The θ-Join is a general join in that it allows any expression in the condition F. However, there are more specialized joins that are frequently used. • A equijoin only contains the equality operator (=) in formula F. • e.g. WorksOn WorksOn.pno = Proj.pnoProj • A natural join over two relations R and S denoted by R * S is the equijoin of R and S over a set of attributes common to both R and S. • It removes the “extra copies” of the join attributes. • Normally assumes the attributes have the same name in both relations.
9. Equijoin Example
10. Natural join Example
11. Join Practice Questions
12. Outer Joins • Outer joins are used in cases where performing a join "loses“ some tuples of the relations. These are called dangling tuples. • There are three types of outer joins: • Left outer join – R S - The output contains all tuples of R that match with tuples of S. If there is a tuple in R that matches with no tuple in S, the tuple is included in the final result and is padded with nulls for the attributes of S. • Right outer join - R S - The output contains all tuples of S that match with tuples of R. If there is a tuple in S that matches with no tuple in R, the tuple is included in the final result and is padded with nulls for the attributes of R. • Full outer join – R S - All tuples of R and S are included in the result whether or not they have a matching tuple in the other relation.
13. Outer Join Operators Full outer join Left Outer Join Right Outer Join Join Unmatched rows of the left table Matched rows using the join condition Unmatched rows of the right table
14. Right Outer Join Example
15. Division Operator • The division operator on relations R and S, denoted as R ÷ S produces a relation that consists of the set of tuples from R defined over the attributes C that match the combination of every tuple in S, where C is the set of attributes that are in R but not in S. • For the division operation to be defined the set of attributes of S must be a subset of the attributes of R. • The division operator is used when you want to determine if all combinations of a relationship are present. • E.g. Return the list of employees who work on all the projects that 'John Smith' works on. • Note that R ÷ S = ΠR-S(R)−ΠR-S((ΠR-S(R)×S)− R).
16. Division Example
17. Division Operation – Example 2 • Relations R, S: A B B 1 2 3 1 1 1 3 4 6 1 2 1 2 S • R S: A R
18. A Third Division Example • Relations R, S: A B C D E D E a a a a a a a a a a b a b a b b 1 1 1 1 3 1 1 1 a b 1 1 S R • R S: A B C a a
19. Operator Precedence • Just like mathematical operators, the relational operators have precedence. • The precedence of operators from highest to lowest is: • unary operators - σ, Π • Cartesian product and joins - x, *, • intersection, division - ∩, ÷ • union and set difference - , - • Parentheses can be used to changed the order of operations.
20. Complete Set ofRelational Algebra Operators • It has been shown that the relational operators {σ, Π, ×, , -} form a complete set of operators. • That is, any of the other operators can be derived from a combination of these 5 basic operators. • Examples: • Intersection - R ∩ S ≡ R S − ((R - S) (S - R)) • We have also seen how a join is a combination of a Cartesian product followed by a selection. • Division operator: R(Z) ÷ S(X) where X Z and Y = Z - X: • T1 ← ΠY(R) • T2 ← ΠY((S × T1) -R) • T ← T1 - T2
21. Conclusion • The relational model represents data as relations which are sets of tuples. Each relational schema consists of a set of attribute names which represent a domain. • The relational model has several forms of constraints to guarantee data integrity including: • domain, entity integrity and referential integrity constraints • Keys are used to uniquely identify tuples in relations. • Relational algebra is a set of operations for answering queries on data stored in the relational model. • The 5 basic relational operators are: {σ, Π, ×, , -}. • By combining relational operators, queries can be answered over the base relations. | 1,765 | 6,488 | {"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-2019-26 | latest | en | 0.871203 |
https://socratic.org/questions/how-do-you-condense-1-2-ln-9-ln-3-x#270856 | 1,725,745,150,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700650920.0/warc/CC-MAIN-20240907193650-20240907223650-00426.warc.gz | 515,145,976 | 5,596 | How do you condense 1/2 ln 9 + ln 3 x?
$\frac{1}{2} \ln 9 + \ln 3 x = \ln {9}^{\frac{1}{2}} + \ln 3 x = \ln \sqrt{9} + \ln 3 x = \ln 3 + \ln 3 x = \ln 9 x$ | 88 | 156 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 1, "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} | 4 | 4 | CC-MAIN-2024-38 | latest | en | 0.269377 |
https://math.answers.com/other-math/What_times_what_equals_144_except_12_times_12 | 1,670,532,323,000,000,000 | text/html | crawl-data/CC-MAIN-2022-49/segments/1669446711360.27/warc/CC-MAIN-20221208183130-20221208213130-00300.warc.gz | 409,652,032 | 49,564 | 0
# What times what equals 144 except 12 times 12?
Wiki User
2010-02-03 03:31:02
1x144= 144 2x72=144
3x48=144
4x36=144
6x24=144
8x18=144
9x16=144
Wiki User
2010-02-03 03:31:02
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Q: What times what equals 144 except 12 times 12? | 190 | 476 | {"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-2022-49 | latest | en | 0.639127 |
https://www.physicsforums.com/threads/gravity-and-its-effect-on-particles-molecules-and-bonds.246159/ | 1,485,300,836,000,000,000 | text/html | crawl-data/CC-MAIN-2017-04/segments/1484560285315.77/warc/CC-MAIN-20170116095125-00524-ip-10-171-10-70.ec2.internal.warc.gz | 949,468,443 | 17,656 | # Gravity and its effect on particles/molecules and bonds.
1. Jul 21, 2008
### g__ritchie
To start off with I am only a layman in the subject, in actual fact I've just finished my GCSE year. Please forgive me if I have misinterpreted any area. To this end, my question is whether particles/molecules that are not moving are affected by gravity? Using Einstein's theory of gravity as opposed to the Newtonian theory, a disruption in the space-time has to occur for gravity to exist. Ergo, I am lead to believe that if a sole particle/molecule is not moving, it would not be affected by gravity. However, is it the energy in bonds that form between the particles/molecules that disrupt the space-time and hence will induce gravity? Furthermore, could the moving electrons, whether they are in cloud or particle form, induce gravity by their movement and unequal spread of negativity? As I said I am only a layman so please if any off this question doesn't make sense or is wrong, please correct me. Thank you in advance.
2. Jul 21, 2008
### peter0302
Not sure how to interpret your question. On the one hand, nothing is ever "not" moving strictly speaking. Leaving that nit-pick aside, neither GR or Newtonian gravity care whether the particle is moving. Not sure what your'e getting at.
It's definitely not just the binding energy that causes gravity. It's the total mass/energy - which includes the binding energy of course. But solo protons and electrons and neutrons still fall to the earth.
3. Jul 21, 2008
### maverick280857
For a precise description of the 'motion' of particles/molecules, one needs to invoke the quantum theory. Now, if something is not moving, its momentum is zero (so that it is known precisely) and so by the uncertainty principle, its position has infinite uncertainty meaning that it can be anywhere. So except for a free particle (one that is not subject to any potential, or force, if you will) everything else will have non-infinite uncertainty in position.
Now, whether or not something moves, gravity will certainly be acting on it but the small scales at which quantum behavior is predominant will usually not allow for a great variation in or strength of the gravitational force. Thus, while theoretically these particles are affected by gravity, the force is usually neglected (this is not to be confused with the quantum theory of gravity, which is under development at the moment).
The mere presence of matter in spacetime without motion will be sufficient for it to experience a force of gravity.
Let me see if I can come up with a better explanation...
4. Jul 22, 2008
### peter0302
Does a free electron not fall to the ground at 9.8 m/s^2?
5. Jul 22, 2008
### maverick280857
Peter, does it have to "fall"? I'm sorry but I don't understand your question. Perhaps you're trying to point out a mistake in my post..please elaborate.
And btw, my post was about the classical picture. I am trying not to get into quantum mechanics here. But I believe Sakurai has a brief theoretical description of a situation in which gravity does play a role in quantum mechanics...I'll find the exact reference and post it back here.
EDIT: This is page 138 of JJ Sakurai's book "Modern Quantum Mechanics", Revised Edition..under the section "Gravity in Quantum Mechanics."
To g__ritchie: I think I made too classical a statement there. The point I was trying to make was that the force of gravity is always there, even in the quantum 'realm'. So just ignore what I said in the paragraph quoted by peter0302. As for your last question, the essence of GR is captured in "Wheeler's Ditty":
Matter tells spacetime how to curve.
Spacetime tells matter how to move.
Last edited: Jul 22, 2008
6. Jul 22, 2008
### Creator
Of course gravity affects quantum particles....The so called COW experiment ,1975,(Coella, Overhauser, and Werner) (in cold neutron interferometry) has shown that the phase of a neutron wavefunction changes as a result of its different position in a gravitational potential.
More recent experimental studies have indeed shown that quantum particles (neutrons) in a confining potential can only fall in quantum 'jumps' in earth's gravitational field...see http://www.nature.com/nature/journal/v415/n6869/full/415297a.html
More here:
http://backreaction.blogspot.com/2007/06/bouncing-neutrons-in-gravitational.html
BTW, Good discussion...
Typically a neutral particle is used in these type of experiments since the electric field strength of a charged particle would overwhelm the gravitational force measurement.
Creator
Last edited: Jul 22, 2008
7. Jul 23, 2008
### peter0302
Well I think the confusion is in the OP, but the reason I ask that is because I thought he was asking whether two objects with no relative motion between them will still feel a gravitational force. When you said gravity was negligible in subatomic particles, that's certainly true when you're talking about the gravitational force between them, but the gravitational force - in classical gravity or GR - between the earth and an electron should be just as observeable as the gravitational force between the earth and a baseball. So it shouldn't matter whether the electron is moving or is bound to an atom. A free electron feels the earth's gravity like anything else and should fall at 9.8 m/s^2 in a vacuum.
Maybe that wasn't the question but if not I'm totally confused.
8. Jul 24, 2008
### maverick280857
Yes, in a purely classical space it should fall, i.e. if you totally disregard quantum behavior.
To the OP: But if you bring in quantum mechanics, the equation of "motion" of the electron would be Schrodinger's equation with the potential equal to the gravitational potential. This is in contrast to classical mechanics, where the equation of motion is Newton's second law, which would give you the acceleration of the electron as that due to gravity (with mass of the electron playing no role). | 1,332 | 5,954 | {"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-2017-04 | longest | en | 0.945332 |
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### What is a cubature scheme?
Ideally an intuitive explanation with an example, please. | 491 | 2,345 | {"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} | 2.796875 | 3 | CC-MAIN-2014-49 | longest | en | 0.930919 |
https://math.stackexchange.com/questions/3943569/ols-lad-on-linear-quadratic-programming-type-problem | 1,618,572,976,000,000,000 | text/html | crawl-data/CC-MAIN-2021-17/segments/1618038056325.1/warc/CC-MAIN-20210416100222-20210416130222-00169.warc.gz | 494,866,670 | 37,589 | I have a list of equations that define halfspaces (3 equation list example below)
$$x_1 + x_2 + x_3 + x_5 < x_4 + x_6 + x_7 \\ x_4 + x_6 + x_7 < x_8 + x_9 + x_{21} + x_{43} + x_1 \\ x_4 + x_6 + x_7 < x_1 + x_2 + x_3 + x_5$$
As shown, sometimes this system will not be solvable (I've shown a simple case; in n-dim, it's obvious how this may happen in a more complex way). In this case, I want to find the values of all $$x_n$$ that has the lowest euclidean distance from being viable.
I'm not entirely sure if I want euclidean distance or squared euclidean distance., but my first thoughts jump to OLS, LAD, and linear programming. However, I've always seen OLS/LAD done with a bunch of real number valued points, not to solve a linear programming system.
I also got informed that this may be reformulateable as a classic nonlinear (specifically quadratic) programming problem, although I'm unfamiliar with the space as a whole.
Any ideas on how to best find the values of this system.?
If your problem is defined by $$g_j(x) \le 0, j \in J$$, you want to minimize $$\sum_{j \in J} ||\max(0, g_j(x))||$$ for a given norm.
$$\min_x \sum_{j \in J} \max(0, g_j(x))$$
which is not differentiable. However you can reformulate it into a smooth problem by introducing the variables $$s_j = \max(0, g_j(x))$$:
$$\min_{x, s} \sum_{j \in J} s_j$$
s.t. $$s_j \ge 0, s_j \ge g_j(x)$$
• What is $g_j$ here? – user760900 Dec 10 '20 at 22:55 | 458 | 1,431 | {"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": 8, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.65625 | 4 | CC-MAIN-2021-17 | latest | en | 0.887599 |
http://betterlesson.com/lesson/reflection/8702/bar-diagram | 1,477,579,398,000,000,000 | text/html | crawl-data/CC-MAIN-2016-44/segments/1476988721347.98/warc/CC-MAIN-20161020183841-00007-ip-10-171-6-4.ec2.internal.warc.gz | 27,957,343 | 17,829 | ## Reflection: Modeling Towering Fractions - Section 3: Guided Practice
A bar diagram is a more "mature version" of the part- part-whole model used to teach students addition and subtraction.
In the case of this lesson, the bar diagrams students are creating to organize their thinking is in fact a part part whole model. Students are using fractions, rather than whole numbers.
The reason we call these diagrams bar diagrams and not part-part-whole models is because at this level, the name can become limiting. If a problem requires addition of more than one addend, if repeated addition is used (multiplication), or if a problem is about division. All of these operations can be represented by extending the part-part-whole model. This progression is taught to the students as they learn the new concepts.
Bar Diagram
Modeling: Bar Diagram
# Towering Fractions
Unit 2: Adding and Subtracting Fractions
Lesson 9 of 11
## Big Idea: Today students work to showcase their knowledge of working with fractions with unlike denominators.
Print Lesson
1 teacher likes this lesson
Standards:
Subject(s):
Math, Fractions, problem solving, Critical Area, Literacy in Math
75 minutes | 261 | 1,185 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.390625 | 3 | CC-MAIN-2016-44 | longest | en | 0.928128 |
https://www.physicsforums.com/threads/angle-of-incidence-and-refraction.869756/ | 1,521,569,262,000,000,000 | text/html | crawl-data/CC-MAIN-2018-13/segments/1521257647519.62/warc/CC-MAIN-20180320170119-20180320190119-00740.warc.gz | 850,895,731 | 15,890 | # Angle of incidence and refraction
1. Apr 30, 2016
### Zelko
Hello PF users hope all is well!
I need a reminder of the formulas needed in order to get
"Sine of angle of incidence"
"Sine of angle of refraction"
And "Index of refraction".
The only information I have available now is
"Angle of incidence" And "Angle of refraction"
I'm guessing they're all along the lines of Snell's law
2. May 1, 2016
### drvrm
i hope you wish to know about calculating the refractive index of a medium through the info about angle of incidence and angle of refraction.
what is snell's law? and how it is applied?
and how to calculate sine of an angle.
its simple to draw a right angle triangle with base angle 'equal to angle of your choice' and take the ratio of perpendicular length with hypoteneuse , then you get the sine of that angle.
or go to the trigonometric table of sine of the angles and get values and calculate index of refraction = ratio of sine of the angle of incidence and refraction.
3. May 1, 2016
### Zelko
Thank you for the help, I can clearly recall how to calculate it. | 273 | 1,092 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.765625 | 3 | CC-MAIN-2018-13 | longest | en | 0.896271 |
https://www.unitconverters.net/length/centiinch-to-fermi.htm | 1,571,068,496,000,000,000 | text/html | crawl-data/CC-MAIN-2019-43/segments/1570986653876.31/warc/CC-MAIN-20191014150930-20191014174430-00009.warc.gz | 1,136,748,706 | 4,517 | Home / Length Conversion / Convert Centiinch to Fermi
# Convert Centiinch to Fermi
Please provide values below to convert centiinch [cin] to fermi [F, f], or vice versa.
From: centiinch To: fermi
### Centiinch to Fermi Conversion Table
Centiinch [cin]Fermi [F, F]
0.01 cin2540000000 F, f
0.1 cin25400000000 F, f
1 cin254000000000 F, f
2 cin508000000000 F, f
3 cin762000000000 F, f
5 cin1270000000000 F, f
10 cin2540000000000 F, f
20 cin5080000000000 F, f
50 cin12700000000000 F, f
100 cin25400000000000 F, f
1000 cin2.54E+14 F, f
### How to Convert Centiinch to Fermi
1 cin = 254000000000 F, f
1 F, f = 3.9370078740157E-12 cin
Example: convert 15 cin to F, f:
15 cin = 15 × 254000000000 F, f = 3810000000000 F, f | 279 | 721 | {"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} | 3.203125 | 3 | CC-MAIN-2019-43 | longest | en | 0.380089 |
https://edurev.in/course/quiz/attempt/-1_Test-Signal-Flow-Graphs-2/f0a2df2b-ffd2-4bad-bf7f-8d1e38108c61 | 1,702,052,008,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679100762.64/warc/CC-MAIN-20231208144732-20231208174732-00421.warc.gz | 245,869,493 | 47,705 | Test: Signal Flow Graphs - 2
# Test: Signal Flow Graphs - 2 - Electrical Engineering (EE)
Test Description
## 10 Questions MCQ Test GATE Electrical Engineering (EE) 2024 Mock Test Series - Test: Signal Flow Graphs - 2
Test: Signal Flow Graphs - 2 for Electrical Engineering (EE) 2023 is part of GATE Electrical Engineering (EE) 2024 Mock Test Series preparation. The Test: Signal Flow Graphs - 2 questions and answers have been prepared according to the Electrical Engineering (EE) exam syllabus.The Test: Signal Flow Graphs - 2 MCQs are made for Electrical Engineering (EE) 2023 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Signal Flow Graphs - 2 below.
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Test: Signal Flow Graphs - 2 - Question 1
### Mason's rule is applied to
Detailed Solution for Test: Signal Flow Graphs - 2 - Question 1
Mason's rule or Mason’s gain formula is applied to signal flow graph for finding the transfer function.
Test: Signal Flow Graphs - 2 - Question 2
### Assertion (A): Signal flow graph is applicable to the linear systems. Reason (R): Signal flow graph method of finding the transfer function of a system is very simple and does not require any reduction technique.
Detailed Solution for Test: Signal Flow Graphs - 2 - Question 2
Signal flow graph is applicable to the linear systems because output is proportional to gain of the system
Reason (R) is also true but is not a correct explanation of assertion (A)
Test: Signal Flow Graphs - 2 - Question 3
### Consider the following three cases of signal flow graph and their corresponding transfer functions: Q. Which of the above relations is/are correctly matched?
Detailed Solution for Test: Signal Flow Graphs - 2 - Question 3
Hence, only 1 is correctly matched.
Test: Signal Flow Graphs - 2 - Question 4
The signal flow graph shown below has M number of forward path and N number of individual loops.
Q. What are the values of M and N ?
Detailed Solution for Test: Signal Flow Graphs - 2 - Question 4
There are three forward paths. The gain of the forward path are:
• M1 = G1G2G3G4G5
• M2 = G1G6G4G5
• M3 = G1G2G7
There are four loops with loop gains:
N1= - G4H1
N2= - G2G7H2
N3= - G6G4G5H2
N4= - G2G3G4G5H2
Test: Signal Flow Graphs - 2 - Question 5
The signal flow graph for a certain feedback control system is given below.
Now, consider the following set of equations for the nodes:
1. x2= a1x1+a5x3+a6x4+a7x5
2. x3=a2x
3. x4=a3x
4. x5=a4x4+a8x3
Q. Which of the above equations are correct?
Detailed Solution for Test: Signal Flow Graphs - 2 - Question 5
Correct Answer :- b
Explanation : x2 = a1x1 + a5x3 + a6x4 + a7x5
x3 = a2x2
x4 a3x3 + a9x5
x5 = a4x4 + a8x3
Test: Signal Flow Graphs - 2 - Question 6
The gain C(s)/R(s) of the signal flow graph shown below is
Detailed Solution for Test: Signal Flow Graphs - 2 - Question 6
Gain of forward paths are:
P1 = G1G2G3 and P2 = G4
Here, Δ1 = 1
and Δ2 = (1 + G1G2— G2G3)
Individual loops are:
L1 = -G1G2
and L2 = G2G3
Non-touching loop = Nil
Test: Signal Flow Graphs - 2 - Question 7
The number of forward paths and the number of non-touching loop pairs for the signal flow graph shown in the figure below are respectively
Detailed Solution for Test: Signal Flow Graphs - 2 - Question 7
Forward paths are
P1 = G1G2G3 and P2 = G3G4
Gain product of non-touching loop pairs are:
L1 L2 = G1H1H4
and L1L3 = G1G3H1H2
Thus, there are two forward paths and two non touching loop pairs
Test: Signal Flow Graphs - 2 - Question 8
The signal flow graph of the RLC circuit of figure (i) is shown in figure (ii)
The values of G1 and H1 are respectively
Detailed Solution for Test: Signal Flow Graphs - 2 - Question 8
Converting the given circuit in s-domain and writing the equations, we get:
Also, from given SFG, we have
Test: Signal Flow Graphs - 2 - Question 9
The closed loop transfer function CIR for the signal graph shown below is
Detailed Solution for Test: Signal Flow Graphs - 2 - Question 9
Number of forward paths are two,
Test: Signal Flow Graphs - 2 - Question 10
Consider the following statements with regards to the signal flow graph shown below.
1. The number of forward paths are 2.
2. The number of forward paths are 5.
3. The number of loops are 3.
4. The number of loops are 5,
5. The number of non-touching loop pairs is 1.
6. The number of non-touching loop pairs is nil.
Q. Which of these statements are correct?
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## GATE Electrical Engineering (EE) 2024 Mock Test Series
23 docs|285 tests | 1,570 | 5,685 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.03125 | 3 | CC-MAIN-2023-50 | latest | en | 0.863757 |
http://en.wikipedia.org/wiki/Adler-32 | 1,438,172,123,000,000,000 | text/html | crawl-data/CC-MAIN-2015-32/segments/1438042986423.95/warc/CC-MAIN-20150728002306-00096-ip-10-236-191-2.ec2.internal.warc.gz | 83,208,496 | 11,960 | Adler-32 is a checksum algorithm which was invented by Mark Adler in 1995,[1] and is a modification of the Fletcher checksum. Compared to a cyclic redundancy check of the same length, it trades reliability for speed (preferring the latter). Adler-32 is more reliable than Fletcher-16, and slightly less reliable than Fletcher-32.[2]
History
The Adler-32 checksum is part of the widely used zlib compression library, as both were developed by Mark Adler. A "rolling checksum" version of Adler-32 is used in the rsync utility.
The algorithm
An Adler-32 checksum is obtained by calculating two 16-bit checksums A and B and concatenating their bits into a 32-bit integer. A is the sum of all bytes in the stream plus one, and B is the sum of the individual values of A from each step.
At the beginning of an Adler-32 run, A is initialized to 1, B to 0. The sums are done modulo 65521 (the largest prime number smaller than 216). The bytes are stored in network order (big endian), B occupying the two most significant bytes.
The function may be expressed as
```A = 1 + D1 + D2 + ... + Dn (mod 65521)
B = (1 + D1) + (1 + D1 + D2) + ... + (1 + D1 + D2 + ... + Dn) (mod 65521)
= n×D1 + (n−1)×D2 + (n−2)×D3 + ... + Dn + n (mod 65521)
Adler-32(D) = B × 65536 + A
```
where D is the string of bytes for which the checksum is to be calculated, and n is the length of D.
Example
The Adler-32 sum of the ASCII string "`Wikipedia`" would be calculated as follows:
Character ASCII code A B
(shown as base 10)
W 87 1 + 87 = 88 0 + 88 = 88
i 105 88 + 105 = 193 88 + 193 = 281
k 107 193 + 107 = 300 281 + 300 = 581
i 105 300 + 105 = 405 581 + 405 = 986
p 112 405 + 112 = 517 986 + 517 = 1503
e 101 517 + 101 = 618 1503 + 618 = 2121
d 100 618 + 100 = 718 2121 + 718 = 2839
i 105 718 + 105 = 823 2839 + 823 = 3662
a 97 823 + 97 = 920 3662 + 920 = 4582
```A = 920 = 398 hex (base 16)
B = 4582 = 11E6 hex
Output = 4,582 × 65,536 + 920 = 300286872 = 11E60398 hex
```
The modulo operation had no effect in this example, since none of the values reached 65521.
Comparison with the Fletcher checksum
The first difference between the two algorithms is that Adler-32 sums are calculated modulo a prime number, whereas Fletcher sums are calculated modulo 24−1, 28−1, or 216−1 (depending on the number of bits used), which are all composite numbers. Using a prime number makes it possible for Adler-32 to catch differences in certain combinations of bytes that Fletcher is unable to detect.
The second difference, which has the largest effect on the speed of the algorithm, is that the Adler sums are computed over 8-bit bytes rather than 16-bit words, resulting in twice the number of loop iterations. This results in the Adler-32 checksum taking between one-and-a-half to two times as long as Fletcher's checksum for 16-bit word aligned data. For byte-aligned data, Adler-32 is faster than a properly implemented Fletcher's checksum (e.g., one found in the Hierarchical Data Format).
Example implementation
In C, an inefficient but straightforward implementation is :
```const int MOD_ADLER = 65521;
uint32_t adler32(unsigned char *data, size_t len) /* where data is the location of the data in physical memory and
len is the length of the data in bytes */
{
uint32_t a = 1, b = 0;
size_t index;
/* Process each byte of the data in order */
for (index = 0; index < len; ++index)
{
a = (a + data[index]) % MOD_ADLER;
b = (b + a) % MOD_ADLER;
}
return (b << 16) | a;
}
```
See the zlib source code for a more efficient implementation that requires a fetch and two additions per byte, with the modulo operations deferred with two remainders computed every several thousand bytes.
• Like the standard CRC-32, the Adler-32 checksum can be forged easily and is therefore unsafe for protecting against intentional modification.
• It's faster than CRC-32 on many platforms.[3]
• Adler-32 has a weakness for short messages with few hundred bytes, because the checksums for these messages have a poor coverage of the 32 available bits.
Weakness
Adler-32 is weak for short messages because the sum A does not wrap. The maximum sum of a 128-byte message is 32640, which is below the value 65521 used by the modulo operation, meaning that roughly half of the output space is unused, and the distribution within the used part is nonuniform. An extended explanation can be found in RFC 3309, which mandates the use of CRC32C instead of Adler-32 for SCTP, the Stream Control Transmission Protocol.[4] Adler-32 has also been shown to be weak for small incremental changes,[5] and also weak for strings generated from a common prefix and consecutive numbers (like auto-generated label names by typical code generators).[6] | 1,288 | 4,705 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.25 | 3 | CC-MAIN-2015-32 | latest | en | 0.880606 |
https://api-project-1022638073839.appspot.com/questions/how-do-you-integrate-int-1-x-3dx | 1,725,808,882,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651013.49/warc/CC-MAIN-20240908150334-20240908180334-00323.warc.gz | 90,715,692 | 6,064 | # How do you integrate int 1/x^3dx?
Nov 5, 2016
Rewrite as $\int {x}^{-} 3 \mathrm{dx}$ and take the anti-derivative.
#### Explanation:
We first need to recognize that $\frac{1}{x} ^ 3$ is equivalent to ${x}^{-} 3$.
Once we get that far, the problem becomes quite simple to solve.
Do be careful, however, as we are dealing with a negative exponent, so when we add one to the power as we take the anti-derivative, the magnitude of the power will decrease. This also means that our constant will have to be negative as well, since the x term in the integral is positive. Taking the anti-derivative, we get:
$- \frac{1}{2} \cdot {x}^{-} 2 + C$
This is equivalent to $- \frac{1}{2 {x}^{2}} + C$
As usual, you can check this answer by taking the derivative, which gives you ${x}^{-} 3$. | 233 | 790 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 6, "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} | 4.3125 | 4 | CC-MAIN-2024-38 | latest | en | 0.942481 |
https://tickertape.tdameritrade.com/trading/portfolio-margin-profit-loss-expiration-16036 | 1,713,628,402,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296817670.11/warc/CC-MAIN-20240420153103-20240420183103-00391.warc.gz | 523,783,556 | 16,761 | # Capiche? Portfolio Margin Part 3: Profit, Loss, and Expiration
Photo by Fredrik Brodén
Continuing our portfolio margin (PM) series, let’s look at how profit and loss are calculated, and what can be expected at option expiration.
In a PM account, a position’s margin requirement is based on two things. One, how much the position might lose if the price of its underlying changes by some percentage. And two, whether volatility, that is, uncertainty about changes in a stock's value, moves. This is a stress test, which is why knowing how to calculate profit and loss (P/L), and understanding what happens to an option position at expiration, are important.
## Figuring It Out
Here’s an example to help explain P/L. Say you buy one share of XYZ at \$50. If the price rises to \$51, you can make a \$1 profit. If the price drops to \$49, you lose \$1. Multiply that profit or loss by the number of shares you own, and you have the total P/L.
Now, PM tests the P/L if the underlying changes. In other words, what’s the P/L if XYZ drops 15%? If you're long 100 shares of XYZ at \$50, and XYZ drops 15%, the price of XYZ drops by \$7.50 (\$50 x 15%) and goes from \$50 to \$42.50. The loss on 100 shares would be \$750.
P/L for options works the same way, except that for most equity options, when the option price changes \$1, the P/L changes \$100 because of the option’s 100 contract multiplier. So if you buy one 50-strike call on XYZ for \$3, and the value of the option drops to \$2, the loss is \$1 x 100, or \$100. If the call option rises from \$3 to \$3.50, the profit would be \$50.
## Reality At Expiration
The PM algorithm calculates the theoretical value for the options in the account positions. It comes up with a theoretical P/L based on changes in the underlying price and volatility. You don't need to figure this out, but you should know that at expiration, an option will either be out of the money (OTM) and worthless, or in the money (ITM) and worth its intrinsic value (difference between stock price and option's strike price).
Remember, the intrinsic value of a call is the prevailing stock price minus the call’s stock price. The intrinsic value of a put is the put’s strike price minus the prevailing stock price.
For example, if you buy a 50-strike call for \$3, and the stock is \$49 at expiration, the 50-strike call is OTM, which means it’s worthless at that time. The P/L would be (\$0 – \$3) x 100 = \$300 loss.
If you buy a 50-strike call for \$3 and the stock is \$52 at expiration, the call will have \$2 of intrinsic value. The P/L on the long call would be (\$2 – \$3) x 100 = \$100 loss. If the stock is \$55 at expiration, the call will have \$5 of intrinsic value. The P/L on the long call would be (\$5 – \$3) x \$100 = \$200 profit.
## Exercised Or Assigned?
These P/L calculations assume you close the ITM option position at expiration. If an option is ITM at expiration, and is not closed before the close of trading, it will likely be exercised or assigned and turned into stock. ITM long calls and short puts turn into long stock, while ITM short calls and long puts turn into short stock. If the stock is exactly at the strike price at expiration, it’s not automatically exercised or assigned. In this case, if you’re long that option, you’ll have to notify your broker of the intention to exercise it. And the person who’s short that option doesn’t know if it will be assigned because it depends on whether or not the long option holder exercises it.
Now that you have some idea of how theoretical P/L is calculated in a PM account, you’ll know what to keep an eye on as your option approaches expiration. Don’t end up owning something you didn’t want.
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Thomas Preston is not a representative of TD Ameritrade, Inc. The material, views, and opinions expressed in this article are solely those of the author and may not be reflective of those held by TD Ameritrade, Inc. | 1,102 | 4,792 | {"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} | 3.453125 | 3 | CC-MAIN-2024-18 | latest | en | 0.904054 |
http://docs.w3cub.com/tensorflow~guide/tutorials/linear/ | 1,539,954,464,000,000,000 | text/html | crawl-data/CC-MAIN-2018-43/segments/1539583512400.59/warc/CC-MAIN-20181019124748-20181019150248-00512.warc.gz | 105,702,183 | 6,120 | # W3cubDocs
/TensorFlow Guide
# Large-scale Linear Models with TensorFlow
The tf.estimator API provides (among other things) a rich set of tools for working with linear models in TensorFlow. This document provides an overview of those tools. It explains:
• what a linear model is.
• why you might want to use a linear model.
• how tf.estimator makes it easy to build linear models in TensorFlow.
• how you can use tf.estimator to combine linear models with deep learning to get the advantages of both.
Read this overview to decide whether the tf.estimator linear model tools might be useful to you. Then do the Linear Models tutorial to give it a try. This overview uses code samples from the tutorial, but the tutorial walks through the code in greater detail.
To understand this overview it will help to have some familiarity with basic machine learning concepts, and also with tf.estimator.
## What is a linear model?
A linear model uses a single weighted sum of features to make a prediction. For example, if you have data on age, years of education, and weekly hours of work for a population, you can learn weights for each of those numbers so that their weighted sum estimates a person's salary. You can also use linear models for classification.
Some linear models transform the weighted sum into a more convenient form. For example, logistic regression plugs the weighted sum into the logistic function to turn the output into a value between 0 and 1. But you still just have one weight for each input feature.
## Why would you want to use a linear model?
Why would you want to use so simple a model when recent research has demonstrated the power of more complex neural networks with many layers?
Linear models:
• train quickly, compared to deep neural nets.
• can work well on very large feature sets.
• can be trained with algorithms that don't require a lot of fiddling with learning rates, etc.
• can be interpreted and debugged more easily than neural nets. You can examine the weights assigned to each feature to figure out what's having the biggest impact on a prediction.
• provide an excellent starting point for learning about machine learning.
• are widely used in industry.
You can build a linear model from scratch in TensorFlow without the help of a special API. But tf.estimator provides some tools that make it easier to build effective large-scale linear models.
### Feature columns and transformations
Much of the work of designing a linear model consists of transforming raw data into suitable input features. Tensorflow uses the `FeatureColumn` abstraction to enable these transformations.
A `FeatureColumn` represents a single feature in your data. A `FeatureColumn` may represent a quantity like 'height', or it may represent a category like 'eye_color' where the value is drawn from a set of discrete possibilities like {'blue', 'brown', 'green'}.
In the case of both continuous features like 'height' and categorical features like 'eye_color', a single value in the data might get transformed into a sequence of numbers before it is input into the model. The `FeatureColumn` abstraction lets you manipulate the feature as a single semantic unit in spite of this fact. You can specify transformations and select features to include without dealing with specific indices in the tensors you feed into the model.
#### Sparse columns
Categorical features in linear models are typically translated into a sparse vector in which each possible value has a corresponding index or id. For example, if there are only three possible eye colors you can represent 'eye_color' as a length 3 vector: 'brown' would become [1, 0, 0], 'blue' would become [0, 1, 0] and 'green' would become [0, 0, 1]. These vectors are called "sparse" because they may be very long, with many zeros, when the set of possible values is very large (such as all English words).
While you don't need to use categorical columns to use tf.estimator linear models, one of the strengths of linear models is their ability to deal with large sparse vectors. Sparse features are a primary use case for the tf.estimator linear model tools.
##### Encoding sparse columns
`FeatureColumn` handles the conversion of categorical values into vectors automatically, with code like this:
```eye_color = tf.feature_column.categorical_column_with_vocabulary_list(
"eye_color", vocabulary_list=["blue", "brown", "green"])
```
where `eye_color` is the name of a column in your source data.
You can also generate `FeatureColumn`s for categorical features for which you don't know all possible values. For this case you would use `categorical_column_with_hash_bucket()`, which uses a hash function to assign indices to feature values.
```education = tf.feature_column.categorical_column_with_hash_bucket(
"education", hash_bucket_size=1000)
```
##### Feature Crosses
Because linear models assign independent weights to separate features, they can't learn the relative importance of specific combinations of feature values. If you have a feature 'favorite_sport' and a feature 'home_city' and you're trying to predict whether a person likes to wear red, your linear model won't be able to learn that baseball fans from St. Louis especially like to wear red.
You can get around this limitation by creating a new feature 'favorite_sport_x_home_city'. The value of this feature for a given person is just the concatenation of the values of the two source features: 'baseball_x_stlouis', for example. This sort of combination feature is called a feature cross.
The `crossed_column()` method makes it easy to set up feature crosses:
```sport_x_city = tf.feature_column.crossed_column(
["sport", "city"], hash_bucket_size=int(1e4))
```
#### Continuous columns
You can specify a continuous feature like so:
```age = tf.feature_column.numeric_column("age")
```
Although, as a single real number, a continuous feature can often be input directly into the model, Tensorflow offers useful transformations for this sort of column as well.
##### Bucketization
Bucketization turns a continuous column into a categorical column. This transformation lets you use continuous features in feature crosses, or learn cases where specific value ranges have particular importance.
Bucketization divides the range of possible values into subranges called buckets:
```age_buckets = tf.feature_column.bucketized_column(
age, boundaries=[18, 25, 30, 35, 40, 45, 50, 55, 60, 65])
```
The bucket into which a value falls becomes the categorical label for that value.
#### Input function
`FeatureColumn`s provide a specification for the input data for your model, indicating how to represent and transform the data. But they do not provide the data itself. You provide the data through an input function.
The input function must return a dictionary of tensors. Each key corresponds to the name of a `FeatureColumn`. Each key's value is a tensor containing the values of that feature for all data instances. See Building Input Functions with tf.estimator for a more comprehensive look at input functions, and `input_fn` in the linear models tutorial code for an example implementation of an input function.
The input function is passed to the `train()` and `evaluate()` calls that initiate training and testing, as described in the next section.
### Linear estimators
Tensorflow estimator classes provide a unified training and evaluation harness for regression and classification models. They take care of the details of the training and evaluation loops and allow the user to focus on model inputs and architecture.
To build a linear estimator, you can use either the `tf.estimator.LinearClassifier` estimator or the `tf.estimator.LinearRegressor` estimator, for classification and regression respectively.
As with all tensorflow estimators, to run the estimator you just:
1. Instantiate the estimator class. For the two linear estimator classes, you pass a list of `FeatureColumn`s to the constructor.
2. Call the estimator's `train()` method to train it.
3. Call the estimator's `evaluate()` method to see how it does.
For example:
```e = tf.estimator.LinearClassifier(
feature_columns=[
native_country, education, occupation, workclass, marital_status,
race, age_buckets, education_x_occupation,
age_buckets_x_race_x_occupation],
model_dir=YOUR_MODEL_DIRECTORY)
e.train(input_fn=input_fn_train, steps=200)
# Evaluate for one step (one pass through the test data).
results = e.evaluate(input_fn=input_fn_test)
# Print the stats for the evaluation.
for key in sorted(results):
print("%s: %s" % (key, results[key]))
```
### Wide and deep learning
The tf.estimator API also provides an estimator class that lets you jointly train a linear model and a deep neural network. This novel approach combines the ability of linear models to "memorize" key features with the generalization ability of neural nets. Use `tf.estimator.DNNLinearCombinedClassifier` to create this sort of "wide and deep" model:
```e = tf.estimator.DNNLinearCombinedClassifier(
model_dir=YOUR_MODEL_DIR,
linear_feature_columns=wide_columns,
dnn_feature_columns=deep_columns,
dnn_hidden_units=[100, 50])
``` | 1,905 | 9,170 | {"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} | 2.609375 | 3 | CC-MAIN-2018-43 | latest | en | 0.924769 |
https://cs.stackexchange.com/questions/19976/creating-admissible-heuristics-from-functions | 1,582,389,292,000,000,000 | text/html | crawl-data/CC-MAIN-2020-10/segments/1581875145708.59/warc/CC-MAIN-20200222150029-20200222180029-00196.warc.gz | 327,270,851 | 35,098 | # Creating admissible heuristics from functions?
I'm having trouble figuring out how to create admissible heuristics from cost functions. For example, if I was trying to create an admissible heuristic from a cost function that takes in starting position and ending position and returns the cost based on differences in height, I don't understand how to create an admissible heuristic from such a basic function.
Any help would be greatly appreciated.
Most beginners in the field see heuristics construction more as an art than a science. While I am not claiming here that there is a truly scientific (or even computable) method to derive them, I am sure they are not an art and we know about specific procedures to derive them (some of which are truly computable). In any case, we do not consider the differences in cost between the goal and start states as you suggest in the question. In all cases, admissible heuristics are obtained after relaxing any component in the problem formulation.
Let me just introduce you to three different methods to compute admissible heuristics: constraint relaxation, pattern databases and max heuristics. First, I will just introduce the overall idea. Next, I will provide further details of every technique. I will try to mention also some of the most relevant works that went along any of these lines including merge-and-shrink and Linear Programming.
In all cases, I will refer to the definition of state spaces which consist of two main ingredients:
• States: they are defined by any structure that represents the contents of either the start or final state (denoted as $s$ or $t$ respectively) or any other configuration.
• Operators: computable functions that are used to derive the immediately reachable descendants of a given state
Also, I will be using the $N$-puzzle as a running example. The proper definition of a state space in the $N$-puzzle is as follows:
• States: they are defined by a permutation $\pi$ of symbols such that $\pi[i]$ represents the contents of location $i$
• Operators: there is only one move (i,j) which swaps the contents of locations $i$ and $j$ provided that $\pi[i]=0$ (i.e., the blank location) and that $i$ and $j$ are either vertically or horizontally adjacent.
Please, be aware of the following: these techniques are not so simple that I could fully explain them in detail in a single response so that, unfortunately, my explanations will be rather incomplete
Constraint relaxation [Judea Pearl. Heuristics. Addison-Wesley, 1984] Judea Pearl proposed to pay attention to the constraints of the problem (and there should be some, otherwise we would not have an optimization problem), and then to relax a subset of them so that the resulting problem could be optimally solved. The optimal cost of the so-called relaxed problem can be easily proved to be an admissible estimate to reach the goal state. The constraints are usually found (but not only) in the pre-conditions implemented in the operators.
Take the $N$-puzzle. In this case, the constraints are found in the operator move. How would you program such a function? Well, most likely you would verify that $\pi[i]=0$ (i.e., $i$ is the blank location) and that $i$ and $j$ are either vertically or horizontally adjacent locations. Now, select either one of these constraints or both and relax them.
For example, relax both and consider now the resulting (relaxed) problem. For any state, how many moves does it take to get to the target node? If you are not constrained (and this is the point) to consider adjacent locations or the fact that you have to move the blank then you can swap any pair of locations. The optimal solution of the relaxed problems consists just of swapping the misplaced tiles.
Another example, relax only the first one. In this case, you are forced to swap adjacent locations but you are free to ignore the role of the blank tile. Clearly, the optimal solution consists of the sum of the minimum number of horizontal and vertical moves to place every misplaced tile in its goal location. This is known as the Manhattan distance.
In general, the heuristics that relax less constraints produce better estimations and are prefered.
Pattern databases [Culberson, J. C., Schaeffer, J. 1998. Pattern Databases. Computational Intelligence 14(3): 318-334] Constraint relaxation is just a general procedure that you, as an optimizer, have to follow in order to derive an admissible heuristic that you hard-code in your programs. Pattern databases are, instead, computable means to derive automatically the heuristic value of a lot of different configurations which are then stored in a large table.
I will not go here through more detailed explanations and I do suggest you instead to have a look at Need a practical solution for creating pattern database(5-5-5) for 15-Puzzle I am also providing a reply there but I do strongly suggest you to have a look at the response by Shashwat which is more detailed and uses the $N$-puzzle instead for explaining the main ideas. If you are interested in getting the source code for creating Pattern Databases, please e-mail me (carlos.linares@uc3m.es).
In case you are interested in the current state of the art of admissible heuristics in Automated Planning (introduced next) I do recommend you to have a look at merge-and-shrink (which do generalize Pattern Databases). A nice discussion is offered in: Malte Helmert, Patrik Haslum, Jörg Hoffmann and Raz Nissim. Merge-and-Shrink Abstraction: A Method for Generating Lower Bounds in Factored State Spaces. Journal of the ACM. 2013 (which was accepted at the time of writing but has not seen the light yet as far as I know).
Also, there has been some work on using Linear Programming Tasks to get the optimal cost of the relaxed problems:
(NOTE: all this people are really nice, so that if you contact them to get a copy of the paper to appear it is very likely that they will send it to you. The other option is to wait for ICAPS 2014 to take place and then to download the papers: they are absolutely free).
Note please that, in this context, Linear Programming Tasks are used just to derive optimal costs of the relaxed problems precisely in the same way noted by Raphael: you first relax some constraints (according to any procedure) and then you set up a LP task to derive the optimal cost. I do fully believe that this is a hot topic in the field that will get more and more attention.
Max heuristics [Blai Bonet and Héctor Geffner. Planning as Heuristic Search: New Results. Proc. 5th European Conf. on Planning (ECP). Durham, UK. 1999. Springer LNCS 1809. Pages 359-371] The two previous methods for deriving (either automatically or not) admissible heuristics were motivated by the need of creating domain-dependent solvers. However, what if you want to create a single solver that is expected to optimall solve any problem (with some constraints, of course, and not just saying that "The Answer to life, the universe and everything is 42" :) )? This field is known as Automated Planning In this case we relax the reachability analysis by ignoring the delete effects (i.e., the fact that when swapping two locations they are removed from their initial locations; indeed, they are preserved so that the same tile appears in various places at the same time in the relaxed problem).
We just assume that all actions can be executed in parallel and compute the minimum cost to reach every literal (i.e., any atomic observation of our state formulation such as tile 6 is in location 2) from any other literal. You can certainly assume that actions have to be executed in sequence. In this case, the resulting heuristic is known as h add but it is not admissible so I left out of the discussion.
I am just leaving a lot of details out of the discussion here and I do recommend you to have a look at the paper I am just referencing. This is a simple, very simple idea.
Hope all of this helps,
• Arguably, one of the most famous strategies for relaxation is to set up an IP for the problem and relax it to an LP. This strategy even provides approximations now and then. – Raphael Jan 26 '14 at 11:46
• I would not say "arguably". As a matter of fact, using Linear Programming Tasks is becoming more and more effective for solving really hard problems where other heuristics do not work as expected. Your comment is very relevant so that I updated my answer in the light of your comment. – Carlos Linares López Jan 26 '14 at 14:27
• I'm familiar with admissible heuristics, I just don't see how to generate admissible heuristics from functions (i.e. the example I mentioned) – user13134 Jan 28 '14 at 20:00
• Sorry then I misunderstood you. As far as I know (as I mention at the beginning of my response) I am not aware of any admissible heuristics that are computed from the differences of functions (unless they've been relaxed, of course). Could you please elaborate a little bit more? Maybe indicating a particular domain along with heuristic functions computed that way? Cheers, – Carlos Linares López Jan 29 '14 at 7:29 | 1,998 | 9,092 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.53125 | 4 | CC-MAIN-2020-10 | latest | en | 0.946018 |
https://www.biguniverse.com/library/books?category%3AGenre=Numbers+%26+Concepts&category%3AGrade=3rd+Grade&publisher=Sleeping+Bear+Press | 1,553,628,069,000,000,000 | text/html | crawl-data/CC-MAIN-2019-13/segments/1552912205600.75/warc/CC-MAIN-20190326180238-20190326202238-00283.warc.gz | 688,453,373 | 14,013 | ## T is for Time
###### Marie Smith Roland Smith (author), Rene Graef (illustrator)
Publisher: Sleeping Bear Press ISBN: 9781633621299
T is for a Time Alphabet uses poetry and expository text to explore the concept of time, from explaining basic units of measurement to showcasing important scientific achievements. Topics include famous inventors (Albert Einstein and John Harrison) and important structures and landmarks (Kulkulkan Pyramid and Big Ben). Budding scientists will discover what world-famous stone structure is believed to be an early calendar, follow the voyages of explorer Ferdinand Magellan to better understand the International Date Line, and learn to tell time using the Zulu time system.
## Whole-y Cow!: Fractions Are Fun
###### Taryn Souders (author), Tatjana Mai-Wyss (illustrator)
Publisher: Sleeping Bear Press ISBN: 9781585366231
Learning about fractions isn't always easy, but who says it can't be fun? Using one very entertaining cow, math teacher Taryn Souders has devised a very clever (and fun) way of explaining fractions to beginning learners. One whole cow, calmly eating hay, decided to act differently on this particular day. One whole cow - what should we do? I know! Let's paint one half blue! Prompted by a poem and a visual clue, students are asked to answer what fraction is illustrated in the cow's antics, starting with halves and progressing into thirds, fourths, eighths, and tenths. What fraction of the cow is blue? Answer: What fraction of the cow is white? Answer: With the math problem featured as part of the artwork, students get an immediate sense of how to apply and understand the concept of fractions. How moo-velous! Taryn J. Souders lives in Winter Park, Florida. With a background in math education, she is passionate about keeping math fun for young students. This is her first children's book. Tatjana Mai-Wyss was born in Switzerland. She remembers learning about fractions with the help of a typical Swiss cake. Tatjana has illustrated several children's books and her work has been published in books and magazines in the United States and abroad. She lives in South Carolina.
## One Kansas Farmer: A Kansas Number Book
###### Devin Scillian (author), Doug Bowles (illustrator)
Publisher: Sleeping Bear Press ISBN: 9781585365951
Following the success of S is for Sunflower: A Kansas Alphabet, husbandand- wife author team Devin and Corey Scillian join illustrator Doug Bowles in another rousing state tribute. One Kansas Farmer: A Kansas Number Book "counts out" an entertaining and educational travelogue of the state's history, geography, famous people, and places. Topics include the dancing prairie chickens and the invention of the microchip. Corey and Devin Scillian are graduates of the University of Kansas. They now live in Michigan where Devin anchors the news for WDIV-TV in Detroit. Devin's other children's books include the bestselling A is for America: An American Alphabet and Brewster the Rooster. Doug Bowles enjoys working with a wide range of clients in advertising, corporate, and editorial jobs, as well as in the children's book market. He also enjoys working on fine art collections and shows frequently in galleries around Kansas. Doug lives in Leawood, Kansas.
## H is for Hockey: A NHL Alumni Alphabet
###### Kevin Shea (author), Ken Dewar (illustrator)
Publisher: Sleeping Bear Press ISBN: 9781627531009
Where was the first organized indoor hockey game played? When did the tradition of engraving winners' names on the Stanley Cup start? Which six brothers collectively played in more than 5,000 NHL games? Answers to these questions and many more can be found in H is for Hockey: An NHL Alumni Alphabet. Formed in 1999, the National Hockey League Alumni Association is affectionately known as "Hockey's Greatest Family" for good reason. Members of the NHL Alumni are considered hockey ambassadors, supporting the game and its history through many charitable causes and programs. Written by one of the game's foremost historians, this book pays tribute to them and the sport they love. Adding a personal touch are the memorable quotes sprinkled throughout the text. When 17-year-old Sidney Crosby was drafted by the Pittsburgh Penguins in 2005, he said, "This is amazing. It's been a lot of hard work and a lot of sacrifices. It's unbelievable!"
## Number 1 Teacher: A School Counting Book
###### Steven L. Layne (author), Deborah Dover Layne (illustrator)
Publisher: Sleeping Bear Press ISBN: 9781627536424
From the five lines on a music staff to the seven colors of the rainbow, all the way up to the famous 100th day of school, Number 1 Teacher: A School Counting Book takes a by-the-numbers approach to helping young readers understand and identify many of the concepts and lessons they'll learn in elementary school. There are 3 forms of matter we learn in science class-- One is liquid; two is solid; and the third is gas. Geography, music, and how to tell time are just a few of the many topics featured. From the husband-and-wife writing team who brought us T is for Teacher: A School Alphabet now comes Number 1 Teacher to help students focus on what counts to make the most of their school days.Steven L. and Deborah Dover Layne also wrote the popular T is for Teachers: A School Alphabet, which received a Learning magazine Teachers' Choice Award for Children's Books. Well-regarded educators and literacy consultants, the Laynes live with their young children in St. Charles, Illinois. Doris Ettlinger graduated from the Rhode Island School of Design and has numerous picture books to her credit. Her other books with Sleeping Bear Press include T is for Teachers and most recently, The Orange Shoes. Doris lives, draws, and teaches in an old grist mill on the banks of the Musconetcong River in western New Jersey.
## Fishing for Numbers: A Maine Number Book
###### Cynthia Furlong Reynolds (author), Jeannie Brett (illustrator)
Publisher: Sleeping Bear Press ISBN: 9781627531245
Our next stop as we Count Our Way Across the USA is to Maine where we can listen to the call of the loon, hike through the Eastern white pine forests, or enjoy a clambake at the beach while watching whales splash in the ocean. Fishing for Numbers is packed with enough Maine facts, lore, and history to keep readers fishing for hours. Readers will learn why Maine is known for their shipbuilders, how fast a puffin can fly, and which is the only domestic cat native to North America. There is even a recipe for a traditional baked bean supper. Cynthia Reynolds, author of L is for Lobster: A Maine Alphabet, is an eleventh-generation Maine native. She summers on Pleasant River Lake in Maine. The rest of the year she dreams of Maine from her home outside Ann Arbor. Jeannie Brett has illustrated several books including L is for Lobster: A Maine Alphabet. She lives in York, Maine.
## M is for Money: An Economics Alphabet
###### Debbie Shoulders, Michael Shoulders (author), Marty Kelley (illustrator)
Publisher: Sleeping Bear Press ISBN: 9781634704274
This alphabet book brings the topic of economics down to a child's level, using tangible examples and scenarios to explain complex ideas. M is for Money uses snappy rhymes and expository text to introduce subjects ranging from supply and demand to taxes. Dynamic and witty artwork brings each topic to life.
## Zero, Zilch, Nada: Counting to None
###### Wendy Ulmer (author), Laura Knorr (illustrator)
Publisher: Sleeping Bear Press ISBN: 9781585365760
Harry is excited! Today is the first day at his new job at the Four Color Balloon Factory. Harry loves balloons almost more than anything! When Mr. Huffy, his new boss, tells him to blow up 100 balloons for Mrs. Doopido's birthday party, Harry can't wait to get started. But when Harry wants to make sure he has the correct number of balloons for the birthday party, counting the balloons gets confusing. And no matter what he does, the number still comes out wrong. What is the best way to count to 100? Colorful illustrations and a clever storyline will help young readers figure out what Harry needs to do to solve his math dilemma. A former music and English teacher, Wendy Ulmer was inspired to write Zero, Zilch, Nada because of her own "math phobia" and struggles with math as a child. She also wrote A Isn't for Fox: An Isn't Alphabet. Wendy lives in Arrowsic, Maine. Laura Knorr is also the illustrator of the popular holiday title, The Legend of Papa Nol. Zero, Zilch, Nada is her second book with Wendy Ulmer and her fifth book with Sleeping Bear Press. Laura lives in Commerce, Georgia.
## Full Count: A Baseball Number Book
###### Brad Herzog (author), Bruce Langton (illustrator)
Publisher: Sleeping Bear Press ISBN: 9781585365975
Following his H is for Home Run: A Baseball Alphabet, Brad Herzog once again steps to the plate to bring the game of baseball to fans of every age. Using numbers as its backdrop, Full Count: A Baseball Number Book goes behind the batter's box and into the dugout to explain game basics and showcase historic moments. Starting with the signal for a fastball (1), to the miles-per-hour speed on some of the fastest pitches ever thrown (100+), Full Count counts out the players, the plays, and pulse-stopping moments in America's favorite sport. Brad Herzog has won several awards from the Council for the Advancement and Support of Education. He has published more than two dozen books, including his sports alphabet books, H is for Home Run: A Baseball Alphabet and K is for Kick: A Soccer Alphabet. Brad lives on California's Monterey Peninsula. Following successful careers as a commercial illustrator and a wildlife artist, Bruce Langton started illustrating children's books. His books include P is for Putt: A Golf Alphabet and Win One for the Gipper: America's Football Hero. Bruce lives in Granger, Indiana.
## Hat Tricks Count: A Hockey Number Book
###### Matt Napier (author), Melanie Rose (illustrator)
Publisher: Sleeping Bear Press ISBN: 9781627531900
The companion volume to our bestselling, Blue Spruce Award winner, Z is for Zamboni: A Hockey Alphabet. Like our alphabet series our counting books are written in a two-tier format with charming poems for young readers and expository text for older readers. Young sports fans see numbers everywhere--the scoreboard, the retired jerseys in the rafters, the numerology of sports stats--and Hat Tricks Count: A Hockey Number Book delivers them faster than an assist from the Great One, number 99 himself. Hat Tricks Count will answer many of the fast paced questions kids have. What is a Hat Trick, anyway? Cross checking, high sticking, and hooking penalties add up to what? Who scored more career goals--Gordie Howe or Wayne Gretzky?
## Times Square: A New York Number Book
###### Ann E. Burg (author), Maureen K. Brookfield (illustrator)
Publisher: Sleeping Bear Press ISBN: 9781627531368
A perfect companion to our "E is for Empire: A New York State Alphabet", "Times Square: A New York State Number Book" teaches children about numbers, using state landmarks, historical events, and famous faces; from finger lakes to the stitches on a baseball, readers of all ages will know the number they represent and their ties to New York. There are so many number questions to answer about New York State. Where do the two lions -- Patience and Fortitude -- reside? Can you name the six major Finger Lakes? Can you name the five boroughs of New York City? Ann E. Burg is the author of E is for Empire: A New York State Alphabet. She lives in Albany, New York. Maureen K. Brookfield has illustrated several books including E is for Empire: A New York State Alphabet. She lives in Marshfield, Massachusetts.
## No Year of the Cat
###### Mary Dodson Wade (author), Nicole Wong (illustrator)
Publisher: Sleeping Bear Press ISBN: 9781627531078
The Emperor has a problem. He wants his people to remember the year in which his son was born. But there is no way to keep track of the years. So the Emperor devises a race in which animals will cross a river. The first twelve animals to reach the opposite side will have a year named after them. Thus, the people will be able to remember the years and the events that occurred. And so the race is set. Rat, knowing he is no match for the rushing water, schemes with Cat on how to cross the river. Together the two convince Ox to carry them across. But halfway across the river, Rat shows his true colors. Will Cat make it to the other side? Which animals will have a year named after them? Accompanied by exquisite watercolor artwork, this charming story explains the origins of the Chinese calendar. | 2,764 | 12,684 | {"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-2019-13 | latest | en | 0.936931 |
https://justpaste.it/1m4ee | 1,603,181,468,000,000,000 | text/html | crawl-data/CC-MAIN-2020-45/segments/1603107871231.19/warc/CC-MAIN-20201020080044-20201020110044-00315.warc.gz | 373,068,152 | 7,914 | # Can be Chasing Sports Betting Deficits complete Strategy?
For just as long as video games regarding chance have already been about there have been recently bettors who’re convinced that they can beat the house by way of doubling their particular bets following losses. It is so favorite that it even provides a new name. It’s the Martingale system.
Most Martingale users stick with games like roulette, but quite a few sports gamblers try to use it to help make benefit at the sportsbooks. Find out if going after sports betting losses is usually a being successful strategy as well as not under.
The Math of Chasing after
Most gambling bets gamblers help make when that they are starting a new string exactly where they plan to double his or her bets following cutbacks till they have the get are on in addition funds wagers. Gamblers learning roulette bet on purple or maybe black or strange or even and win a single to 1 on successful gambling bets.
안전 놀이터 makes typically the math simple. You keep duplicity your wager right after failures and when you get you secure a revenue equal to your first guess amount.
Sports betting is additional challenging because you spend vig on losing gambles.
Using the common vig involving paying 110 to be able to triumph 100, you have to bet a lot more than 2 times your last getting rid of guess to lock in money equal to your primary bet within the string.
\$110 to gain \$100
\$231 to succeed \$210
\$485 to succeed \$441
\$1, 019 to help win \$926
\$2, one hundred forty to get \$1, 945
\$4, 494 to succeed \$4, 085
As you can see, often the bet size expected to secure a \$265.21 profit swiftly becomes higher. Starting with some sort of wager of \$110, if you lose five bets in a very row you’re risking \$4, 494. This is too a lot to stomach for many handicappers. And this also is often the main reason why specialized sports activities bettors don’t have a tendency to follow losses.
The particular different point you need to have to know is that will even though the majority of seldom like to say the idea, even the best handicappers get rid of five, six, as well as more gamble in the row from time in order to time. That are folks who make a long lasting profit betting on sports.
This means that any different activities bettor within the world is sure to lose five or more games within a line from time to period.
NFL Device Catching the particular Ball
The mathematics is also more complicated and turns into bigger faster after you make moneyline bets on most favorite. This is one method many sports bettors make use of a pursuing system. They will believe that a big favorite on the moneyline is likely to win most regarding the time, so these people can afford to pursuit losses, depending on a new be successful in the 1st a couple of or three bets.
But take into account the math and gamble shapes you’re forced in order to make soon after just a couple of losses in a row with favored groups. I’m working with a reasonably conservative moneyline of -300 in that case in point, so imagine just how unsightly it receives selecting even bigger favorites.
You choose a bet of three hundred to win \$100 and even lose. Now you have to gamble enough for you to cover the three hundred a person lost plus a profit of \$100.
Your following wager is \$1, 250 for you to win \$400. When you lose this bet you have to deal with the \$1, 200, plus your original \$300, plus some sort of \$22.99 profit.
This makes your last bet \$4, 800 to help win \$1, 600. In mere two practices you gone from endangering \$300 to \$4, eight hundred.
Betting Restrictions
If a person ignore everything else, the initial issue you’re going to be able to run across is betting restrictions. You should be able to obtain large table bets down for you to keep chasing your losses. The numbers within the last section are based on modest primary bets of sometimes \$110 or \$300. And the truth is that typically the risk for a tiny come back of \$100 isn’t well worth the idea.
But if you start at a higher number, like \$550 to be able to win \$500 or \$1, 100 to win \$1, 000, you can immediately run up from the top betting limits no more than sportsbooks. This happens even faster when you’re using moneyline wagers on favorites to help chase losses.
Bankroll Limitations
Even if you can easily figure out a good way around the top betting limits, the other enormous problem is your bankroll. In the event that you have hundreds of thousands or perhaps millions to place close to chasing losses, an individual likely have better selections for investment your money.
If you’re like the majority of of us, an individual don’t have this variety of funds to toss around. Simply how much can a person find the money for to risk for a good relatively small returning? Just how much can you afford to reduce without dropping almost everything, as well as your house, cars, and even almost certainly your family?
Get a hard look at the restricts of your bankroll just before you ever consider running after sports betting losses.
That Can Work – Nonetheless It is very Hazardous
Every sports gambler really wants to think that these people can handicap adventures good enough that they are not about to lose more when compared with two or three found in the row. But typically the truth is that possibly the best handicappers inside the world aren’t excellent enough to stop losing lines, so there is no method you’re going to prevent them.
With all associated with that being said, there are never been a better a chance to chase sports betting losses. I’ve covered the problems with chasing after losses, and you have gain access to to a little something today that bettors in the past didn’t. You have access to a large and diverse sports wagering market.
There are a lot more places available to anyone to place bets than actually before.
Sportsbooks are legitimate in more places than ever, and more are currently being legalized just about every year. An individual also have access to be able to online sportsbooks where you can place bets.
This means that it’s much easier than ever to acquire a new lot of action down on a game. You might have to break up your current action up among a pair of or more sportsbooks, although you can get a major amount in action less difficult when compared to how at any time before.
I actually cannot do anything concerning your bankroll scenario. An individual either have a large enough bankroll to chase failures until you win as well as you don’t. But in the event that you do have a good big plenty of bankroll and even can stomach endangering thousands for the chance to help lock in a small return after a selection of losses, the opportunity is generally there.
All this leads to the particular conclusion of which chasing cutbacks in wagering can job, but it’s hazardous. Many gamblers have gone broke chasing losses. They think that they’re due for the win so they keep wagering more and more until they drop almost everything. Don’t make this exact same mistake.
Should You Pursue Sports Betting Failures?
The fact is that you have by now made up your imagination with regards to pursuing losses. Almost nothing I say here is going to change what you do. Nevertheless I’m still planning to offer you two pieces of assistance.
The first thing is I don’t suggest going after losses in any playing situation, as well as sports bets. Raise the risk is simply as well great for a small to medium sized reward. Any time you start to think regarding chasing losses or notice something special in a system that involves chasing loss, run away as fast as you can.
The second thing I want to share using you is some guidance if you’re convinced that you have to try chasing cutbacks. Place a total budget regarding chasing losses in athletics betting and stick to it not any matter what. When a person shed your current chasing budget, stop pursuing. I likewise recommend making the most basic bet possible to start.
Closeup of Two NBA Players During a Sport
If you established a good budget of \$1, 000 and start with a good \$11 for you to win \$12 wager you can try to run after without losing your property. Yet you’re only going to be protected if you stop if you lose your \$1, 1000 budget. Another thing you can do is ignore the gamble acceleration I included throughout the first area and simply double the win amount.
Using a establishing bet of \$11 in order to win \$10, use a good development of \$20, \$40, \$80, \$160, and \$320. As soon as you lose a couple bets in the row you are not going to succeed enough to make a great deal funds, but you may come close to breaking even overall until a person reduce six wagers within a row. And when this happens, ideally you have learned that chasing can be a bad idea plus you move on to help a sort of handicapping that allows you a much better longer term chance at good results.
토토Realization
Please allow myself to save you quite a new bit of as well as a good great deal of money. Chasing gambling losses is a terrible thought. When you can afford to help do the idea, you currently have better choices to create income. If you can’t afford to do it, you need to be able to stop gambling. In case you simply have to give the idea a try, find a great online sportsbook that takes \$1 bets and set aside \$465.21 you can easily afford to lose. It may be still a bad plan, but at least anyone won’t get rid of too significantly showing the idea. | 2,048 | 9,521 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.9375 | 3 | CC-MAIN-2020-45 | latest | en | 0.958108 |
https://www.physicsforums.com/threads/gravity-between-3-objects.804258/ | 1,516,097,313,000,000,000 | text/html | crawl-data/CC-MAIN-2018-05/segments/1516084886397.2/warc/CC-MAIN-20180116090056-20180116110056-00366.warc.gz | 973,066,701 | 17,160 | # Gravity between 3 objects
Tags:
1. Mar 20, 2015
### GiantSheeps
1. The problem statement, all variables and given/known data
PART 1: Objects with masses of 125 kg and 548 kg are separated by 0.385 m. A 63.5 kg mass is placed midway between them.
Find the magnitude of the net gravitational force exerted by the two larger masses on the 63.5 kg mass. The value of the universal gravitational constant is 6.672 × 10−11 N · m2 /kg2 . Answer in units of N.
PART 2: Leaving the distance between the 125 kg and the 548 kg masses fixed, at what distance from the 548 kg mass (other than infinitely remote ones) does the 63.5 kg mass experience a net force of zero? Answer in units of m.
2. Relevant equations
F = Gmm/(d^2)
3. The attempt at a solution
So i got part 1 no problem, the answer is .00004836 N, but part 2 is a real tough one. For my first attempt, i set up the formula ( (548)(63.5)(6.67E-11)/x^2 ) + ( (125)(63.5)(6.672E-11)/(x+.385)^2 ) = 0
x being distance, and (x + .385) distance from smaller mass since it remains fixed
I got 0.8165837351598118 as an answer, but that was wrong.
Where did I go wrong? How can I solve this? Any help would be greatly appreciated
Thanks!
2. Mar 20, 2015
### TSny
I would recommend setting up the equation in symbols first. Then you can simplify by cancelling common factors on each side of the equation.
The expression x + .385 does not represent the correct distance.
Your equation reads ( (548)(63.5)(6.67E-11)/x^2 ) + ( (125)(63.5)(6.672E-11)/(x+.385)^2 ) = 0. Note that both terms on the left are positive. So, they can't add to zero.
3. Mar 20, 2015
### GiantSheeps
How would I do that? Gmm/d^2 - Gmm/d^2 = 0?
I used - because as you said if it were addition it could not add to zero, but am I setting that up right at all? Wouldn't the gravity of the two objects on the smaller one have to end up being equal to zero?
Here's my reasoning behind the x + .385 distance
(its really large image, sorry, i have no idea why)
4. Mar 20, 2015
### TSny
In order for the total force on the 63.5 kg mass to be zero, does the 63.5 kg mass need to be between the other two masses or somewhere else? Think about the direction of the forces on the 63.5 kg mass. | 653 | 2,222 | {"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-2018-05 | longest | en | 0.937115 |
http://essay2.fsbets.icu/Order-Of-Operations-Worksheets-And-Answer-Key.html | 1,575,676,285,000,000,000 | text/html | crawl-data/CC-MAIN-2019-51/segments/1575540491491.18/warc/CC-MAIN-20191206222837-20191207010837-00112.warc.gz | 52,166,461 | 5,206 | # Order Of Operations Worksheets And Answer Key
This order of operations math rap and song comes with games, worksheet, practice sheets, Lyrics ClozeWorksheetsQuizDrillsHomeworkAnswer KeyLesson. Order of operations worksheets includes four operators, braces, nested Easy level has positive integers on both questions and answers; medium level. Order Of Operations For 5th Grade. Showing top 8 worksheets in the category - Order Of Operations For 5th Grade. Some of the worksheets displayed are Order of operations pemdas practice work, Order of operations, Order of operations, Using order of operations, Order of operations, Order of operations, In such problems always follow the order bodmas, Georgia standards of excellence curriculum.
The second order of operations worksheet (PDF) continues this focus on understanding the rules of the order of operations, but can be tricky for some students who are new to the subject. It is important for teachers to explain what would happen if the order of operations is not followed which could drastically impact the solution to the equation. Worksheets to practice order of operations (PEMDAS or BEDMAS) with solutions, Use the Hint button to get a free letter if an answer is giving you trouble. Use these worksheets to review orders of operations. Order of Operations (No Parenthesis) FREE Solve the problems and answer the short question. This practice sheet requires students to use all operations, as well as basic exponents.
©Q q2 80V1d2 v PKbuBt1a 9 mSponfLtUw4aUr2ea eL SLYCn.3 U RAPlClJ WrNiLg2h EtYsk trbe cs te or qv pe1dy. t 4 FMPafdQeR xw Zi 4t Lh2 kIyn DfIi In ki rt ZeL lA rlTg4e ObZroa f J1 Z.e Worksheet by Kuta Software LLC Kuta Software - Infinite Algebra 1 Name_____ Order of Operations Date_____ Period____. It seems that each student interpreted the problem differently, resulting in two different answers. Student 1 performed the operation of addition first. Order of Operations Worksheets for 5th Grade, 6th Grade and 7th Grade.
A pre-assessment worksheet that assesses students readiness to evaluate simple expressions. Show Answers. Order of Operations: Pre-assessment. Order of Operations - Level 1. This two page worksheet introduces the Order of Operations. It covers multiplication and division, and addition and subtraction. Helpful idea: Use an example like, 3 + 2 x 4, and solve it two different ways to show why we need the Order of Operations. If we do not use it our answers will vary. Preview Print Answers. ©W y2 R0a1Q2I iK UuMtra v DSsoKfdt Dwxa Ir Lev mLeLMCG.L D TA Jl MlT 6rFidg2h Ct4sE Yraevshe2rXvXeqd v.8 N PMGaId oe7 Ew0istRhA EIfn gfpi5niNtFeY yPsr9e f- bAkl3gye ib Brzaz.O Worksheet by Kuta Software LLC Kuta Software - Infinite Pre-Algebra Name_____ Order of Operations Date_____ Period____.
These order of operations worksheets will get your PEMDAS skills in operational order! PEMDAS is a mnemonic for Parentheses, Exponents, Multiplication, Division, Addition and Subtraction. This is the order in which operations are applied to solve more complex math problems that have multiple terms and multiple operations. Order of operations worksheet for 7th grade children. This is a math PDF printable activity sheet with several exercises. It has an answer key attached on the second page. This worksheet is a supplementary seventh grade resource to help teachers, parents and children at home and in school. Guided Lesson Explanation - I created my own rendition of PEMDAS in this one. Practice Worksheet - I View Answer Keys- All the answer.
Free Worksheets for Order of Operations. Find here an unlimited supply of worksheets for the order of operations for grades 2-9 that use addition, subtraction, multiplication, division, exponents, and/or parentheses. The worksheets are available both in PDF and html formats (html is editable) and can be customized in multitudes. Learning the order of operations is super important since you cannot solve an equation containing Click the buttons to print each worksheet and answer. All of our worksheets come with answer keys and are available as an individual order of operations worksheet PDF for easy downloading and printing. They also feature Prodigy Epics your students will love! This post includes: Order of operations worksheet without e xponents or parentheses; Order of operations worksheet with parentheses. | 996 | 4,364 | {"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-2019-51 | latest | en | 0.904661 |
https://lanl.github.io/LaGriT/pages/docs/edges | 1,561,529,522,000,000,000 | text/html | crawl-data/CC-MAIN-2019-26/segments/1560628000175.78/warc/CC-MAIN-20190626053719-20190626075719-00296.warc.gz | 494,944,675 | 3,753 | I. Edges: Each edge is tested separately to see if it should be tagged for refinement or derefinement.
Definition:
c = a user supplied tolerance
f(i) = value of the field variable f at node i
L = length of the edge
For the edge between nodes 1 and 2, we have
“129” “55”
Criteria:
1) Junction: Refine if the edge field values straddle c.
Tag for refinement if
f(1) > c and f(2) < c or f(1) < c and f(2) > c
example: For c = 0, refine if f changes sign across the edge.
2) Constant: Refine if the edgeís field values exceed c.
Tag for refinement if
f(1) > c or f(2) > c
3) Maxsize: Refine if the edge length exceeds c.
Tag if l > c
4) Delta: Refine if the magnitude of the difference of the field values at the edge ends exceeds c.
Tag if
``````f(1) - f(2) > c
``````
5) Lambda Refine: Refine if lambda/dx < c. Where dx is a scale length (here taken to be the edge length
Generally lambda/dx is a quality measure of the discretization. A larger value of usually indicates a better grid discretization. There are some special cases. If one of the field values is zero as could happen on a boundary, then lambda/dx 1/2. If f(1) is equal to f(2) then lambda/dx is divergent but the algorithm uses a small number e = .000001 added to the denominator lambda/dx to give a large but finite value of lambda/dx thus indicating a good discretization.
“167” “55” | 401 | 1,398 | {"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-2019-26 | latest | en | 0.695274 |
http://mathhelpforum.com/number-theory/150373-every-prime-3-congruent-pm-1-mod-6-a.html | 1,527,395,994,000,000,000 | text/html | crawl-data/CC-MAIN-2018-22/segments/1526794867995.55/warc/CC-MAIN-20180527024953-20180527044953-00531.warc.gz | 187,138,156 | 11,689 | # Thread: Every prime > 3 is congruent to \pm 1 mod 6
1. ## Every prime > 3 is congruent to \pm 1 mod 6
Every prime > 3 is congruent to $\displaystyle \pm 1 \ \mbox{mod 6}$
Induction maybe?
$\displaystyle 5\equiv\pm 1\ \mbox{(mod 6)}$ This isn't true though
2. any number can be
0,1,2,3,4,5 mod 6
because the number is prime - 0,2,3,4 can be ruled out
3. $\displaystyle 5\equiv -1\ \mbox{(mod 6)},$ since $\displaystyle 5-(-1)=6\times 1$.
You could try arguing along these lines: all primes greater than 3 are odd. Therefore, they must be congruent to either -1, 1, or 3 mod 6. (5 and -1 are equivalent). However, any number greater than 3 that is congruent to 3 mod 6 would be divisible by 3, and hence not prime. Therefore, all primes greater than 3 are congruent to 1 or -1 mod 6.
[EDIT]: This is essentially the same as what aman_cc said.
4. Originally Posted by dwsmith
Every prime > 3 is congruent to $\displaystyle \pm 1 \ \mbox{mod 6}$
Induction maybe?
$\displaystyle 5\equiv\pm 1\ \mbox{(mod 6)}$ This isn't true though
You can generalize and consider integers $\displaystyle a$ that are relatively prime to $\displaystyle 6$ and the result will follow, in particular, to any prime $\displaystyle p>3$.
Let $\displaystyle a=6q+r$, with $\displaystyle 0\leq r<6$. Then $\displaystyle gcd(a,6)=gcd(6,r)$, so we need only to look at values $\displaystyle r$ such that $\displaystyle gcd(6,r)=1$. These are $\displaystyle r=1,5$.
Now, $\displaystyle a\equiv 1(mod\ 6)$,or $\displaystyle a\equiv 5\equiv -1(mod\ 6)$.
5. Keep it simple ... I assume that $\displaystyle p > 3$ in the whole post by the way ... since the fact $\displaystyle 3 | 3$ does not contradict the primality of $\displaystyle p$ ... just adjust what is below as you wish ...
Let $\displaystyle p \equiv x \pmod{n} \Rightarrow p = kn + x$, $\displaystyle k \in \mathbb{Z}$, $\displaystyle x \in \mathbb{Z}/n\mathbb{Z}$
Then it follows that $\displaystyle \gcd{(n, x)} | p$
But if $\displaystyle p$ is prime we must have $\displaystyle \gcd{(n, x)} = 1$ (otherwise there is a contradiction with respect to the definition of a prime number)
Applying this to the current problem with $\displaystyle n = 6$, the only $\displaystyle x$ that are coprime to $\displaystyle 6$ (in the congruence ring $\displaystyle \mathbb{Z}/6\mathbb{Z}$ of course) are, surprisingly enough, $\displaystyle 1$ and $\displaystyle 5$ (which turns out to be congruent to $\displaystyle -1 \pmod{6}$).
It follows that if $\displaystyle p$ is indeed prime then it must be congruent to $\displaystyle \pm 1 \pmod{6}$
...
Interestingly, it is also possible to prove that this implies that $\displaystyle \gcd{(k, n)} = 1$ for any prime $\displaystyle p$ ... This gives me an idea, I'll be right back !
6. To Bacterius
gcd(n,x) = 1 or p
i.e. p = p mod p^2, so gcd(p^2,p) = p, and p|p
But since n is 6, then we can say that gcd(n,x) should be 1
7. I don't understand what you mean, can you develop ?
8. I was just pointing out that gcd(n,x) isn't necessarily 1, it could be p also, at least in general ... for this particular case, since n is 6, then gcd(n,x) would be 1 ... | 988 | 3,143 | {"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} | 4.34375 | 4 | CC-MAIN-2018-22 | latest | en | 0.804973 |
https://www.physicsforums.com/threads/mechanics-question.449636/ | 1,686,045,320,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224652494.25/warc/CC-MAIN-20230606082037-20230606112037-00725.warc.gz | 1,061,848,451 | 14,760 | Mechanics Question
• AZhang
AZhang
A 2kg block is attached to an ideal spring (for which k = 200 N/m) and is initially at rest on a horizontal frictionless surface. A 100 gram ball of clay is thrown at the block. The clay is moving horizontally with speed V when it hits and sticks to the block. As a result, the pring is compressed a maximum distance of 0.4m.
a) Calculate the speed of the clay ball and 2kg block immediately after the clay sticks to the block but before the spring compresses significantly.
Ok, I kind of don't understand how the set-up is supposed to look like, so if someone can do ths problem, can they explain to me why they set it up the way they did?
THANKS :) | 171 | 691 | {"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-2023-23 | latest | en | 0.953953 |
https://discuss.codecademy.com/t/factorial-how-did-you-complete-it/39437 | 1,534,519,611,000,000,000 | text/html | crawl-data/CC-MAIN-2018-34/segments/1534221212598.67/warc/CC-MAIN-20180817143416-20180817163416-00080.warc.gz | 658,048,459 | 5,134 | # Factorial - how did you complete it?
#1
How did everyone else complete this exercise. I ended up with the code below, but it doesn't feel quite right even though it gives the right answer!!
``````def factorial(x):
numlist = []
while x > 0:
numlist.append(x)
x -= 1
total = 1
for i in range(0, len(numlist)):
total *= numlist[i]
return total``````
#2
Why not just `for i in range(0, x);` & `total *= i`?
Edit: I meant `for i in range(1, x + 1):`
#3
Here is an alternate solution
``````def factorial(x):
total = 1
for counter in range(1, x + 1):
total *= counter
return total``````
#4
This is what i did:
``````def factorial(x):
r = 1
while x - 1 > 0:
r *= x
x -= 1
return r``````
it worked.
#5
A recursive example is missing here.
Python Recursion: Factorial
``````factorial = lambda num: 1 if (num < 1) else num * factorial(num-1)
factorial(4)
# OUTPUT: 24
factorial(10)
# OUTPUT: 3628800``````
Reads simply enough.
Return 1 if the `num` is less than 1 else return `num * (num - 1)`
#6
def factorial(x):
if x == 0 or x == 1:
return 1
else:
return x * factorial(x-1)
#7
For those not familiar with lambda expressions (borrowed from functional programming languages like Haskell), here is a python function that is equivalent
``````def factorial(num):
if (num < 1):
return 1
else:
return num * factorial(num - 1)``````
#8
Guys, its too simple using the features of math module, like this:
import math
def factorial(x):
x = math.factorial(x)
return x
print factorial(4)
the print is for testing purpose
#9
Thank you all, some interesting responses here. I needed to think about some of the responses to figure out how they would work, so it has been educational.
Not sure I agree on the use of the math module; whilst it gives the correct answer, the point of the exercise is the process by which you manage to arrive at it surely?
#10
I don't understand how this continue to loops? | 560 | 1,914 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.875 | 4 | CC-MAIN-2018-34 | latest | en | 0.876945 |
http://users.wfu.edu/rouseja/2adic/X211m.html | 1,575,755,337,000,000,000 | text/html | crawl-data/CC-MAIN-2019-51/segments/1575540502120.37/warc/CC-MAIN-20191207210620-20191207234620-00204.warc.gz | 146,766,838 | 1,840 | ## The modular curve $X_{211m}$
Curve name $X_{211m}$
Index $96$
Level $16$
Genus $0$
Does the subgroup contain $-I$? No
Generating matrices $\left[ \begin{matrix} 5 & 5 \\ 0 & 5 \end{matrix}\right], \left[ \begin{matrix} 9 & 0 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 5 & 5 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 1 & 0 \\ 8 & 7 \end{matrix}\right]$
Images in lower levels
Level Index of image Corresponding curve $2$ $3$ $X_{6}$ $4$ $12$ $X_{13f}$ $8$ $48$ $X_{85l}$
Meaning/Special name
Chosen covering $X_{211}$
Curves that $X_{211m}$ minimally covers
Curves that minimally cover $X_{211m}$
Curves that minimally cover $X_{211m}$ and have infinitely many rational points.
Model $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by $y^2 = x^3 + A(t)x + B(t), \text{ where}$ $A(t) = -27t^{16} - 12960t^{15} - 232416t^{14} - 1088640t^{13} - 1975104t^{12} + 1451520t^{11} + 5377536t^{10} + 22394880t^{9} + 48176640t^{8} - 89579520t^{7} + 86040576t^{6} - 92897280t^{5} - 505626624t^{4} + 1114767360t^{3} - 951975936t^{2} + 212336640t - 1769472$ $B(t) = 54t^{24} - 54432t^{23} - 3595104t^{22} - 50730624t^{21} - 316540224t^{20} - 838688256t^{19} - 733404672t^{18} + 2414168064t^{17} + 12561246720t^{16} + 20149420032t^{15} + 16335323136t^{14} + 1226244096t^{13} - 268429787136t^{12} - 4904976384t^{11} + 261365170176t^{10} - 1289562882048t^{9} + 3215679160320t^{8} - 2472108097536t^{7} - 3004025536512t^{6} + 13741068386304t^{5} - 20744780120064t^{4} + 13298728697856t^{3} - 3769739771904t^{2} + 228304355328t + 905969664$
Elliptic curve whose $2$-adic image is the subgroup $y^2 + xy = x^3 - 1920800x - 1024800150$, with conductor $210$
Generic density of odd order reductions $1/28$ | 750 | 1,736 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.09375 | 3 | CC-MAIN-2019-51 | longest | en | 0.442566 |
https://blog.csdn.net/weixin_45697774/article/details/109228971 | 1,606,204,932,000,000,000 | text/html | crawl-data/CC-MAIN-2020-50/segments/1606141171126.6/warc/CC-MAIN-20201124053841-20201124083841-00036.warc.gz | 228,411,630 | 34,179 | UVA10003 切木棍 Cutting Sticks（区间DP、细节）
#include<cstdio>
#include<cmath>
#include<algorithm>
#include<iostream>
#include<cstring>
using namespace std;
typedef long long ll;
const int N = 507, M = 5000007, INF = 0x3f3f3f3f;
const double eps = 1e-6;
int n, m;
int f[N][N];
int len;
int a[N];
int main()
{
while(scanf("%d", &len) != EOF && len){
scanf("%d", &n);
memset(f, 0x3f, sizeof f);
for(int i = 1; i <= n; ++ i){
scanf("%d", &a[i]);
f[i][i] = f[i][i + 1] = 0;
}
//0是左端点n + 1是右端点
a[n + 1] = len;//n个点分成n+1段
for(int length = 2; length <= n + 1; ++ length){//从0开始0,1,2,这样才能在1点切开,0是左端点不是切割点
for(int i = 0; i <= n - length + 1; ++ i){
int j = i + length;
int minv = INF;
for(int k = i + 1; k < j; ++ k){
minv = min(minv, f[i][k] + f[k][j]);
}
f[i][j] = minv + a[j] - a[i];
}
}
printf("The minimum cutting is %d.\n", f[0][n + 1]);
}
return 0;
}
09-21 84
11-10 606
05-21 315
05-06 473 | 394 | 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": 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} | 2.75 | 3 | CC-MAIN-2020-50 | latest | en | 0.221579 |
http://lesswrong.com/lw/h60/willing_gamblers_spherical_cows_and_ais/ | 1,455,217,777,000,000,000 | text/html | crawl-data/CC-MAIN-2016-07/segments/1454701162648.4/warc/CC-MAIN-20160205193922-00095-ip-10-236-182-209.ec2.internal.warc.gz | 127,774,275 | 26,451 | # Willing gamblers, spherical cows, and AIs
15 08 April 2013 09:30PM
Note: posting this in Main rather than Discussion in light of recent discussion that people don't post in Main enough and their reasons for not doing so aren't necessarily good ones. But I suspect I may be reinventing the wheel here, and someone else has in fact gotten farther on this problem than I have. If so, I'd be very happy if someone could point me to existing discussion of the issue in the comments.
tldr; Gambling-based arguments in the philosophy of probability can be seen as depending on a convenient simplification of assuming people are far more willing to gamble than they are in real life. Some justifications for this simplification can be given, but it's unclear to me how far they can go and where the justification starts to become problematic.
In "Intelligence Explosion: Evidence and Import," Luke and Anna mention the fact that, "Except for weather forecasters (Murphy and Winkler 1984), and successful professional gamblers, nearly all of us give inaccurate probability estimates..." When I read this, it struck me as an odd thing to say in a paper on artificial intelligence. I mean, those of us who are not professional accountants tend to make bookkeeping errors, and those of us who are not math, physics, engineering, or economics majors make mistakes on GRE quant questions that we were supposed to have learned how to do in our first two years of high school. Why focus on this particular human failing?
A related point can be made about Dutch Book Arguments in the philosophy of probability. Dutch Book Arguments claim, in a nutshell, that you should reason in accordance with the axioms of probability because if you don't, a clever bookie will be able to take all your money. But another way to prevent a clever bookie from taking all your money is to not gamble. Which many people don't, or at least do rarely.
Dutch Book Arguments seem to implicitly make what we might call the "willing gambler assumption": everyone always has a precise probability assignment for every proposition, and they're willing to take any bet which has a non-negative expected value given their probability assignments. (Or perhaps: everyone is always willing to take at least one side of any proposed bet.) Needless to say, even people who gamble a lot generally aren't that eager to gamble.
So how does anyone get away with using Dutch Book arguments for anything? A plausible answer comes from a joke Luke recently told in his article on Fermi estimates:
Milk production at a dairy farm was low, so the farmer asked a local university for help. A multidisciplinary team of professors was assembled, headed by a theoretical physicist. After two weeks of observation and analysis, the physicist told the farmer, "I have the solution, but it only works in the case of spherical cows in a vacuum."
If you've studied physics, you know that physicists don't just use those kinds of approximations when doing Fermi estimates; often they can be counted on to yield results that are in fact very close to reality. So maybe the willing gambler assumption works as a sort of spherical cow, that allows philosophers working on issues related to probability to generate important results in spite of the unrealistic nature of the assumption.
Some parts of how this would work are fairly clear. In real life, bets have transaction costs; they take time and effort to set up and collect. But it doesn't seem too bad to ignore that fact in thought experiments. Similarly, in real life money has declining marginal utility; the utility of doubling your money is less than the disutility of losing your last dollar. In principle, if you know someone's utility function over money, you can take a bet with zero expected value in dollar terms and replace it with a bet that has zero expected value in utility terms. But ignoring that and just using dollars for your thought experiments seems like an acceptable simplification for convenience's sake.
Even making those assumptions so that it isn't definitely harmful to accept bets with zero expected (dollar) value, we might still wonder why our spherical cow gambler should accept them. Answer: because if necessary you could just add one penny to the side of the bet you want the gambler to take, but always having to mention the extra penny is annoying, so you may as well assume the gambler takes any bet with non-negative expected value rather than require positive expected value.
Another thing that keeps people from gambling more in real life is the principle that if you can't spot the sucker in the room, it's probably you. If you're unsure whether an offered bet is favorable to you, the mere fact that someone is offering it to you is pretty strong evidence that it's in their favor. One way to avoid this problem is to stipulate that in Dutch Book Arguments, we just assume the bookie doesn't know anything more about whatever the bets are about than the person being offered the bet, and the person being offered the bet knows this. The bookie has to construct her book primarily based on knowing the propensities of the other person to bet. Nick Bostrom explicitly makes such an assumption in a paper on the sleeping beauty problem. Maybe other people explicitly make this assumption, I don't know.
In this last case, though, it's not totally clear whether limiting the bookie's knowledge is all you need to bridge the gap between the willing gambler assumption and how people behave in real life. In real life, people don't often make very exact probability assignments, and may be aware of their confusion about how to make exact probability assignments. Given that, it seems reasonable to hesitate in making bets (even if you ignore transaction costs and declining marginal utility and know that the bookie doesn't know any more about the subject of the bet than you do), because you'd still know the bookie might be trying to exploit your confusion over how to make exact probability assignments.
At an even simpler level, you might adopt a rule, "before making multiple bets on related questions, check to make sure you aren't guaranteeing you'll lose money." After all, real bookies offer odds such that if anyone was stupid enough to bet on each side of a question with the same bookie, they'd be guaranteed to lose money. In a sense, bookies could be interpreted as "money pumping" the public as a whole. But somehow, it turns out that any single individual will rarely be stupid enough to take both sides of the same bet from the same bookie, in spite of the fact that they're apparently irrational enough to be gambling in the first place.
In the end, I'm confused about how useful the willing gambler assumption really is when doing philosophy of probability. It certainly seems like worthwhile work gets done based on it, but just how applicable are those results to real life? How do we tell when we should reject a result because the willing gambler assumption causes problems in that particular case? I don't know.
One possible justification for the willing gambler assumption is that even those of us who don't literally gamble, ever, still must make decisions where the outcome is not certain, and we therefore we need to do a decent job of making probability assignments for those situations. But there are lots of people who are successful at their chosen field (including in fields that require decisions with uncertain outcomes) who aren't weather forecasters or professional gamblers, and therefore can be expected to make inaccurate probability estimates. Conversely, it doesn't seem that the skills acquired by successful professional gamblers give them much of an edge in other fields. Therefore, it seems that the relationship between being able to make accurate probability estimates and success in fields that don't specifically require them is weak.
Another justification for pursing lines of inquiry based on the willing gambler assumption, a justification that will be particularly salient for people on LessWrong, is that if we want to build an AI based on an idealization of how rational agents think (Bayesianism or whatever), we need tools like the willing gambler assumption to figure out how to get the idealization right. That sounds like a plausible thought at first. But if we flawed humans have any hope of building a good AI, it seems like an AI that's as flawed as (but no more flawed than) humans should also have a hope of self-improving into something better. An AI might be programmed in a way that makes it a bad gambler, but aware of this limitation, and left to decide for itself whether, when it self-improves, it wants to focus on improving its gambling ability or improving other aspects of itself.
As someone who cares a lot about AI, this issue of just how useful various idealizations are for thinking about AI and possibly programming an AI one day are especially important to me. Unfortunately, I'm not sure what to say about them, so at this point I'll turn the question over to the comments.
Sort By: Best
Comment author: 09 April 2013 03:25:33PM 17 points [-]
Dutch-book arguments in fact have the form "be rational or else you'll accept a sure-losing bet OR refuse a sure-winning bet". The second case negates the need for a "willing gambler" assumption.
Comment author: 08 April 2013 09:50:37PM * 14 points [-]
Humans are not only gambling when another human explicitly offers them a bet. Humans implicitly gamble all the time: for example, when you cross the street, you're gambling that the probability that you might get hit by a car and die doesn't outweigh whatever gain you expect from crossing the street (e.g. getting to school or work). Dutch book arguments in this context are an argument that if an agent doesn't play according to the rules of probability, then under adversarial assumptions the world can screw them over. It's valuable to know what can happen under adversarial assumptions even if you don't expect those assumptions to hold.
Therefore, it seems that making inaccurate probability estimates is compatible with success in a fields that require making decisions with uncertain outcomes.
This isn't strong evidence; you're mixing up P(is successful | makes good probability estimates) with P(makes good probability estimates | is successful).
Comment author: 09 April 2013 06:28:14AM 6 points [-]
Don't you think humans cross the street not because they've weighed the benefits versus the dangers, or some such, but because that's what they've been taught to do, and probability calculations be damned?
When you live in a county where many people drive without seatbealts, you're prone to emulate that behavior. It's not like you're collectively "betting" in a different manner, or evaluating the dangers differently. It's more of a monkey-see, monkey-do heuristic.
Comment author: 09 April 2013 06:37:50AM * 11 points [-]
Just because you don't understand the game you're playing doesn't mean you're not playing it. The street is offering you a bet, and if you don't understand that, then... well, not much happens, but the bet is still there.
Comment author: 09 April 2013 06:42:37AM 6 points [-]
By the same token, fish in an aquarium - or Braitenberg vehicles - are constantly engaging in bets they don't realize. Swim to this side, be first to the food but exert energy getting there.
Your perspective is valid, but if the agents refuse/are incapable of seeing the situation from a betting perspective, you have to ask how useful it is (not necessarily thinking in estimated utility, best case, worst case etcetera, but in the "betting" aspect of it). It may be a good intuition pump, as long as we keep in mind that people don't work that way.
Comment author: 09 April 2013 03:33:01PM 6 points [-]
Do fish think in terms of expected value? Of course not. Evolutions make bets, and they can't think at all. Refactored Agency is a valuable tool--anything that can be usefully as a goal-seeking process with uncertain knowledge can also be modeled usefully as making bets. How useful is it to view arbitrary things through different models? Well, Will Newsome makes a practice of it. So, it's probably good for having insights, but caveat emptor.
Comment author: 09 April 2013 03:48:40PM 2 points [-]
The more complete the models describe the underlying phenomenon, the more isomorphic all models should be (in their Occamian formulation), until eventually we're only exchanging variable names.
Comment author: 09 April 2013 05:07:23PM 2 points [-]
Yes; to check your visual acuity, you block off one eye, then open that one and block the other. To check (and improve) your conceptual acuity, you block off everything that isn't an agent, then you block of everything that isn't an algorithm, then you block of everything that isn't an institution, etc.
Unless you can hypercompute, in which case that's probably not a useful heuristic.
Comment author: 10 April 2013 06:21:40PM 4 points [-]
this is off topic but I'm really disappointed that braitenberg vehicles didn't turn out to be wheeled fish tanks that allowed the fish to explore your house
Comment author: 09 April 2013 10:15:26AM 0 points [-]
Don't you think humans cross the street not because they've weighed the benefits versus the dangers, or some such, but because that's what they've been taught to do, and probability calculations be damned?
What they've been taught to do is weigh the benefits versus the dangers (although there are not necessarily any probability calculations gong on). The emphasis in teaching small children how to cross the road is mainly on the dangers, since those will invariably be of a vastly larger scale than the trifling benefit of saving a few seconds by not looking.
Comment author: 09 April 2013 10:33:18AM 1 point [-]
Does "Mommy told me to look for cars, or bad things happen" and "if I don't look before I cross, Mommy will punish me" count as weighing the benefits versus the dangers? If so, we agree.
I just wonder if the bet analogy is the most natural way of carving up reality, as it were.
Comment author: 09 April 2013 10:45:55AM * 5 points [-]
Does "Mommy told me to look for cars, or bad things happen" and "if I don't look before I cross, Mommy will punish me" count as weighing the benefits versus the dangers?
Perhaps these things are done differently in different cultures. This is how it is done in the U.K. Notice the emphasis throughout on looking to see if it is safe, not on rules to obey because someone says so and punishment, which figures not at all.
The earlier "Kerb Drill" mentioned in that article was a set of rules: look right, look left, look right again, and if clear, cross. That is why it was superceded.
Comment author: 08 April 2013 10:05:02PM 2 points [-]
Comment author: 08 April 2013 11:09:21PM * 13 points [-]
I'm standing at a 4-way intersection. I want to go the best restaurant at the intersection. To the west is a three-star restaurant, to the north is a two-star restaurant, and to the northwest, requiring two street-crossings, is a four-star restaurant. All of the streets are equally safe to cross except for the one in between the western restaurant and the northern one, which is more dangerous. So going west, then north is strictly dominated by going north, then west. Going north and eating there is strictly dominated by going west and eating there. This means that if I cross one street, and then change my mind about where I want to eat based on the fact that I didn't die, I've been dutch-booked by reality.
That might need a few more elements before it actually restricts you to VNM-rationality.
Comment author: 23 April 2013 08:21:05PM 0 points [-]
Where is reality's corresponding utility gain?
Comment author: 30 April 2013 03:46:58PM 0 points [-]
The bad news is there is none. The good news is that this means, under linear transformation, that there is such a thing as a free lunch!
Comment author: 09 April 2013 05:27:39AM 2 points [-]
One thing I should have mentioned earlier: it's one thing to claim that humans implicitly gamble all the time, another to claiming that they implicitly assign probabilities when they do. It seems like when people make decisions whose outcomes they aren't sure of, most of the time "they're using heuristics that bypass probability" is a better model of their behavior than "they're implicitly assigning such-and-such probabilities."
Comment author: 09 April 2013 05:30:15AM * 3 points [-]
Well, I think that depends on what you mean by "implicitly." As I mentioned in another comment, I think there's a difference between assigning probabilities in System 1 and assigning probabilities in System 2, and that probably many people are good at the former in their domains of expertise but bad at the latter. Which do you mean?
Comment author: 08 April 2013 11:59:49PM -2 points [-]
It's valuable to know what can happen under adversarial assumptions even if you don't expect those assumptions to hold.
That sounds right, the question is the extent of that value, and what it means for doing epistemology and decision theory and so on.
This isn't strong evidence; you're mixing up P(is successful | makes good probability estimates) with P(makes good probability estimates | is successful).
Tweaked the wording, is that better? ("Compatible" was a weasel word anyway.)
Comment author: 09 April 2013 12:05:57AM * 2 points [-]
Therefore, it seems that the relationship between being able to make accurate probability estimates and success in fields that don't specifically require them is weak.
I would still dispute this claim. My guess of how most fields work is that successful people in those fields have good System 1 intuitions about how their fields work and can make good intuitive probability estimates about various things even if they don't explicitly use Bayes. Many experiments purporting to show that humans are bad at probability may be trying to force humans to solve problems in a format that System 1 didn't evolve to cope with. See, for example, Cosmides and Tooby 1996.
Comment author: 09 April 2013 12:34:37AM -1 points [-]
Thanks. I was not familiar with that hypothesis, will have to look at C&T's paper.
Comment author: 09 April 2013 02:33:45AM 5 points [-]
Qiaochu_Yuan already made much of the point that I wanted to make. I'd like to add to it that there are a lot of non-gambling examples of things that work like decision-making under uncertainty and probability.
IIRC, Eliezer used an example about an economic pundit trying to allocate preparation time to explaining why the market went up or why it went down. Even if you can't get them to take a bet, they have only so much time, and must divide it between the two cases.
Anyhow, my point is that when you map "willing to spend \$X on lottery Y" to "willing to spend X time preparing for eventuality Y", getting dutch-booked looks a lot sillier. You'd be trying to spend more time than you had for all eventualities, for example.
Comment author: 08 April 2013 10:19:27PM 3 points [-]
If you're unsure whether an offered bet is favorable to you, the mere fact that someone is offering it to you is pretty strong evidence that it's in their favor.
It seems to me that this is potentially informative -- if you're not certain enough that you're right to be willing to take the bet, this is a signal that maybe you should rethink your probability estimates or position. (Really of course you'd want to update according to Bayes, of course, but that's hard in general.)
(Spelling nitpick -- you've repeatedly misspelled "lose" as "loose". Would you mind fixing that?)
Comment author: 08 April 2013 11:57:23PM * -2 points [-]
It's not a sign that your initial probability estimate was off.
Suppose that... I dunno, elections and sports matches aren't great examples, I'm just going to use an arbitrary proposition p and it helps if you imagine p isn't the kind of thing people make dumb bets about out of enthusiasm for "their team." If you'd reject an even-odds bet for both p and ~p (even ignoring transaction costs and declining marginal utility and tossing in the extra penny and so on), plausibly that's because you should start off with a probability estimate of 0.5 or so but once you know which side of the bet the other guy wants to take, you should update to give the side of the bet the other guy wants a probability higher than 0.5.
That's the motivation for stipulating the bookie doesn't know anything more about the proposition they want to bet on on than you do.
Also, thanks for catching the spelling errors.
Comment author: 10 April 2013 09:38:55AM 0 points [-]
"loosing" is still incorrect.
In a sense, bookies could be interpreted as "money pumping" the public as a whole. But somehow, it turns out that any single individual will rarely be stupid enough to take both sides of the same bet from the same bookie, in spite of the fact that they're apparently irrational enough to be gambling in the first place.
Suggest making the link explicit with something like this: "in spite of the fact that they're apparently irrational enough to be part of that public in the first place."
Comment author: 11 April 2013 07:48:13PM -1 points [-]
Gah. Now it should be fixed.
Comment author: 08 April 2013 10:04:39PM 4 points [-]
Comment author: 11 April 2013 11:16:58AM 2 points [-]
Comment author: 11 April 2013 04:42:36PM 2 points [-]
Heh.
Comment author: 09 April 2013 12:25:44AM 6 points [-]
The somewhat less anti-intellectual words for this are "summary" and "abstract".
Comment author: 09 April 2013 07:24:06PM 16 points [-]
I like TL;DR. It reminds the author of the basic writing principle that nobody wants to read anything you write, they're doing you a favor by reading the first two sentences and if you're still saying boring things by the third sentence that's it. Writing is terrible in proportion to how its circumstances cause writers to ignore this principle, for example school textbooks that children are forced to read, or journal papers that adults are either forced to read or that aren't being written for the sake of producing understanding in anyone.
Comment author: 10 April 2013 05:20:05PM 5 points [-]
Whatever you call them, I like seeing them at the top. Your own postings would be hugely improved by the addition of abstracts.
Comment author: 11 April 2013 11:08:08AM * 5 points [-]
I like TL;DR. It reminds the author of the basic writing principle that nobody wants to read anything you write, they're doing you a favor by reading the first two sentences and if you're still saying boring things by the third sentence that's it. Writing is terrible in proportion to how its circumstances cause writers to ignore this principle, for example school textbooks that children are forced to read, or journal papers that adults are either forced to read or that aren't being written for the sake of producing understanding in anyone.
You present a strong argument that "TL;DR" is an excellent thing to keep in your mind while writing. It is not a terribly good reason to write "TL;DR" as the first section header in a post.
"Too Long; Didn't Read" is just wrong. It doesn't mean "short summary of the key point which can be used to establish whether to bother reading the body". That's what we have words like 'summary', 'abstract', 'introduction' and 'synopsis' for.
Comment author: 11 April 2013 09:32:23AM * 2 points [-]
"Abstract" is typically used for academic papers, and often has a certain formal structure. (See also this explanation.) Using it for a LW post sounds pretentious (unless of course the post happens to consist of an academic paper or paper draft).
Comment author: 09 April 2013 12:01:36AM 1 point [-]
Comment author: 10 April 2013 05:37:20PM * 1 point [-]
One needs to keep in mind that a lot of the time, "correct" probability is either very close to 0 or very close to 1, you just can't figure out which because of limited computing time. It does feel like you should use probability that's somewhere in the middle in those cases, but a: there's no formalism for doing so, and even more devastatingly, b: spending time on consistent probabilities leaves less time for actual simulation, inference, or what ever it is that you do to find if its very close to 1 or very close to 0.
Comment author: 10 April 2013 05:47:05PM * 0 points [-]
Remember, that by the Bayesian formulation of probability, there is no such thing as the "correct" probability. All probabilities are conditional on your personal knowledge. Using frequentist language like you are just muddles up the issue. If you had written your post in the Bayesian formulation, your point would be trivial. (And that, by the way, is the argument for using the Bayesian formulation and not the frequentist one.)
Comment author: 10 April 2013 06:24:05PM 2 points [-]
Often, you do have enough knowledge to get to something close to 1 or close to 0, you just can't run the computation because its too expensive.
Comment author: 09 April 2013 09:46:50AM * 1 point [-]
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https://www.formulaconversion.com/formulaconversioncalculator.php?convert=cubiccentimeters_to_centiliters | 1,537,400,235,000,000,000 | text/html | crawl-data/CC-MAIN-2018-39/segments/1537267156311.20/warc/CC-MAIN-20180919220117-20180920000117-00146.warc.gz | 732,610,781 | 16,385 | # Cubic centimeters to centiliters (cm³ to cl) Metric conversion calculator
Welcome to our cubic centimeters to centiliters (cm³ to cl) conversion calculator. You can enter a value in either the cubic centimeters or centiliters input fields. For an understanding of the conversion process, we include step by step and direct conversion formulas. If you'd like to perform a different conversion, just select between the listed Volume units in the 'Select between other Volume units' tab below or use the search bar above. Tip: Use the swap button to switch from converting cubic centimeters to centiliters to centiliters to cubic centimeters.
## centiliters (cl)
(not bookmarks)
Swap
< == >
1 cm³ = 0.1 cl 1 cl = 10 cm³
Algebraic Steps / Dimensional Analysis Formula
cm³ * 1 cl10 cm³ = cl
cubic feet 0 cubic meters 0 cubic millimeters 0 cubic yards 0 cups 0 fluid ounces 0 gallons (liquid) 0 liters 0 milliliters 0
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bushels centiliters cubic centimeters cubic decimeters cubic dekameters cubic feet cubic gigameters cubic hectometers cubic inches cubic kilometers cubic megameters cubic meters cubic micrometers cubic miles cubic millimeters cubic nanometers cubic yards cups cups (metric) deciliters dekaliters fluid ounces gallons (dry) gallons (liquid) gigaliters gills hectoliters imperial gallon kiloliters liters megaliters microliters milliliters nanoliters pecks pints (dry) pints (liquid) quarts (dry) quarts (liquid) tablespoons teaspoons < == > bushels centiliters cubic centimeters cubic decimeters cubic dekameters cubic feet cubic gigameters cubic hectometers cubic inches cubic kilometers cubic megameters cubic meters cubic micrometers cubic miles cubic millimeters cubic nanometers cubic yards cups cups (metric) deciliters dekaliters fluid ounces gallons (dry) gallons (liquid) gigaliters gills hectoliters imperial gallon kiloliters liters megaliters microliters milliliters nanoliters pecks pints (dry) pints (liquid) quarts (dry) quarts (liquid) tablespoons teaspoons
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# «The University of Sydney Math3024 Elementary Cryptography and Protocols Introduction to Cryptography Cryptography is the study of mathematical ...»
-- [ Page 2 ] --
Exercise. What is the order of a permuation with cycle lengths d1,..., dt ? How does this solve the previous exercise concerning the order of a permuation?
– – –
## UROOHATGATVALSHBHEULETIERLTA
Exercise. What is the block length m of an (r, s)-simple columnar transposition? Describe the permutation. Hint: it may be easier to describe the permutation if the index set is {0,..., m − 1}.
Exercise. Show that the (r, r)-simple columnar transposition has order 2. What is the order of the cipher for (r, s) = (3, 5)? What are the cycle lengths?
– – –
A transposition cipher can easily be recognized by an analysis of character frequencies.
Iterating transposition ciphers can greatly increase security, but as with substitution ciphers, almost all such ciphers can be broken. Although many modern cryptosystems Rotor Machines incorporate transposition ciphers, the operation on large blocks has the disadvantage of requiring a lot of memory.
– – –
Background on rotor machines and, in particular, the Enigma, will be covered in the lectures only.
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If you do not agree with the fact that your material is placed on this site, please, email us, we will within 1-2 business days delete him. | 869 | 3,695 | {"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-2017-43 | latest | en | 0.769381 |
https://newt.phys.unsw.edu.au/jw/chladni.html | 1,563,820,234,000,000,000 | text/html | crawl-data/CC-MAIN-2019-30/segments/1563195528208.76/warc/CC-MAIN-20190722180254-20190722202254-00450.warc.gz | 484,323,654 | 9,018 | # Chladni patterns for violin plates
Chladni patterns show the geometry of the different types of vibration of violin plates. This site has an introductory explanation of modes of vibration and a library of photographs of the Chladni patterns of the bellies and backplates of two different violins (one mass-produced and one hand-made). It also has photographs of plates with regular geometries which assist in understanding the violin modes. For some related history, see Chladni's law. For some Chladni patterns on metal plates, with sound files, see Acoustics of bell plates. To make your own Chladni patters, try this site.
#### Modes of vibration
How a violin works, Bows and strings and Strings, harmonics and standing waves.) A mode of vibration is just a way of vibration. Think what happens when you strike a xylophone bar in the middle and set it vibrating. The bar is supported at two points towards the ends. The simplest mode of vibration is this: when the middle of the bar goes up (as shown by the solid lines in the figure) the ends of the bar go down. When the middle goes down (dashed lines), the ends go up. The two points that do not move are called nodes and are marked N in the diagram. (If "modes" and "nodes" sound confusing, remember that the node has no motion.)
Here is a sketch of a simple mode of vibration of a bar. Think of it as a xylophone bar, which would be supported at the nodes, and you would excite this mode by striking it in the middle. This first mode of the bar is rather similar to one of the modes of vibration of a simple rectangular plate, one that is called the (0,2) mode (the naming convention is explained below.)
Now let's look at photographs of the Chladni patterns of (left) mode (0,2) of a uniform rectangular aluminium plate and (right) mode 2 of a violin back plate.
. .
In these pictures, the lines are formed from sand that has collected at the nodes, but has been shaken off the moving regions. The violin back is more complicated in shape, and so the nodes also have a more complicated shape. White sand was used for the black-painted aluminium plate, and black sand for the violin back.
#### Why are there nodes?
The supports of the xylophone bar do not cause the nodes, rather they are placed at the positions which are nodes so as to facilitate this vibration. In an object which is not firmly clampled, a vibration cannot easily move the centre of mass of the object. It follows that, if some part is going up, another part is going down. In the simple motion at resonance, the point(s) that divide(s) these regions are nodes. When a violin or an isolated part is vibrating, the centre of mass doesn't move much, so once again it can be divided into parts that are going up and others that are going down. In these simple modes of vibration, the motion of different parts is either exactly in phase or exactly out of phase, and the two regions are separated by nodes. The nodes are points for a quasi one-dimensional object like a string, or lines for a quasi two-dimensional object like a plate. (There is more explanation in Strings, harmonics and standing waves.)
#### Modes of violin plates
The violin plate has many modes of vibration, and in general each one occurs at a different frequency. About seven of them (those with lowest frequency) are well studied and are included in this document. Of these, three or more are considered useful in the process of shaping the plates by violin makers. For several different types of plate, the mode with the lowest frequency has two node lines, both approximately straight, which intersect at about ninety degrees.
The three photographs below show the lowest frequency mode for a violin back [mode 1], a uniform rectangular plate [mode (1,1)] and a uniform circular plate [mode (2,0)].
In this mode, opposite sectors of the plate are going up together, while adjacent sectors (separated by one node) are always moving in opposite directions. In the animation, the mode of the circular plate is shown, with the vertical motion both slowed and exaggerated to make it clear.
This sketch represents (with exaggerated amplitude) an instant in the motion of the mode for the rectangular plate which is shown in the second photo above.
The following links take you to a library of Chladni patterns for the first seven modes of the belly and back plates of two violins. One is a mass-produced "Lark" model from China. The other is a hand-made German violin from about 1870. For further comparisons between Chladni patterns of simple plates and violin plates, follow this link.
#### Naming of modes
The modes of plates of different geometries have different systems of naming. For a rectangular plate, they are identified by two numbers (n,m) where n is the number of modes running parallel to the long axis and m the number in the perpendicular direction (see the examples above). For a circular plate, they are called (n,m) too, but in this case n is the number of nodes that are diameters (straight lines) and m is the number of circular nodes. For the violin plates, the modes have more complicated shapes. They are numbered in a way that, for most violins, corresponds to increasing frequency. That is why the modes in the photographs shown above have the names given in square brackets.
Mode 5 for the violin (called the ring mode) is comparable with the (0,1) mode of a circular plate. For a free plate, the centre of mass does not move, so when part of the plate moves up, another part moves down. In this mode, the central region moves in the opposite direction to the perimeter and only a ring remains motionless, as the animation shows.
The modes for the belly are complicated by the presence of the f-holes (which make the plate more flexible to bending of the short axis) and the bass bar (which makes the plate less flexible to bending of the long axis). Compare the second mode, in which the modes of the top plate could be considered to have rotated by 90 degrees. (see the photographs below) The bass bar also breaks the symmetry for most of the modes of the belly.
#### How are Chladni patterns formed?
There are at least three different methods.
• The plate can be made to resonate by a powerful sound wave which is tuned to the frequency of the desired mode.
• The plate can be bowed with a violin bow. This is easiest if one choses a point that is a node for most of the modes that one doesn't want, but not for the desired node.
• The plate can be excited mechanically or electromechanically at the frequency of the desired mode.
For the photographs on this site, a small (0.2 g) magnet was fixed to the plate. An oscillating magnetic field (provided by a coil connected to an audio amplifier and a signal generator) is used to provide an oscillating force whose frequency is tuned to the resonance of the mode. Experiments using different masses showed that the mass of the magnets caused us to underestimate the frequency by about 1 Hertz.
In all cases, some finely divided material is placed on the plate. The material used in the photos on this site is fine sand. When the plate resonates, the motion becomes large over most of the surface and this causes the sand to bounce and to move about. Only at or near the node is the sand stationary. Thus the sand is either bounced off the plate or else collects at the nodes, as shown in the photographs. We used white sand from Coogee Beach to the East of the campus, and black sand from Rainbow Beach on Fraser Island. Emmanuel and Renaud are now leaving on a "research" trip to bring back supplies of diverse colours from Rainbow Beach.
This movie showing the ring mode of a violin back is provided by Atelier Labussiere.
#### Why are Chladni patterns useful?
The shaping the back and belly plates is very important to the properties of the final instrument. Chladni patterns provide feedback to the maker during the process of scraping the plate to its final shape. Symmetrical plates give symmetrical patterns; asymmetrical ones in general do not. Further, the frequencies of the modes of the pair of free plates can be empirically related to the quality of the completed violin. Many scientists have been interested in the acoustics of violins, and many violin makers have been interested in science, so a lot has been written about the acoustical properties of violins and their parts. See:
### Some links to related sites
The visiting researchers, Emmanuel Bossy and Renaud Carpentier were students at the Ecole Normale Superieure de Cachan in France.
UNSW team: John Smith, John Tann and Joe Wolfe | 1,843 | 8,610 | {"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} | 3.3125 | 3 | CC-MAIN-2019-30 | longest | en | 0.942789 |
http://www.protocol-online.org/biology-forums/posts/35569.html | 1,516,595,390,000,000,000 | text/html | crawl-data/CC-MAIN-2018-05/segments/1516084890991.69/warc/CC-MAIN-20180122034327-20180122054327-00467.warc.gz | 540,919,358 | 4,822 | # How to do graphs with mean value plus error bars for replicates? St deviation or - (Apr/07/2008 )
Pages: 1 2 Next
Dear All,
I have been doing a time course experiment (analysed by Real Time PCR) and I have repeated it 3 times (independently), obtaining 3 different and independent sets of results for the same time course.
I want to represent it in a graph with columns and error bars, but I am not too sure of how to do it and what statistical commands to use in Excel.
As far as I know, the average between the 3 values for a certain time point would be used for the column, right? But how about the error bars? Do we use standard deviation for that? Or standard error? SEM? Or something else?
If we are supposed to use standard deviation, then which type should it be? I noticed in Excel there are at least 4 different ways of finding standard deviation (STDEVP, STDEV, etc)
I would really appreciate if you could help me out here, I've checked some tutorials on the internet but I still couldn't figure it out.
Thank you very much!
Julianne.
-Julianne W-
Error bars - ahhhh, MS-Excel can be hard to understand for this but still doable.
Firstly, for standard deviation use STDEV.
There is no easy command for standard error but you can set up formula like <=STDEV(A1:F1)/SQRT(6)> where cells A1 to F1 contain the values you have averaged and 6 is the number of values (n) i.e. A1, B1, C1, D1, E1 + F1 = 6.
Hope this helps,
AussieUSA.
-AussieUSA-
I think most error bars are SEM.
So first you calculate your stdev.
then SEM = stdev/sqrt(n)
I think that's right It IS early in the morning!
-Clare-
Hi! Thank you so much for all the tips! It helped so much, now I have my graphs all nicely...
I talked to my supervisor and he asked me to calculate the P value now for the different values, to know if they are significantly different from each other. Any idea on how to do it?
I checked my old statistics book, but I am still a bit clueless of how to proceed... do I have to do also any kind of ANOVA or other fancy analysis, to know if they are significantly different from each other?
Thank you a lot!
Julianne.
-Julianne W-
QUOTE (Julianne W @ Apr 10 2008, 10:11 PM)
Hi! Thank you so much for all the tips! It helped so much, now I have my graphs all nicely...
I talked to my supervisor and he asked me to calculate the P value now for the different values, to know if they are significantly different from each other. Any idea on how to do it?
I checked my old statistics book, but I am still a bit clueless of how to proceed... do I have to do also any kind of ANOVA or other fancy analysis, to know if they are significantly different from each other?
Thank you a lot!
Julianne.
Awesome You'd have to work out the best stats test to get your p-values. Unfortunately my stats sucks ! but t-tests ring a bell...
-Clare-
QUOTE (Julianne W @ Apr 7 2008, 03:04 PM)
Dear All,
I have been doing a time course experiment (analysed by Real Time PCR) and I have repeated it 3 times (independently), obtaining 3 different and independent sets of results for the same time course.
I want to represent it in a graph with columns and error bars, but I am not too sure of how to do it and what statistical commands to use in Excel.
As far as I know, the average between the 3 values for a certain time point would be used for the column, right? But how about the error bars? Do we use standard deviation for that? Or standard error? SEM? Or something else?
If we are supposed to use standard deviation, then which type should it be? I noticed in Excel there are at least 4 different ways of finding standard deviation (STDEVP, STDEV, etc)
I would really appreciate if you could help me out here, I've checked some tutorials on the internet but I still couldn't figure it out.
Thank you very much!
Julianne.
I think to answer your stats question that a One-Way ANOVA would be the appropiate test with "time" being the variable of interest. Because each set of experÃments are different then I don't think using a repeated measures approach is appropiate.
Any stats program like Sigma Stat has an (near)idiot proof way of doing this test.
Hope that helps.
-Racingstud-
Stats ... not doable in Excel.
One-way ANOVA a little too much for your experiment. Students T-test should be sufficient. Whether to do paired or unpaired ... is it the same cell undergoing different treatments or different cell types undergoing treatments? If same = paired. Different = unpaired.
Use any basic stats program.
Hope this helps,
AussieUSA.
-AussieUSA-
lots of papers use the mann-whitney test to see if they have a significant p-value (the closer it is to zero the higher probability of your samples being different). it has the advantage it is a non parametric test, that way you don't have to standarize your data (in case it has a high std deviation)
-toejam-
Thank you so much for all your replies, it has been very helpful!! However, I have to admit I don't have a good statistical background.
Do you have any suggestions of a book/paper/websites to look up? I have my statistical books, but I find it very hard to apply to lab and real life experiments.
Thank u!
All the Best,
Julianne.
-Julianne W-
look for "experimental design" online or books. if you have a specific problem it might be easier to help you. if your experiment is not set properly from the beginning it might be a bit complicated (not impossible tho) to find a test that suits your data best.
-toejam-
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# chapter 15 review questions ANSWERS UPDATED III - Cl(g acts...
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1) For the reaction 2A + B products Determine the rate law and the rate constant, given the following data: [A] [B] Initial Rate 0.10 0.10 2x10 -2 0.30 0.10 1.8x10 -1 0.20 0.20 8.0x10 -2 Rate = k[A] 2 2) For a first order reaction k = 0.00300 s -1 at 298 K. a) Determine the time in seconds required for 75% reaction (that means that 75% of the reactant has reacted) ln(.25) = -0.003t t = 462 seconds b) If the activation energy is 35.5 kJ/mol what is the rate constant at 350 K? ln(k 2 /0.003) = -35,500/(8.314) (1/350-1/298) k 2 = 0.0252 3) What is the rate law for the following mechanism? Cl 2 (g) 2 Cl(g) K 1 , fast Cl(g) + CO(g) COCl (g) K 2 , fast COCl(g) + Cl 2 (g) COCl 2 (g) + Cl(g) k 3 , slow Rate = (K 1 ) 1/2 K 2 k 3 [Cl 2 ] 3/2 [CO] 4) For the above mechanism, is the following statement true:
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Unformatted text preview: Cl(g) acts as a catalyst. Justify your answer. Cl is an INTERMEDIATE NOT a CATALYST 5) Draw a reaction coordinate diagram (energy vs. progress of reaction) for an endothermic reaction. Label the transition state, the ΔE for the reaction and the E a See Figure 15.10 for an exothermic reaction – the only difference is that the Products should be at higher energies than the reactants 6) Explain why raising the temperature increases the rate of reaction. Use a diagram showing the distribution of energies for molecules at high and low temperatures in you answer See Figure 15.13 and the caption...
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15-Moonstone
## Matric
Dear all
how to make multiple element by element and result as matrix? (Function As(DB,n,i)
Thank you
1 ACCEPTED SOLUTION
Accepted Solutions
24-Ruby V
(To:Werner_E)
Here is an attempt from what I understood so far.
Vectorization as suggested by Terry sure is the clue, but its not so straightforward as you may think because we don't want to vectorize the elements of DB or n but just the elements of the results of the function n.s1() and A.sDB().
Here is one possible way to do it:
Additional remark: Its not necessary to vectorize the call A.sDB(DB) because the function uses DB^2 and squaring a vector is not defined in mathematics. So Prime automatically applies vectorization.
But in my opinion its good habit to apply the vectorization explicitly yourself in cases like this - just to be on the safe side in case you later change the function A.sDB.
10 REPLIES 10
21-Topaz I
(To:SPRstructur)
Hi,
Try "vectorisation".
On the ribbon at Math | Operators - lower right hand corner.
Cheers
Terry
24-Ruby V
(To:SPRstructur)
And state clearly, what exactly you expect as desired result. For this it might be helpful if you change the input matrices DB and n in a way so not all entries are the same value.
24-Ruby V
(To:Werner_E)
Here is an attempt from what I understood so far.
Vectorization as suggested by Terry sure is the clue, but its not so straightforward as you may think because we don't want to vectorize the elements of DB or n but just the elements of the results of the function n.s1() and A.sDB().
Here is one possible way to do it:
Additional remark: Its not necessary to vectorize the call A.sDB(DB) because the function uses DB^2 and squaring a vector is not defined in mathematics. So Prime automatically applies vectorization.
But in my opinion its good habit to apply the vectorization explicitly yourself in cases like this - just to be on the safe side in case you later change the function A.sDB.
15-Moonstone
(To:Werner_E)
Now I am not near my pc. Yep that I prefer but when I enlarge matrix DB 1x4 or higher it will work ?
i will test tomorrow, I will be back
big thank Werner_E &Terry
24-Ruby V
(To:SPRstructur)
@SPRstructur wrote:
...
when I enlarge matrix DB 1x4 or higher it will work ?
...
You will have to enlarge the matrix n, too.
As long as DB and n will have the same number of rows, it should work OK without any changes.
23-Emerald II
(To:SPRstructur)
As I'm in a cat-skinning mood, here's another approach that uses functions to achieve the desired outcome.
Element-by-element multiplication is conventionally referred to as Hadamard (or Schur) multiplication. The attached worksheet implements it as the function hadamard and applies it to your problem. The worksheet also includes the map, zeros, ones and seq functions.
Here are the hadamard and map functions,
And here are the zeros, ones and seq functions.
zeros, ones, and seq functions
Stuart
24-Ruby V
(To:StuartBruff)
Always nice to see your thought son problems and your consequent use a (useful) custom functions.
There is no need for "i" anyway. Neither as range, nor as argument in function "A.s".
23-Emerald II
(To:Werner_E)
Vielen Dank, Werner. I'm pretty sure any one of a number of the "core" Mathcadders (yourself included) would have come up with a similar solution if you too came late to the party! 😎
Working with Prime Express somewhat forces a purer functional mindset. If I could find nice (ie, quick and short), non-programming ways to return an array after setting an element and to convert an n-parameter function into an n-1 parameter function, I'd be happy.
Well, I would be if the recursion depth wasn't so shallow, although that in itself is just one more challenge to work around. The lack of expression wrap-around is also a limiting factor as far as readability goes.
Sowieso zurück zur Geschichte, yes, I wondered about the 'i' and guessed it might have been intended for some future use when the OP got the function working.
Stuart
23-Emerald III
(To:StuartBruff)
Nice, Stuart,
However there's no need to define the _one() and _zero() functions, see below:
Caution: With the 'min' function, you have to set the label of it to 'function'. Prime doesn't understand simple things...
Luc
23-Emerald II
(To:LucMeekes)
@LucMeekes wrote:
Nice, Stuart,
However there's no need to define the _one() and _zero() functions, see below:
Caution: With the 'min' function, you have to set the label of it to 'function'. Prime doesn't understand simple things...
Luc
Hi, Luc.
Yes, I've been bitten a few times by forgetting that Prime treats min a bit differently.
The reason I use zero and one is simply to avoid having to do further operations on larger matrices ... I grew up in an era when milliseconds counted and it paid to be familiar with the number of clock cycles the processor took to perform an operation!
The real nuisance is not being able to use partial application in Prime. What I'd have done (and did do) in M15 would be to write a function like matseq(m,i,j) := i + m * j and then define a function matint(m,n) := matrix(m,n,matseq(m)) to generate a matrix of successive integers, increasing in normal Mathcad order.
Unfortunately, I can't think of a neat way of doing this in Prime Express (it would be straightforward in Prime Premium, of course, by defining a local function matrix(m,n,l(i,j)<-matseq(m,i,j)). The best I've been able to come up with is a double-matrix addition function, and a recursive replicator-adder. On the other hand, they both seem to execute as quickly as the matrix function alone, with the edge going to the recursive function for large matrices.
Anyway, enough rambling, here's a plot of the times for the two approaches to generating an all-ones matrix:
Stuart
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https://numberworld.info/1011000101 | 1,585,622,693,000,000,000 | text/html | crawl-data/CC-MAIN-2020-16/segments/1585370499280.44/warc/CC-MAIN-20200331003537-20200331033537-00381.warc.gz | 567,377,171 | 3,796 | Number 1011000101
Properties of number 1011000101
Cross Sum:
Factorization:
Divisors:
Count of divisors:
Sum of divisors:
Prime number?
Yes
Fibonacci number?
No
Bell Number?
No
Catalan Number?
No
Base 3 (Ternary):
Base 4 (Quaternary):
Base 5 (Quintal):
Base 8 (Octal):
3c42a325
Base 32:
u458p5
sin(1011000101)
-0.25206863583222
cos(1011000101)
-0.96770935865563
tan(1011000101)
0.26047969214889
ln(1011000101)
20.734205876886
lg(1011000101)
9.0047511989775
sqrt(1011000101)
31796.227779408
Square(1011000101)
Number Look Up
Look Up
1011000101 (one billion eleven million one hundred one) is a amazing number. The cross sum of 1011000101 is 5. If you factorisate the figure 1011000101 you will get these result . The number 1011000101 has 2 divisors ( 1, 1011000101 ) whith a sum of 1011000102. 1011000101 is a prime number. The figure 1011000101 is not a fibonacci number. The figure 1011000101 is not a Bell Number. 1011000101 is not a Catalan Number. The convertion of 1011000101 to base 2 (Binary) is 111100010000101010001100100101. The convertion of 1011000101 to base 3 (Ternary) is 2121110101010102012. The convertion of 1011000101 to base 4 (Quaternary) is 330100222030211. The convertion of 1011000101 to base 5 (Quintal) is 4032304000401. The convertion of 1011000101 to base 8 (Octal) is 7420521445. The convertion of 1011000101 to base 16 (Hexadecimal) is 3c42a325. The convertion of 1011000101 to base 32 is u458p5. The sine of the number 1011000101 is -0.25206863583222. The cosine of 1011000101 is -0.96770935865563. The tangent of 1011000101 is 0.26047969214889. The root of 1011000101 is 31796.227779408.
If you square 1011000101 you will get the following result 1022121204222010201. The natural logarithm of 1011000101 is 20.734205876886 and the decimal logarithm is 9.0047511989775. that 1011000101 is very special number! | 656 | 1,846 | {"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-2020-16 | latest | en | 0.71016 |
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# Chapter 8
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### Chapter 8
1. 1. Chapter 8 Analysis of Financial Statements ANSWERS TO BEGINNING-OF-CHAPTER QUESTIONS Answers and Solutions: 8 - 1
2. 2. The answers to these questions are all contained in the BOC Excel model for this chapter, where they are illustrated with actual data and the ratios are calculated. A B C D E F G H I 1 Worksheet for Chapter 8 BOC Questions 3/12/2005 2 We like to answer the Chapter 8 questions by going through the following model, which also helps 3 students become more familiar with Excel. Note that the data used in this file are the same as for the 4 Chapter 7 BOC questions. 5 6 1. Why are financial ratios used? Name five categories of ratios, and then list several ratios in each category. Would a bank loan officer, a bond analyst, a stock analyst, and a manager be likely to put the same emphasis 7 and interpretation on each ratio? Answer: (1) Liquidity (Current, Quick), (2) Asset Management (Inventory Turnover, DSO), Debt Management 8 (Debt/Total Assets, TIE), (3), Profitability (ROE, Profit Margin), Market Value ((P/E, Market/Book). Different analysts would probably emphasize somewhat different types of ratios. A banker considering a short-term loan would be especially interested in liquidity ratios and the debt/assets ratio to assess the short- term probability of repayment and the firm's liquidating value. Stock and bond analysts would be more 9 interested in the long-term situation, and they would consider all types of ratios, as would managers. The data provided in the financial statements are used to illustrate a number of the following 10 questions. 11 12 2. Suppose Company X has the data shown in the following financial statements. Answer the 13 following questions, giving numbers if all the required data are available or in general terms if the 14 necessary data are not available. Note that additional data are provided in the chapter BOC model. (a) 15 What is X’s DSO? If the industry average DSO is 30 days, and if X could reduce its accounts 16 receivable to the point where its DSO became 50 without affecting its sales or operating costs, how 17 would this affect: (b) Its free cash flow? (c) Its ROE? (d) Its debt ratio? (e) Its TIE ratio? (f) Its 18 Loan/EBITDA ratio? (g) Its P/E ratio? (h) Its M/B ratio? 19 Balance Sheets 2005 2006 Income Statements 2005 2006 20 Cash in bank \$5 \$6 Sales (net of discounts) \$ 90.00 \$ 100.00 21 Marketable securities \$5 \$6 Cost of goods sold (COGS) 73.00 76.00 22 Accounts receivable \$10 \$12 Admin and credit costs 5.00 6.00 23 Inventories \$25 \$26 Deprn and amortization 4.00 5.00 24 Current assets \$45 \$50 Operating Income (EBIT) \$ 8.00 \$ 13.00 25 Net fixed assets \$45 \$50 Interest expense 3.00 3.00 26 Total assets \$90 \$100 Taxable income \$ 5.00 \$ 10.00 27 Taxes (40%) 2.00 4.00 28 Accounts payable \$35 \$36 Net income \$ 3.00 \$ 6.00 29 Notes payable \$9 \$8 Dividends \$ 1.00 \$ 2.00 30 Accrued wages & taxes \$5 \$6 Additions to R.E. \$ 2.00 \$ 4.00 31 Current liabilities \$49 \$50 32 Long-term debt \$25 \$30 33 Total liabilities \$74 \$80 34 Common stock \$1 \$1 35 Retained earnings \$15 \$19 36 Total common equity \$16 \$20 37 Total liabilities & equity \$90 \$100 Answers and Solutions: 8 - 2
3. 3. A B C D E F G H I 38 2-a. 39 DSO: Days sales outstanding = Receivables/(sales/365) = 43.80 40 2-a. FCF: = Receivables/(sales/365) 30 41 Receivables = 30(Sales/365) 42 = \$ 8.22 vs. \$12 Originally 43 Difference = -\$3.78 44 This would be an addition to FCF in the year the change was made. Also, going forward, FCF 45 would be higher each year because receivables would increase less than under the old situation. 46 47 2-b. ROE: effect on the ROE would depend on what was done with the extra FCF. If it were used to repurchase The 48 stock, then equity would decline, earnings would presumably remain constant, and thus ROE would 49 increase. Similarly, if the FCF were used to retire debt, interest would decline, earnings would 50 increase, and ROE would again rise. Alternatively, the FCF could be reinvested in the business, which 51 would presumably incre4ase net income and again increase ROE. If the FCF were paid out in dividends, 52 then the future net income and equity would remain unchanged, hence there would be no effect on 53 ROE. Overall, though, the change would probably increase ROE under the assumed conditions. 54 See question 5 for the results if stock were repurchased; the ROE rises sharply. 55 56 2-c.D/A: If the FCF were used to retire debt, then the assets and the debt would both decline by the same amount. 57 The result would be a decline in the debt ratio: 58 Old ratio: \$80/\$100 = 80% 59 New ratio: (80-3.78)/(100-3.78) = 79% 60 If the FCF were used to retire stock, then assets would decline but debt would remain constant, and 61 the result would be an increase in the debt ratio: 62 Old ratio: \$80/\$100 = 80% 63 New ratio: (80)/(100-3.78) = 83% 64 65 2-d.TIE: The effect on the TIE ratio would depend on how the FCF was used. If used to retire debt, then interest 66 would decline, raising the TIE. If used to increase operating assets, added operating income would 67 presumably raise EBIT, hence the TIE. Stock repurchases would presumably not affect the TIE. 68 69 2-e. The effects here would be similar to the ones in 2-e. Retiring debt and purchasing assets would lower 70 Loan/EBITDA: and retiring stock would not affect it. the ratio, 71 72 2-f.P/E: Earnings should increase, and so should the price. However, it's hard to say which would increase 73 more, hence what the effect on the P/E would be. 74 75 2-g.M/B:The market value should increase if we add assets. The market value of the stock should also increase 76 if we retire debt. The market value of the equity might decline if we retire stock (but stockholders 77 would get cash, hence not be hurt. The book value would decline if stock were repurchased but remain 78 constant if the cash were used to retire debt or add assets (receivables would be replaced with other 79 assets). The M/B would probably increase, but this is not certain. 80 Answers and Solutions: 8 - 3
4. 4. A B C D E F G H I 81 3. How do managers, bankers, and security analysts use (a) trend analysis, (b) benchmarking, 82 (c) percent change analysis, and common size analysis? 83 84 Trend analysis is used to detect trends, which could show improving or deteriorating or improving 85 situations. Benchmrking would be used to compare the company with others in its peer group. 86 Common size analysis would be used to facilitate comparisons of balance sheets and income statements 87 of companies of different sizes. Managers would use the analysis to see where corrective actions were 88 needed, while bankers and security analysts would use the analysis to decide whether or not to invest in 89 the company. Bankers would also establish loan terms, or covenants, that incorporated these and other 90 ratios. Thus, in 2002 a number of energy trading companies and telcos got into trouble when their 91 results declined, they failed to satisfy loan covenants, and their loans were either called or their 92 interest rates were increased. This led to a number of bankruptcies. 93 94 4. Explain how ratio analysis in general, and the Du Pont System in particular, can be used by managers to 95 help maximize their firms’ stock prices. Use the data in Question 2 to illustrate the Du Pont equation. 96 97 The Du Pont system ties together three key ratios—the profit margin, the total assets turnover 98 ratio, and the equity ratio—to show how they interact to determine the ROE: 99 100 (Profit Margin)(Total Assets Turnover)(Equity Multiplier) = ROE 101 102 Net Income Sales Total Assets = ROE 103 Sales Total Assets Common Equity 104 6 1 0 0 1 0 0 105 = ( 6% )(1.0 )( 5) = 3 0.0% under the original conditions. 1 0 0 1 0 0 2 0 106 107 If the DSO were lowered to 30 days and the \$3.78 of freed capital were used to repurchase stock at book 108 value, then the total assets turnover would rise to 100/(100-3.78) = 1.0393, and the equity multiplier 109 would rise to (100-3.78)/(20-3.78) = 5.9322, and these two changes would increase the ROE to 110 (6%)(1.0393)(5.9322) =36.99%. 111 112 5. How would each of the following factors affect ratio analysis: (a) The firm’s sales are highly seasonal. (b) 113 The firm uses some type of window dressing. (c) The firm issues more debt and uses to proceeds to repurchase 114 stock. (d) The firm leases more of its fixed assets than most firms in its industry. (e) In an effort to stimulate 115 sales, the firm eases its credit policy by offering 60 day credit terms rather than the current 30 day terms. 116 Answer these questions in words; do not attempt to quantify your answer, but explain how one might use 117 sensitivity analysis to help quantify the answers. 118 119 5-a. If sales were seasonal, then inventories, receivables, payables, and accrual would vary over the year. 120 That would cause the ratios to fluctuate, making the analysis date quite important. Trend analysis on 121 an annual basis would be OK, but not quarterly without seasonal adjustments. Also, it would be 122 important to be sure that benchmark comparisons were based on comparable seasonal data. 123 Answers and Solutions: 8 - 4
5. 5. A B C D E F G H I 124 5-b. Window dressing involves making temporary changes toward the end of an accounting period to make 125 the balance sheet look better on the statement date. Mutual funds often sell losing stock, and purchase 126 ones that have gone up, to make it look like they have mainly winners in their portfolios. Enron sold 127 losing assets to trust accounts to get them off its books, and it had related trusts borrow money to keep 128 the debt off Enron's books. Similarly, Dynergy and some other energy traders sold electricity to one 129 another, causing both companies' revenues to appear to be higher than it really was. 130 Window dressing is designed to deceive investors. Some window dressing is legal, but Enron and 131 some other companies went too far and did things that were illegal as well as unethical. The SEC 132 and the accounting industry are under pressure to stop deceiving investors, so window dressing may 133 be less of a problem in the future than it has been in the past. 134 135 5-c. This would change many of the ratios, including the debt ratio, theTIE, the ROE, and so forth. The 136 effects could (and would) be simulated using the Excel model. 137 138 5-d. If a firm leases assets rather than buying and owning them, then its assets will be low relative to its 139 sales. It will have a liability--payments under the lease. If it bought, it might well have more debt as 140 shown on its balance sheet. Mainly, leasing might distort the debt ratio. 141 142 Note, though, that if the lease is determined to be a "capital lease" under accounting rules, then it must 143 be capitalized and shown on the balance sheet. The leased asset and the current value of the lease 144 obligation will be reported as an asset and an offsetting liability. 145 146 5-e. Extending the credit terms from 30 to 60 days would probably more than double the amount of receivables 147 reported on the balance sheet. If sales were constant, then receivables would probably double, but higher 148 sales would lead to even more receivables. The firm would also have to finance the higher level of 149 receivables, and if debt were used, that would affect the debt ratio. Moreover, higher sales would require 150 more inventory and perhaps more fixed assets, again bringing with it the requirement for more debt 151 and/or equity. Also, higher sales might result in greater profits, but the strategy could backfire and 152 cause lower profits. 153 In any event, it is clear that a change in policy can affect both the balance sheet and the income 154 statement, and the result is a change in many ratios. Computer simulation can be used to help 155 determine the effects of a credit policy change on the statement and the ratios. 156 157 6. How might one establish norms (or target values) for the financial ratios of a company that is just being 158 started? Where might data for this purpose be obtained? Could this type information be used to help determine 159 how much capital a new company would require? 160 161 One would look at other companies in the industry to get an idea of comparable companies' ratios. It might be 162 necessary to adjust for size and other factors, but some sort of comparison would surely be used. 163 164 Several sources of data are available, including the U.S. Department of Commerce, Dun & Bradstreet, 165 and banking associations. It might be hard to get exact data, though, because companies don't like to 166 provide information to their competitors. 167 168 If good ratio data were available, a start-up company could use it to get an idea of its financial 169 requirement. First, the start-up would forecast its sales, or a range of sales. Then, it would use the 170 ratios to forecast asset requirements. For example, if the sales/inventory ratio for other firms was 8, 171 then if our company anticipated sales of \$10 million, then its required inventory would be \$10/8 = \$1.25 172 million. Similar procedures could be use to estimate the requirements for other assets. Of course, 173 the firm would have to obtain the funds to buy the required assets, raising those funds either as debt or 174 equity. The comparable firms' debt ratios could be examined to get an idea of how successful firms in the 175 industry were financed. Answers and Solutions: 8 - 5
6. 6. ANSWERS TO END-OF-CHAPTER QUESTIONS 8-1 a. A liquidity ratio is a ratio that shows the relationship of a firm’s cash and other current assets to its current liabilities. The current ratio is found by dividing current assets by current liabilities. It indicates the extent to which current liabilities are covered by those assets expected to be converted to cash in the near future. The quick, or acid test, ratio is found by taking current assets less inventories and then dividing by current liabilities. b. Asset management ratios are a set of ratios that measure how effectively a firm is managing its assets. The inventory turnover ratio is sales divided by inventories. Days sales outstanding is used to appraise accounts receivable and indicates the length of time the firm must wait after making a sale before receiving cash. It is found by dividing receivables by average sales per day. The fixed assets turnover ratio measures how effectively the firm uses its plant and equipment. It is the ratio of sales to net fixed assets. Total assets turnover ratio measures the turnover of all the firm’s assets; it is calculated by dividing sales by total assets. c. Financial leverage ratios measure the use of debt financing. The debt ratio is the ratio of total debt to total assets, it measures the percentage of funds provided by creditors. The times-interest-earned ratio is determined by dividing earnings before interest and taxes by the interest charges. This ratio measures the extent to which operating income can decline before the firm is unable to meet its annual interest costs. The EBITDA coverage ratio is similar to the times-interest-earned ratio, but it recognizes that many firms lease assets and also must make sinking fund payments. It is found by adding EBITDA and lease payments then dividing this total by interest charges, lease payments, and sinking fund payments over one minus the tax rate. d. Profitability ratios are a group of ratios, which show the combined effects of liquidity, asset management, and debt on operations. The profit margin on sales, calculated by dividing net income by sales, gives the profit per dollar of sales. Basic earning power is calculated by dividing EBIT by total assets. This ratio shows the raw earning power of the firm’s assets, before the influence of taxes and leverage. Return on total assets is the ratio of net income to total assets. Return on common equity is found by dividing net income into common equity. Answers and Solutions: 8 - 6
7. 7. e. Market value ratios relate the firm’s stock price to its earnings and book value per share. The price/earnings ratio is calculated by dividing price per share by earnings per share--this shows how much investors are willing to pay per dollar of reported profits. The price/cash flow is calculated by dividing price per share by cash flow per share. This shows how much investors are willing to pay per dollar of cash flow. Market-to-book ratio is simply the market price per share divided by the book value per share. Book value per share is common equity divided by the number of shares outstanding. f. Trend analysis is an analysis of a firm’s financial ratios over time. It is used to estimate the likelihood of improvement or deterioration in its financial situation. Comparative ratio analysis is when a firm compares its ratios to other leading companies in the same industry. This technique is also known as benchmarking. g. The Du Pont equation is a formula, which shows that the rate of return on assets can be found as the product of the profit margin times the total assets turnover. Window dressing is a technique employed by firms to make their financial statements look better than they really are. Seasonal factors can distort ratio analysis. At certain times of the year a firm may have excessive inventories in preparation of a “season” of high demand. Therefore an inventory turnover ratio taken at this time as opposed to after the season will be radically distorted. 8-2 The emphasis of the various types of analysts is by no means uniform nor should it be. Management is interested in all types of ratios for two reasons. First, the ratios point out weaknesses that should be strengthened; second, management recognizes that the other parties are interested in all the ratios and that financial appearances must be kept up if the firm is to be regarded highly by creditors and equity investors. Equity investors are interested primarily in profitability, but they examine the other ratios to get information on the riskiness of equity commitments. Long-term creditors are more interested in the debt ratio, TIE, and fixed-charge coverage ratios, as well as the profitability ratios. Short-term creditors emphasize liquidity and look most carefully at the liquidity ratios. 8-3 Given that sales have not changed, a decrease in the total assets turnover means that the company’s assets have increased. Also, the fact that the fixed assets turnover ratio remained constant implies that the company increased its current assets. Since the company’s current ratio increased, and yet, its quick ratio is unchanged means that the company has increased its inventories. Answers and Solutions: 8 - 7
8. 8. 8-4 Differences in the amounts of assets necessary to generate a dollar of sales cause asset turnover ratios to vary among industries. For example, a steel company needs a greater number of dollars in assets to produce a dollar in sales than does a grocery store chain. Also, profit margins and turnover ratios may vary due to differences in the amount of expenses incurred to produce sales. For example, one would expect a grocery store chain to spend more per dollar of sales than does a steel company. Often, a large turnover will be associated with a low profit margin, and vice versa. 8-5 a. Cash, receivables, and inventories, as well as current liabilities, vary over the year for firms with seasonal sales patterns. Therefore, those ratios that examine balance sheet figures will vary unless averages (monthly ones are best) are used. b. Common equity is determined at a point in time, say December 31, 2006. Profits are earned over time, say during 2006. If a firm is growing rapidly, year-end equity will be much larger than beginning-of-year equity, so the calculated rate of return on equity will be different depending on whether end-of-year, beginning-of-year, or average common equity is used as the denominator. Average common equity is conceptually the best figure to use. In public utility rate cases, people are reported to have deliberately used end-of-year or beginning-of-year equity to make returns on equity appear excessive or inadequate. Similar problems can arise when a firm is being evaluated. 8-6 Firms within the same industry may employ different accounting techniques, which make it difficult to compare financial ratios. More fundamentally, comparisons may be misleading if firms in the same industry differ in their other investments. For example, comparing Pepsico and Coca-Cola may be misleading because apart from their soft drink business, Pepsi also owns other businesses such as Frito-Lay, Pizza Hut, Taco Bell, and KFC. Answers and Solutions: 8 - 8
9. 9. SOLUTIONS TO END-OF-CHAPTER PROBLEMS CA CA - I 8-1 CA = \$3,000,000; = 1.5; = 1.0; CL CL CL = ?; I = ? CA = 1.5 CL \$3,000,000 = 1.5 CL 1.5 CL = \$3,000,000 CL = \$2,000,000. CA - I = 1.0 CL \$3,000,000 - I = 1.0 \$2,000,000 \$3,000,000 - I = \$2,000,000 I = \$1,000,000. 8-2 DSO = 40 days; ADS = \$20,000; AR = ? AR DSO = S 365 AR 40 = \$20,000 AR = \$800,000. Answers and Solutions: 8 - 9
10. 10. 8-3 A/E = 2.4; D/A = ? D 1 = 1 - A A E D 1 = 1 - A 2.4 D = 0.5833 = 58.33%. A 8-4 ROA = 10%; PM = 2%; ROE = 15%; S/TA = ?; A/E = ? ROA = NI/A; PM = NI/S; ROE = NI/E ROA = PM × S/TA NI/A = NI/S × S/TA 10% = 2% × S/TA S/TA = 5. ROE = PM × S/TA × TA/E NI/E = NI/S × S/TA × TA/E 15% = 2% × 5 × TA/E 15% = 10% × TA/E TA/E = 1.5. Answers and Solutions: 8 - 10
11. 11. 8-5 We are given ROA = 3% and Sales/Total assets = 1.5×. From Du Pont equation: ROA = Profit margin × Total assets turnover 3% = Profit margin (1.5) Profit margin = 3%/1.5 = 2%. We can also calculate the company’s debt ratio in a similar manner, given the facts of the problem. We are given ROA(NI/A) and ROE(NI/E); if we use the reciprocal of ROE we have the following equation: E NI E D E = _ and =1- , so A A NI A A E 1 = 3% _ A 0.05 E = 60% . A D = 1 - 0.60 = 0.40 = 40% . A Alternatively, ROE = ROA × EM 5% = 3% × EM EM = 5%/3% = 5/3 = TA/E. Take reciprocal: E/TA = 3/5 = 60%; therefore, D/A = 1 - 0.60 = 0.40 = 40%. Thus, the firm’s profit margin = 2% and its debt ratio = 40%. Answers and Solutions: 8 - 11
12. 12. \$1,312,500 8-6 Present current ratio = = 2.5. \$525,000 \$1,312,500 + ∆ NP Minimum current ratio = = 2.0. \$525,000 + ∆ NP \$1,312,500 + ∆NP = \$1,050,000 + 2∆NP ∆NP = \$262,500. Short-term debt can increase by a maximum of \$262,500 without violating a 2 to 1 current ratio, assuming that the entire increase in notes payable is used to increase current assets. Since we assumed that the additional funds would be used to increase inventory, the inventory account will increase to \$637,500, and current assets will total \$1,575,000. Quick ratio = (\$1,575,000 - \$637,500)/\$787,500 = \$937,500/\$787,500 = 1.19×. Current assets \$810,000 8-7 1. = 3.0× = 3.0× Current liabilities Current liabilities Current liabilities = \$270,000. Current assets - Inventories \$810,000 - Inventories 2. = 1.4× = 1.4× Current liabilities \$270,000 Inventories = \$432,000. Current Marketable Accounts 3. = Cash + + + Inventories assets Securities receivable \$810,000 = \$120,000 + Accounts receivable + \$432,000 Accounts receivable = \$258,000. Sales Sales 4. = 6.0× = 6.0× Inventory \$432,000 Sales = \$2,592,000. Accounts receivable \$258,000 5. DSO = = = 36.33 days. Sales/ 365 \$2,592,000 / 365 Answers and Solutions: 8 - 12
13. 13. 8-8 TIE = EBIT/INT, so find EBIT and INT. Interest = \$500,000 × 0.1 = \$50,000. Net income = \$2,000,000 × 0.05 = \$100,000. Pre-tax income = \$100,000/(1 - T) = \$100,000/0.7 = \$142,857. EBIT = \$142,857 + \$50,000 = \$192,857. TIE = \$192,857/\$50,000 = 3.86×. Answers and Solutions: 8 - 13
14. 14. 8-9 a. (Dollar amounts in thousands.) Industry Firm Average Current assets \$655,000 = = 1.98× 2.0× Current liabilities \$330,000 Accounts receivable \$336,000 DSO = = = 76 days 35 days Sales/ 365 \$4,404.11 Sales \$1,607,500 = = 6.66× 6.7× Inventory \$241,500 Sales \$1,607,500 = = 5.50× 12.1× Fixed assets \$292,500 Sales \$1,607,500 = = 1.70× 3.0× Total assets \$947,500 Net income \$27,300 = = 1.7% 1.2% Sales \$1,607,500 Net income \$27,300 = = 2.9% 3.6% Total assets \$947,500 Industry Firm Average Net income \$27,300 = = 7.6% 9.0% Common equity \$361,000 Total debt \$586,500 = = 61.9% 60.0% Total assets \$947,500 b. For the firm, \$947,500 ROE = PM × T.A. turnover × EM = 1.7% × 1.7 × = 7.6%. \$361,000 For the industry, ROE = 1.2% × 3 × 2.5 = 9%. Answers and Solutions: 8 - 14
15. 15. Note: To find the industry ratio of assets to common equity, recognize that 1 - (total debt/total assets) = common equity/total assets. So, common equity/total assets = 40%, and 1/0.40 = 2.5 = total assets/common equity. c. The firm’s days sales outstanding is more than twice as long as the industry average, indicating that the firm should tighten credit or enforce a more stringent collection policy. The total assets turnover ratio is well below the industry average so sales should be increased, assets decreased, or both. While the company’s profit margin is higher than the industry average, its other profitability ratios are low compared to the industry--net income should be higher given the amount of equity and assets. However, the company seems to be in an average liquidity position and financial leverage is similar to others in the industry. d. If 2006 represents a period of supernormal growth for the firm, ratios based on this year will be distorted and a comparison between them and industry averages will have little meaning. Potential investors who look only at 2005 ratios will be misled, and a return to normal conditions in 2007 could hurt the firm’s stock price. 8-10 1. Debt = (0.50)(Total assets) = (0.50)(\$300,000) = \$150,000. 2. Accounts payable = Debt – Long-term debt = \$150,000 - \$60,000 = \$90,000 Total liabilities 3. Common stock = - Debt - Retained earnings and equity = \$300,000 - \$150,000 - \$97,500 = \$52,500. 4. Sales = (1.5)(Total assets) = (1.5)(\$300,000) = \$450,000. 5. Inventory = Sales/5 = \$450,000/5 = \$90,000. 6. Accounts receivable = (Sales/365)(DSO) = (\$450,000/365)(36.5) = \$45,000. 7. Cash + Accounts receivable = (0.80)(Accounts payable) Cash + \$45,000 = (0.80)(\$90,000) Cash = \$72,000 - \$45,000 = \$27,000. 8. Fixed assets = Total assets - (Cash + Accts rec. + Inventories) = \$300,000 - (\$27,000 + \$45,000 + \$90,000) = \$138,000. 9. Cost of goods sold = (Sales)(1 - 0.25) = (\$450,000)(0.75) = \$337,500. Answers and Solutions: 8 - 15
16. 16. 8-11 a. Here are the firm’s base case ratios and other data as compared to the industry: Firm Industry Comment Quick 0.8× 1.0× Weak Current 2.3 2.7 Weak Inventory turnover 4.8 7.0 Poor Days sales outstanding 37 days 32 days Poor Fixed assets turnover 10.0× 13.0× Poor Total assets turnover 2.3 2.6 Poor Return on assets 5.9% 9.1% Bad Return on equity 13.1 18.2 Bad Debt ratio 54.8 50.0 High Profit margin on sales 2.5 3.5 Bad EPS \$4.71 n.a. -- Stock Price \$23.57 n.a. -- P/E ratio 5.0× 6.0× Poor P/CF ratio 2.0× 3.5× Poor M/B ratio 0.65 n.a. -- The firm appears to be badly managed--all of its ratios are worse than the industry averages, and the result is low earnings, a low P/E, P/CF ratio, a low stock price, and a low M/B ratio. The company needs to do something to improve. b. A decrease in the inventory level would improve the inventory turnover, total assets turnover, and ROA, all of which are too low. It would have some impact on the current ratio, but it is difficult to say precisely how that ratio would be affected. If the lower inventory level allowed the company to reduce its current liabilities, then the current ratio would improve. The lower cost of goods sold would improve all of the profitability ratios and, if dividends were not increased, would lower the debt ratio through increased retained earnings. All of this should lead to a higher market/book ratio and a higher stock price. Answers and Solutions: 8 - 16
17. 17. SOLUTION TO SPREADSHEET PROBLEM 8-12 The detailed solution for the problem is available both on the instructor’s resource CD- ROM (in the file Solution to IFM9 Ch 08 P12 Build a Model.xls) and on the instructor’s side of the web site, http://now.swlearning.com/brigham. Answers and Solutions: 8 - 17
18. 18. MINI CASE Notes to Instructors: (1)Some instructors choose to assign the Mini Case as homework. Therefore, the PowerPoint slides for the mini case, IFM9 Ch 08 Show.ppt, and the accompanying Excel file, IFM9 Ch 08 Mini Case.xls, are not included for the students on ThomsonNow. However, many instructors, including us, want students to have copies of class notes. Therefore, we make the PowerPoint slides and Excel worksheets available to our students by posting them to our password-protected Web. We encourage you to do the same if you would like for your students to have these files. The first part of the case, presented in Chapter 7, discussed the situation that Computron Industries was in after an expansion program. Thus far, sales have not been up to the forecasted level, costs have been higher than were projected, and a large loss occurred in 2006, rather than the expected profit. As a result, its managers, directors, and investors are concerned about the firm’s survival. Donna Jamison was brought in as assistant to Fred Campo, Computron’s chairman, who had the task of getting the company back into a sound financial position. Computron’s 2005 and 2006 balance sheets and income statements, together with projections for 2007, are shown in the following tables. Also, the tables show the 2005 and 2006 financial ratios, along with industry average data. The 2007 projected financial statement data represent Jamison’s and Campo’s best guess for 2007 results, assuming that some new financing is arranged to get the company “over the hump.” Jamison examined monthly data for 2006 (not given in the case), and she detected an improving pattern during the year. Monthly sales were rising, costs were falling, and large losses in the early months had turned to a small profit by December. Thus, the annual data looked somewhat worse than final monthly data. Also, it appears to be taking longer for the advertising program to get the message across, for the new sales offices to generate sales, and for the new manufacturing facilities to operate efficiently. In other words, the lags between spending money and deriving benefits were longer than Computron’s managers had anticipated. For these reasons, Jamison and Campo see hope for the company--provided it can survive in the short run. Jamison must prepare an analysis of where the company is now, what it must do to regain its financial health, and what actions should be taken. Your assignment is to help her answer the following questions. Provide clear explanations, not yes or no answers. Mini Case: 8 - 18
19. 19. Balance Sheets Assets 2005 2006 2007e Cash \$ 9,000 \$ \$ 7,282 14,000 Short-Term Investments. 48,600 20,000 71,632 Accounts Receivable 351,200 632,160 878,000 Inventories 715,200 1,287,360 1,716,480 Total Current Assets \$ \$ \$ 1,124,000 1,946,802 2,680,112 Gross Fixed Assets 491,000 1,202,950 1,220,000 Less: Accumulated Depreciation 146,200 263,160 383,160 Net Fixed Assets \$ \$ \$ 344,800 939,790 836,840 Total Assets \$ \$ \$ 1,468,800 2,886,592 3,516,952 Liabilities And Equity 2005 2006 2007e Accounts Payable \$ \$ \$ 145,600 324,000 359,800 Notes Payable 200,000 720,000 300,000 Accruals 136,000 284,960 380,000 Total Current Liabilities \$ \$ \$ 481,600 1,328,960 1,039,800 Long-Term Debt 323,432 1,000,000 500,000 Common Stock (100,000 Shares) 460,000 460,000 1,680,936 Retained Earnings 203,768 97,632 296,216 Total Equity \$ \$ \$ 663,768 557,632 1,977,152 Total Liabilities And Equity \$ \$ \$ 1,468,800 2,886,592 3,516,952 Mini Case: 8 - 19
20. 20. Income Statements 2005 2006 2007e Sales \$ \$ 5,834,400 \$ 3,432,000 7,035,600 Cost Of Goods Sold 2,864,000 4,980,000 5,800,000 Other Expenses 340,000 720,000 612,960 Depreciation 18,900 116,960 120,000 Total Operating Costs \$ \$ 5,816,960 \$ 3,222,900 6,532,960 EBIT \$ \$ 17,440 \$ 209,100 502,640 Interest Expense 62,500 176,000 80,000 EBT \$ \$ \$ 146,600 (158,560) 422,640 Taxes (40%) 58,640 (63,424) 169,056 Net Income \$ \$ \$ 87,960 (95,136) 253,584 Other Data 2005 2006 2007e Stock Price \$ \$ 6.00 \$ 8.50 12.17 Shares Outstanding 100,000 100,000 250,000 EPS \$ \$ \$ 0.880 (0.951) 1.014 DPS \$ \$ 0.110 \$ 0.220 0.220 Tax Rate 40% 40% 40% Book Value Per Share \$ \$ 5.576 \$ 6.638 7.909 Lease Payments \$ \$ 40,000 \$ 40,000 40,000 Mini Case: 8 - 20
21. 21. Ratio Analysis 2005 2006 2007e Industry Average Current 2.3 1.5 2.58 2.7 Quick 0.8 0.5 0.93 1.0 Inventory Turnover 4.8 4.5 4.10 6.1 Days Sales Outstanding 37. 39. 45.5 32.0 4 5 Fixed Assets Turnover 10. 6. 8.4 7.0 0 2 1 Total Assets Turnover 2. 2. 2.0 2.5 3 0 0 Debt Ratio 54.8% 80.7% 43.8% 50.0% TIE 3.3 0.1 6.3 6.2 EBITDA Coverage 2.6 0.8 5.5 8.0 Profit Margin 2.6% -1.6% 3.6% 3.6% Basic Earning Power 14.2% 0.6% 14.3% 17.8% ROA 6.0% -3.3% 7.2% 9.0% ROE 13.3% -17.1% 12.8% 17.9% Price/Earnings (P/E) 9.7 -6.3 12.0 16.2 Price/Cash Flow 8.0 27.5 8.1 7.6 Market/Book 1.3 1.1 1.5 2.9 a. Why are ratios useful? What are the five major categories of ratios? Answer: Ratios are used by managers to help improve the firm’s performance, by lenders to help evaluate the firm’s likelihood of repaying debts, and by stockholders to help forecast future earnings and dividends. The five major categories of ratios are: liquidity, asset management, debt management, profitability, and market value. Mini Case: 8 - 21
22. 22. b. Calculate the 2007 current and quick ratios based on the projected balance sheet and income statement data. What can you say about the company’s liquidity position in 2005, 2006, and as projected for 2007? We often think of ratios as being useful (1) to managers to help run the business, (2) to bankers for credit analysis, and (3) to stockholders for stock valuation. Would these different types of analysts have an equal interest in the liquidity ratios? Answer: Current Ratio07 = Current Assets/Current Liabilities = \$2,680,112/\$1,039,800 = 2.58×. Quick Ratio07 = (Current Assets – Inventory)/Current Liabilities = (\$2,680,112 - \$1,716,480)/\$1,039,800 = 0.93×. The company’s current and quick ratios are higher relative to its 2005 current and quick ratios; they have improved from their 2006 levels. Both ratios are below the industry average, however. c. Calculate the 2007 inventory turnover, days sales outstanding (DSO), fixed assets turnover, and total assets turnover. How does Computron’s utilization of assets stack up against other firms in its industry? Answer: Inventory Turnover07 = Sales/Inventory = \$7,035,600/\$1,716,480 = 4.10×. DSO07 = Receivables/(Sales/365) = \$878,000/(\$7,035,600/365) = 45.5 Days. Fixed Assets Turnover07 = Sales/Net Fixed Assets = \$7,035,600/\$836,840 = 8.41×. Total Assets Turnover07 = Sales/Total Assets = \$7,035,600/\$3,516,952 = 2.0×. The firm’s inventory turnover ratio has been steadily declining, while its days sales outstanding has been steadily increasing. While the firm’s fixed assets turnover ratio is below its 2005 level, it is above the 2006 level. The firm’s total assets turnover ratio is below its 2005 level and equal to its 2006 level. The firm’s inventory turnover and total assets turnover are below the industry average. The firm’s days sales outstanding is above the industry average (which is bad); however, the firm’s fixed assets turnover is above the industry average. (This might be due to the fact that Computron is an older firm than most other firms in the Mini Case: 8 - 22
23. 23. industry, in which case, its fixed assets are older and thus have been depreciated more, or that Computron’s cost of fixed assets were lower than most firms in the industry.) d. Calculate the 2007 debt, times-interest-earned, and EBITDA coverage ratios. How does Computron compare with the industry with respect to financial leverage? What can you conclude from these ratios? Answer: Debt Ratio07 = Total Liabilities/Total Assets = (\$1,039,800 + \$500,000)/\$3,516,952 = 43.8%. Tie07 = EBIT/Interest = \$502,640/\$80,000 = 6.3×. Lease Loan Lease EBITDA Coverage07 = EBITDA + / Interest + + Payments Repayments Payments = (\$502,640 + \$120,000 + \$40,000)/(\$80,000 + \$40,000) = 5.5×. The firm’s debt ratio is much improved from 2005, and is still lower than its 2004 level and the industry average. The firm’s TIE and EBITDA coverage ratios are much improved from their 2005 and 2006 levels. The firm’s TIE is better than the industry average, but the EBITDA coverage is lower, reflecting the firm’s higher lease obligations. e. Calculate the 2007 profit margin, basic earning power (BEP), return on assets (ROA), and return on equity (ROE). What can you say about these ratios? Answer: Profit Margin07 = Net Income/Sales = \$253,584/\$7,035,600 = 3.6%. Basic Earning Power07 = EBIT/Total Assets = \$502,640/\$3,516,952 = 14.3%. Mini Case: 8 - 23
24. 24. ROA07 = Net Income/Total Assets = \$253,584/\$3,516,952 = 7.2%. ROE07 = Net Income/Common Equity = \$253,584/\$1,977,152 = 12.8%. The firm’s profit margin is above 2005 and 2006 levels and is at the industry average. The basic earning power, ROA, and ROE ratios are above both 2005 and 2006 levels, but below the industry average due to poor asset utilization. f. Calculate the 2007 price/earnings ratio, price/cash flow ratios, and market/book ratio. Do these ratios indicate that investors are expected to have a high or low opinion of the company? Answer: EPS = Net Income/Shares Outstanding = \$253,584/250,000 = \$1.0143. Price/Earnings07 = Price Per Share/Earnings Per Share = \$12.17/\$1.0143 = 12.0×. Check: Price = EPS × P/E = \$1.0143(12) = \$12.17. Cash Flow/Share07 = (NI + DEP)/Shares = (\$253,584 + \$120,000)/250,000 = \$1.49. Price/Cash Flow = \$12.17/\$1.49 = 8.2×. BVPS = Common Equity/Shares Outstanding = \$1,977,152/250,000 = \$7.91. Market/Book = Market Price Per Share/Book Value Per Share = \$12.17/\$7.91 = 1.54x. Both the P/E ratio and BVPS are above the 2005 and 2006 levels but below the industry average. g. Perform a common size analysis and percent change analysis. What do these analyses tell you about Computron? Answer: For the common size balance sheets, divide all items in a year by the total assets for that year. For the common size income statements, divide all items in a year by the sales in that year. Mini Case: 8 - 24
25. 25. Common Size Balance Sheets Assets 2005 2006 2007e Ind. Cash 0.6% 0.3% 0.4% 0.3% Short Term Investments 3.3% 0.7% 2.0% 0.3% Accounts Receivable 23.9% 21.9% 25.0% 22.4% Inventories 48.7% 44.6% 48.8% 41.2% Total Current Assets 76.5% 67.4% 76.2% 64.1% Gross Fixed Assets 33.4% 41.7% 34.7% 53.9% Less Accumulated Depreciation 10.0% 9.1% 10.9% 18.0% Net Fixed Assets 23.5% 32.6% 23.8% 35.9% Total Assets 100.0 100.0 100.0 100.0 % % % % Liabilities And Equity 2005 2006 2007e Ind. Accounts Payable 9.9% 11.2% 10.2% 11.9% Notes Payable 13.6% 24.9% 8.5% 2.4% Accruals 9.3% 9.9% 10.8% 9.5% Total Current Liabilities 32.8% 46.0% 29.6% 23.7% Long-Term Debt 22.0% 34.6% 14.2% 26.3% Common Stock (100,000 Shares) 31.3% 15.9% 47.8% 20.0% Retained Earnings 13.9% 3.4% 8.4% 30.0% Total Equity 45.2% 19.3% 56.2% 50.0% Total Liabilities And Equity 100.0 100.0 100.0 100.0 % % % % Common Size Income Statement 2005 2006 2007e Ind. Sales 100.0 100.0 100.0 100.0 % % % % Cost Of Goods Sold 83.4% 85.4% 82.4% 84.5% Other Expenses 9.9% 12.3% 8.7% 4.4% Depreciation 0.6% 2.0% 1.7% 4.0% Total Operating Costs 93.9% 99.7% 92.9% 92.9% EBIT 6.1% 0.3% 7.1% 7.1% Interest Expense 1.8% 3.0% 1.1% 1.1% EBT 4.3% -2.7% 6.0% 5.9% Taxes (40%) 1.7% -1.1% 2.4% 2.4% Net Income 2.6% -1.6% 3.6% 3.6% Mini Case: 8 - 25
26. 26. Computron has higher proportion of inventory and current assets than industry. Computron has slightly more equity (which means less debt) than industry. Computron has more short-term debt than industry, but less long-term debt than industry. Computron has lower COGS than industry, but higher other expenses. Result is that Computron has similar EBIT as industry. Mini Case: 8 - 26
27. 27. For the percent change analysis, divide all items in a row by the value in the first year of the analysis. Mini Case: 8 - 27
28. 28. Percent Change Balance Sheets Assets 2005 2006 2007e Cash 0.0% -19.1% 55.6% Short Term Investments 0.0% -58.8% 47.4% Accounts Receivable 0.0% 80.0% 150.0 % Inventories 0.0% 80.0% 140.0 % Total Current Assets 0.0% 73.2% 138.4 % Gross Fixed Assets 0.0% 145.0 148.5 % % Less Accumulated Depreciation 0.0% 80.0% 162.1 % Net Fixed Assets 0.0% 172.6 142.7 % % Total Assets 0.0% 96.5% 139.4 % Liabilities And Equity 2005 2006 2007e Accounts Payable 0.0% 122.5 147.1 % % Notes Payable 0.0% 260.0 50.0% % Accruals 0.0% 109.5 179.4 % % Total Current Liabilities 0.0% 175.9 115.9 % % Long-Term Debt 0.0% 209.2 54.6% % Common Stock (100,000 Shares) 0.0% 0.0% 265.4 % Retained Earnings 0.0% -52.1% 45.4% Total Equity 0.0% -16.0% 197.9 % Total Liabilities And Equity 0.0% 96.5% 139.4 % Mini Case: 8 - 28
29. 29. Percent Change Income 2005 2006 2007e Statement Sales 0.0% 70.0% 105.0 % Cost Of Goods Sold 0.0% 73.9% 102.5 % Other Expenses 0.0% 111.8% 80.3% Depreciation 0.0% 518.8% 534.9 % Total Operating Costs 0.0% 80.5% 102.7 % EBIT 0.0% -91.7% 140.4 % Interest Expense 0.0% 181.6% 28.0% EBT 0.0% -208.2 188.3 % % Taxes (40%) 0.0% -208.2 188.3 % % Net Income 0.0% -208.2 188.3 % % We see that 2007 sales grew 105% from 2005, and that NI grew 188% from 2005. So Computron has become more profitable. We see that total assets grew at a rate of 139%, while sales grew at a rate of only 105%. So asset utilization remains a problem. Mini Case: 8 - 29
30. 30. h. Use the extended Du Pont equation to provide a summary and overview of Computron’s financial condition as projected for 2007. What are the firm’s major strengths and weaknesses? Profit Total Assets Equity Answer: Du Pont Equation = × × Margin Turnover Multiplier = 3.6% × 2.0 × (\$3,516,952/\$1,977,152) = 3.6% × 2.0 × 1.8 = 13.0%. Strengths: The firm’s fixed assets turnover was above the industry average. However, if the firm’s assets were older than other firms in its industry this could possibly account for the higher ratio. (Computron’s fixed assets would have a lower historical cost and would have been depreciated for longer periods of time.) The firm’s profit margin is slightly above the industry average, despite its higher debt ratio. This would indicate that the firm has kept costs down, but, again, this could be related to lower depreciation costs. Weaknesses: The firm’s liquidity ratios are low; most of its asset management ratios are poor (except fixed assets turnover); its debt management ratios are poor, most of its profitability ratios are low (except profit margin); and its market value ratios are low. i. What are some potential problems and limitations of financial ratio analysis? Answer: Some potential problems are listed below: 1. Comparison with industry averages is difficult if the firm operates many different divisions. 2. Different operating and accounting practices distort comparisons. 3. Sometimes hard to tell if a ratio is “good” or “bad.” 4. Difficult to tell whether company is, on balance, in a strong or weak position. 5. “Average” performance is not necessarily good. 6. Seasonal factors can distort ratios. 7. “Window dressing” techniques can make statements and ratios look better. Mini Case: 8 - 30
31. 31. j. What are some qualitative factors analysts should consider when evaluating a company’s likely future financial performance? Answer: Top analysts recognize that certain qualitative factors must be considered when evaluating a company. These factors, as summarized by the American Association Of Individual Investors (AAII), are as follows: 1. Are the company’s revenues tied to one key customer? 2. To what extent are the company’s revenues tied to one key product? 3. To what extent does the company rely on a single supplier? 4. What percentage of the company’s business is generated overseas? 5. Competition 6. Future prospects 7. Legal and regulatory environment Mini Case: 8 - 31 | 12,899 | 44,846 | {"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} | 3.234375 | 3 | CC-MAIN-2015-35 | longest | en | 0.915063 |
https://stemez.com/subjects/science/DPhysics/DPhysics/DPhysics/D36-1057.htm | 1,653,382,623,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662570051.62/warc/CC-MAIN-20220524075341-20220524105341-00353.warc.gz | 616,681,933 | 5,414 | PROBLEM 36 – 1057: Calculate the mass of the light isotope of helium from the
following reaction, which has a Q−value of 3.945 MeV:
3Li6 + 1H1 = 2He4 + 2He3.
The masses in amu of 1H1 , 2He4, and 3Li6 are 1.00813,
4.00386, and 6.01692, respectively.
Solution: In the reaction 3.945 MeV of energy is released. By Einstein's mass
energy relation
E = mc2 ,
this energy is equivalent to a mass whose value is:
m = E / c2 = (3.945 × 106 eV ) / ( 9 × 1016 m2/s2)
Since 1 eV = 1.6 × 10−19 Joules
m = {(3.945 × 106 eV ) (1.6 × 10−19 Joules / eV) } / ( 9 × 1016 m2/s2)
m = 7.013 × 10−30 kg
Converting this to atomic mass units by noting that
1 kg = 6.024 × 1026 amu
we obtain
m = (7.013 × 10−30 kg ) (6.024 × 1026 amu /kg)
m = 4.23 × 10−3 amu
m = .00423 amu
This must be the difference in mass between reactants and products, or
m = mreact . – m prod. (1)
The sum of the masses of the initial particles is
mreact. = 1.00813 + 6.01692 = 7.02505 amu (2)
But
mprod. = mα + mHe (3)
Using (3) in (1)
m = mreact. − mα − mHe
Hence , mHe = mreact. − mα − m
Using (2)
mHe = 7.02505 amu − 4.00386 amu − .00423 amu
mHe = .01696 amu
This must be the mass of an atom of the light isotope of helium. | 505 | 1,404 | {"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} | 3.71875 | 4 | CC-MAIN-2022-21 | latest | en | 0.753437 |
https://www.finance-tutoring.fr/blog/?tag=Rate | 1,723,114,336,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722640726723.42/warc/CC-MAIN-20240808093647-20240808123647-00800.warc.gz | 573,922,385 | 13,760 | ARTICLES AVEC LE TAG : "Rate"
I. Stochastic Models and Processes · 14. novembre 2023
A caplet is a financial derivative, akin to a call option, used for hedging against interest rate increases. It pays out if the interest rate exceeds a predetermined rate (K) at the end of a period. The payout, calculated as α * max(LT - K, 0), depends on the period's interest rate (LT) and the day count fraction (α), reflecting the time span of the caplet. It effectively caps the borrower's interest rate costs, ensuring they don't exceed the strike rate K
I. Stochastic Models and Processes · 13. novembre 2023
Bond convexity describes the curve-like relationship between bond prices and interest rates, causing prices to rise more when rates drop than they fall when rates rise. This curvature means bond price changes are not linear and convexity corrects pricing models, especially for large rate moves. #BondConvexity
I. Stochastic Models and Processes · 03. novembre 2023
The Cheyette Model is a complex financial tool for predicting interest rate movements, accounting for time-varying mean reversion and volatility. It's more intricate than simpler models like Vasicek due to its detailed parameters, which makes it robust but computationally intensive and less commonly used in practice.
I. Stochastic Models and Processes · 01. novembre 2023
The Bjerksund-Stensland model modifies Black-Scholes-Merton to value American options with dividends. It calculates when to exercise early, using an "early exercise boundary." If the stock's below this, exercising might be wise; if above, holding on could be better. It factors in discrete dividends, unlike the continuous assumption in Black-Scholes.
I. Stochastic Models and Processes · 01. novembre 2023
The Vasicek model predicts interest rates using mean reversion, volatility, and the speed of reversion. Its equation, `dr(t) = κ(θ - r(t)) dt + σ dW(t)`, models rates' return to a mean (θ) with volatility (σ) and randomness (dW(t)). It's vital for financial strategies and simulations.
The Cox-Ingersoll-Ross (CIR) model is essential for modeling interest rate evolution with mean reversion, variable volatility, and a square root process that precludes negative rates. Used for valuing financial instruments sensitive to rate changes, its parameters guide simulations of rate behavior. #CIRModel #InterestRates #Finance
The Libor Market Model (LMM) is like a weather forecast for interest rates. Instead of predicting rain or sunshine, it predicts how "Libor" rates might change over time. Just as you'd carry an umbrella based on a rain forecast, businesses use LMM to prepare for future interest rate changes. By simulating different rate scenarios, companies can make informed decisions, like fixing a rate now to avoid potential hikes later. It's a tool to anticipate the financial climate and act smartly.
FINANCE TUTORING
Organisme de Formation Enregistré sous le Numéro 24280185328
Contact : Florian CAMPUZAN Téléphone : 0680319332
E-mail : fcampuzan@finance-tutoring.fr
© 2024 FINANCE TUTORING, Tous Droits Réservés | 711 | 3,078 | {"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} | 2.53125 | 3 | CC-MAIN-2024-33 | latest | en | 0.821727 |
https://brainly.com/question/329439 | 1,484,735,965,000,000,000 | text/html | crawl-data/CC-MAIN-2017-04/segments/1484560280266.9/warc/CC-MAIN-20170116095120-00360-ip-10-171-10-70.ec2.internal.warc.gz | 807,769,721 | 9,826 | # Ex 3.6 19. find the area bounded by the curve y= (4-x²)^(1/2), the x-axis and the y-axis in the first quadrant
2
by logo88
It's going to take a long time to prove this, so I'm going to answer it using a whiteboard and attachments.
I know that the answer is pi units squared.
• Brainly User
2015-02-28T11:23:11-05:00
### This Is a Certified Answer
Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
This one is very straightforward. You won't need calculus to solve this problem.
What you basically have is a quarter circle with a radius of 2.
We know that the area of a circle is:
A=πr²
But in this case we have to use the formula:
1/4A=1/4πr²=A₂
-----------------------------------------------------------
Therefore:
A₂=1/4 * π * 2²
=1/4 * 4 * π
---------------------------------------------------------
The answer is π units squared, but I'm going to use calculus to prove why it's the case.
Please view the attachments to see the proof.
2015-03-01T12:06:32-05:00
Y = (4 - x²)^1/2
y = √(4 - x²)
y = 2 - x | 343 | 1,248 | {"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-2017-04 | latest | en | 0.910724 |
http://scienceblogs.com/dotphysics/2008/08/ | 1,537,592,942,000,000,000 | text/html | crawl-data/CC-MAIN-2018-39/segments/1537267158045.57/warc/CC-MAIN-20180922044853-20180922065253-00113.warc.gz | 209,728,438 | 14,056 | # How long do you wait for a question to be answered?
I teach classes. I ask questions in class. I wait for answers. All faculty do this, so who cares. If you are in a class or teaching a class, how long do you wait for someone to answer your question? Well, I asked two questions of my class this week. 1. Estimate how long I…
# How about a massive catapult to replace the space shuttle
I recently saw a comment on a blog somewhere about putting satellites into space (I think it was from a post about a rocket that blew up). The poster suggested using a giant catapult to put things in space instead of rockets. Maybe he or she was kidding, or maybe not. But I have heard…
# Another MythBusters Tie in: zero-g in a plane
Maybe you can tell I am watching the MythBuster’s Moon Special. In the show, the MythBusters go in a plane to reproduce the gravitational forces on the moon. I previously went over this, so here is the link: [Tutorial on how gravity and weightlessness (zero-g) work](http://scienceblogs.com/dotphysics/2008/09/gravity-weightlessness-and-apparent-weight.php)
# Mythbusters Moon Stuff and Me
Clearly the MythBusters did this before I did (it’s just airing tonight though). I just wanted to say that I posted some videos of the Apollo “jump salute” video analysis and also sped it up to “Earth-like” accelerations. I then made a video of my daughter doing the same thing on Earth and slowed it…
# Heat. It’s a four letter word
Heat. You have heard it before. You have used it. I have even used it. Do we need this word? No. Is this a useful word? No. Let me start with the definition as usually stated in a physics type text: (this is from [dictionary.com](http://dictionary.reference.com/browse/heat)) *heat:* a nonmechanical energy transfer with reference to a temperature…
# The Iron Cross – or: Why is Gymnastics so Darn Difficult?
I know the olympics are basically over. Really, I should have posted this earlier. Anyway, the gymnastics feat that always impresses me is the Iron Cross (I think that is what it is called). I know you have seen this, but here is a picture from wikipedia:  (http://en.wikipedia.org/wiki/Rings_(gymnastics)) Why is this so impressive?…
# ARRRGGGGG RapidWeaver, why do you hate me?
Dear RapidWeaver, What did I do to you? I like you, I really do – but this is why we broke up. It’s not you, it’s me. No wait, it’s you. I am looking back through my old dotphys posts and most of my introductions are GONE. I was starting to think I was crazy…
# Status of Pluto – Zombie Feynman Replies
I can’t believe there is still all this talk about what to call Pluto. Can’t we just move on? In an effort to help, I have summoned the Zombie Feynman to get his words on the subject. This is what he said:
# Moving my blog
As you may or may not have noticed, I have been using RapidWeaver for my blogging posts. (if you don’t know what that is, it doesn’t matter) Anyway, I think my stuff was getting a little too big for that software. It was a great place to start, but it is time to move to… | 777 | 3,161 | {"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-2018-39 | latest | en | 0.937414 |
https://www.macroption.com/long-straddle-payoff/ | 1,579,916,672,000,000,000 | text/html | crawl-data/CC-MAIN-2020-05/segments/1579250628549.43/warc/CC-MAIN-20200125011232-20200125040232-00152.warc.gz | 922,529,140 | 7,397 | # Long Straddle Payoff, Risk and Break-Even Points
This page explains long straddle profit and loss at expiration and the calculation of its risk and break-even points.
## Long Straddle Basic Characteristics
Long straddle is a position consisting of a long call option and a long put option, both with the same strike and the same expiration date.
It is a non-directional long volatility strategy. It is generally suitable when you expect the underlying security to be very volatile and move a lot, but you are not sure whether the price move will be up or down. The position makes a profit when your expectation is correct and the underlying does make a big move to one or the other side. If you are wrong and the underlying price stays more or less the same, the trade makes a loss.
Long straddle has limited risk, equal to the premium paid for both legs, and unlimited potential profit.
Let’s explain the payoff on an example, and have a look at the sources of its risk and profit exposures.
## Long Straddle Example
Consider a straddle created with the following two transactions:
• Buy a \$45 strike put option for \$2.85 per share.
• Buy a \$45 strike call option with the same expiration date for \$2.88 per share.
The underlying security is trading somewhere close to \$45 at the moment. Typically, at the money options – the strike nearest to the current underlying price – are selected. This helps balance directional exposure of the two legs and make the position non-directional overall, so the trader can focus on volatility, which is really the main idea of a straddle (in some cases, a trader may choose a different strike to intentionally create a straddle with a little directional bias; this is more advanced and we will not consider it for now).
## Initial Cost
Initial cost of the position is very easy to calculate: just add up the money paid for the two legs.
Initial cost = put cost + call cost
In our example:
Initial cost = \$2.85 + \$2.88 = \$5.73 per share = \$573 per contract
(assuming standard US equity option contracts, which represent 100 shares)
## Payoff and Profit Drivers
Because the call and the put have the same strike price (\$45 in our example), only one of them is in the money at any time. When underlying price is above the strike, the call is in the money and the put is out of the money. Below the strike it’s the opposite.
Therefore, at expiration when no time value is left, one of the options can almost always (unless underlying price end up exactly at the strike) be exercised for some gain (which may or may not be enough to cover the initial cost) and the other option expires worthless.
You can see that in the payoff diagram below, which shows the straddle from our example, including the long call (green) and the long put (red).
## Maximum Loss (Risk)
As you can see in the payoff diagram, total P/L reaches its minimum when underlying price is exactly at the strike. This is the only point where both the call and the put have zero value at expiration. Therefore, it is exactly at the strike where the trade’s overall P/L equals maximum loss, which equals initial cost.
Maximum loss = initial cost
Regardless of what happens in the market, you can’t lose more than what you have paid for the options, because the position only includes long options (no shorts) and there is no risk of assignment or negative cash flow at expiration.
When underlying price moves away from the strike to one side or the other, increasing value of the in the money option starts to reduce the loss and, if the underlying moves far enough, eventually turns the trade into a profit. Let’s see a few example scenarios.
## When Underlying Price Goes Up
If underlying price ends up at \$49 at expiration, or \$4 above the strike, the call option is in the money and makes \$4 per share, or \$400 for one contract. The put is out of the money and expires worthless. The \$400 is not enough to cover the initial cost of both options, therefore the trade ends in a loss (\$400 – \$573 = – \$173), although much smaller than the maximum loss possible (\$573).
If underlying price gets further up to \$54, the call is worth \$9 per share, or \$900 per contract and the trade makes a profit (\$900 – \$573 = \$327).
## When Underlying Price Goes Down
Below the strike it works in the same way, only the put is in the money and drives the profitability, while the call expires worthless.
If underlying price is at \$43, the put is worth \$200 and overall P/L is – \$373, still a loss.
If the underlying falls to \$37, the straddle makes a profit of \$227.
## Long Straddle Break-Even Points
Where exactly are the points where the straddle starts being profitable. How far does the underlying need to move? It is very easy to calculate.
A straddle has two break-even points.
The lower break-even point is the underlying price at which the put option’s value equals initial cost of both options.
B/E #1 = strike – initial cost
In our example:
B/E #1 = \$45 – \$5.73 = \$39.27
The upper break-even point is where the call option’s value equals initial cost of both option.
B/E #2 = strike + initial cost
In our example:
B/E #2 = \$45 + \$5.73 = \$50.73
As you can see, the underlying in our example needs to make a fairly big move for the trade to make a profit (12.7% to either side, assuming it is exactly at \$45 when opening the position). High initial cost and often very wide window of loss is one disadvantage of long straddles (and many other long volatility strategies) – while you have the luxury of not having to worry about the direction, you pay for it in the high cost of the position. Therefore, the difficulty and risk of long straddles must not be underestimated. While it looks attractive and safe when looking at the payoff diagrams, it is not that easy to trade straddles profitably in practice.
## Similar Option Strategies
Another strategy very similar to long straddle in virtually all characteristics (non-directional, long volatility, limited risk, unlimited upside) is long strangle. The main difference is that in a strangle the call and the put have different strikes. As a result, initial cost and maximum loss is lower, but the size of the move needed to reach break-even is even further, due to the distance between strikes.
The other side of a long straddle trade is short straddle – a non-directional, short volatility strategy with limited profit and unlimited risk. Similarly, the inverse of long strangle is short strangle. | 1,428 | 6,530 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.6875 | 3 | CC-MAIN-2020-05 | longest | en | 0.919457 |
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For the discussion of the sciences. Physics problems, chemistry equations, biology weirdness, it all goes here.
Moderators: gmalivuk, Moderators General, Prelates
Minerva
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### A quantum mechanics question.
This is a school textbook question. I'm not expecting anybody to feed me the answer; I'll give you what I think the answer is thus far, and if I could get a bit of a nudge in the direction of correctness if it's not correct, or confirmation that it is correct, that would great.
Consider an electron in a hydrogen atom in the quantum state: [imath]\psi = \sqrt{\frac{1}{6}} \psi_{321} + \sqrt{\frac{1}{2}} \psi_{320} + \sqrt{\frac{1}{3}} \psi_{3 2 -1}[/imath]
(Where the subscripts are the quantum numbers n, l, m respectively for the basic states of a hydrogen atom, such that [imath]\psi_{nlm} = R_{nl} Y^{m}_{l}[/imath].)
The energy of the electron, L2 and LZ are measured. What are the value(s) of these quantities that can be measured, and what is the expectation value of LZ?
Now;
Energy: The energy of the electron is determined by the quantum number n, and there is no ambiguity in the measured value of the energy, since n =3 in all of the terms in the wavefunction. E = - 13.6 eV * (1/32), which is equal to about -1.51 eV.
L2: The eigenvalue of L2 is l(l+1)[imath]\hbar^{2}[/imath], and l = 2 for all of the terms, therefore, the measured value of L2 is simply equal to 6[imath]\hbar^{2}[/imath].
The eigenvalue of LZ is [imath]\hbar[/imath]m, so we have three different possible values corresponding to each of the three terms, LZ = [imath]\hbar[/imath] with probability 1/6, LZ = 0 with probability 1/2 and LZ = -[imath]\hbar[/imath] with probability 1/3.
Add up those three terms to get <LZ>, and we have (1/6 - 1/3)[imath]\hbar[/imath] = -(1/6)[imath]\hbar[/imath].
Does that all sound like it's on the right track?
Thanks.
...suffer from the computer disease that anybody who works with computers now knows about. It's a very serious disease and it interferes completely with the work. The trouble with computers is you play with them. They are so wonderful. - Richard Feynman
Certhas
Posts: 301
Joined: Thu Dec 13, 2007 11:16 pm UTC
### Re: A quantum mechanics question.
looks absolutely correct.
"I conclude that all is well," says Edipus, and that remark is sacred.
- Camus, The Myth of Sysiphus
Mental Health Break
danpilon54
Posts: 322
Joined: Fri Jul 20, 2007 12:10 am UTC
### Re: A quantum mechanics question.
Looks good to me too
Mighty Jalapeno wrote:Well, I killed a homeless man. We can't all be good people.
Minchandre
Posts: 524
Joined: Thu Nov 08, 2007 3:36 am UTC
### Re: A quantum mechanics question.
I'll jump on the train of "Everything's a-okay"
Minerva
Posts: 947
Joined: Sat Nov 11, 2006 2:58 pm UTC
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### Re: A quantum mechanics question.
OK, thanks
Looks like I'll have to up the ante a bit so I don't get too confident.
Here's another question which I've got absolutely no idea about:
Suppose a spin-[imath]\frac{1}{2}[/imath] particle experiences a Hamiltonian of the form [imath]\hat{H} = k(S_{Z} + \lambda S_{X})[/imath], for small [imath]\lambda[/imath] and some constant k.
Determine an appropriate basis to express the problem to 0-th order, and describe the qualitative effect of each of the terms of the Hamiltonian on these basis states, and determine the correction, to first order, to the eigenstates and eigenvalues of energy.
OK. So, an appropriate basis to express the problem to zero order? OK, we put lambda = 0, so we simply have the Hamiltonian proportional to Sz. So, can't we just express this Hamiltonian in the z basis?
Describe the qualitative effect of each of each of the terms in the Hamiltonian on these basis states?
Well, I really don't understand what this is asking for.
I'm trying to visualise what kind of physical system this could possibly be. Let's suppose it's something like spin precession in a magnetic field. Suppose the direction of the magnetic field is in the ZX plane, perturbed slightly off the Z-axis. That makes sense, doesn't it? Thus, k quantifies the field strength and/or the gyromagnetic ratio, and lambda quantifies the angular perturbation of the magnetic field off the Z axis in the ZX plane.
OK, so I think that's a physical interpretation of the Hamiltonian, consistent with the Hamiltonian. But what is the interpretation of these terms in terms of the effect of the Hamiltonian on these basis states? What basis states?
Determination of the first order correction to the eigenstates and eigenvalues of energy? So, the first order correction to the eigenstates and eigenvalues of the Hamiltonian. But I don't really know where to begin determining these. Sure, there are plenty of discussions of basic perturbation theory for some small potentials in the textbook(s), but I've not seen discussions of anything that looks like a spin matrix, in the context of perturbation theory.
Could anyone give me a little bit of help with this question?
Thanks.
...suffer from the computer disease that anybody who works with computers now knows about. It's a very serious disease and it interferes completely with the work. The trouble with computers is you play with them. They are so wonderful. - Richard Feynman
ThinkerEmeritus
Posts: 416
Joined: Sat Jan 19, 2008 11:32 pm UTC
### Re: A quantum mechanics question.
Minerva wrote:OK, thanks
Looks like I'll have to up the ante a bit so I don't get too confident.
Here's another question which I've got absolutely no idea about:
Suppose a spin-[imath]\frac{1}{2}[/imath] particle experiences a Hamiltonian of the form [imath]\hat{H} = k(S_{Z} + \lambda S_{X})[/imath], for small [imath]\lambda[/imath] and some constant k.
Determine an appropriate basis to express the problem to 0-th order, and describe the qualitative effect of each of the terms of the Hamiltonian on these basis states, and determine the correction, to first order, to the eigenstates and eigenvalues of energy.
OK. So, an appropriate basis to express the problem to zero order? OK, we put lambda = 0, so we simply have the Hamiltonian proportional to Sz. So, can't we just express this Hamiltonian in the z basis?
Yep. It would help in the next step if you wrote the basis down, presumably in matrix form.
Describe the qualitative effect of each of each of the terms in the Hamiltonian on these basis states?
Well, I really don't understand what this is asking for.
A good response would be to evaluate [imath]k Sz \psi1[/imath] and [imath]k Sz \psi2[/imath] and interpret the results in words, and then do the same for
[imath]k \lambda[/imath] S2.
I'm trying to visualise what kind of physical system this could possibly be. Let's suppose it's something like spin precession in a magnetic field. Suppose the direction of the magnetic field is in the ZX plane, perturbed slightly off the Z-axis. That makes sense, doesn't it? Thus, k quantifies the field strength and/or the gyromagnetic ratio, and lambda quantifies the angular perturbation of the magnetic field off the Z axis in the ZX plane.
OK, so I think that's a physical interpretation of the Hamiltonian, consistent with the Hamiltonian. But what is the interpretation of these terms in terms of the effect of the Hamiltonian on these basis states? What basis states?
The matrix-style eigenstates of Sz is presumably what is wanted. The physical interpretation of the Hamiltonian you have quoted is correct, but may be more than needed. However, if you were asked to find an exact solution, that interpretation would be invaluable.
Determination of the first order correction to the eigenstates and eigenvalues of energy? So, the first order correction to the eigenstates and eigenvalues of the Hamiltonian. But I don't really know where to begin determining these. Sure, there are plenty of discussions of basic perturbation theory for some small potentials in the textbook(s), but I've not seen discussions of anything that looks like a spin matrix, in the context of perturbation theory.
Could anyone give me a little bit of help with this question?
Thanks.
The formulae for perturbation theory will be in terms of matrix elements of the perturbation Hamiltonian. What are the matrix elements of a matrix?
"An expert is a person who has already made all possible mistakes." -- paraphrase of a statement by Niels Bohr
Seen on a bumper sticker: "My other vehicle is a Krebs cycle". | 2,137 | 8,550 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.46875 | 3 | CC-MAIN-2019-26 | latest | en | 0.903238 |
https://oeis.org/A125551 | 1,627,967,500,000,000,000 | text/html | crawl-data/CC-MAIN-2021-31/segments/1627046154420.77/warc/CC-MAIN-20210803030201-20210803060201-00661.warc.gz | 436,323,813 | 4,194 | The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.
Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
A125551 As p runs through primes >= 5, sequence gives { numerator of Sum_{k=1..p-1} 1/k^2 } / p. 2
41, 767, 178939, 18500393, 48409924397, 12569511639119, 15392144025383, 358066574927343685421, 282108494885353559158399, 911609127797473147741660153, 1128121200256091571107985892349 (list; graph; refs; listen; history; text; internal format)
OFFSET 3,1 COMMENTS This is an integer by a theorem of Waring and Wolstenholme. LINKS R. Mestrovic, Wolstenholme's theorem: Its Generalizations and Extensions in the last hundred and fifty years (1862-2011), arXiv:1111.3057, 2011 MAPLE f1:=proc(n) local p; p:=ithprime(n); (1/p)*numer(add(1/i^2, i=1..p-1)); end proc; [seq(f1(n), n=3..20)]; MATHEMATICA a = {}; Do[AppendTo[a, (1/(Prime[x]))Numerator[Sum[1/x^2, {x, 1, Prime[x] - 1}]]], {x, 3, 50}]; a Table[Sum[1/k^2, {k, p-1}]/p, {p, Prime[Range[3, 20]]}]//Numerator (* Harvey P. Dale, Nov 20 2019 *) CROSSREFS Cf. A061002, A034602, A186720, A186722. Sequence in context: A246642 A167737 A268993 * A087856 A010957 A299332 Adjacent sequences: A125548 A125549 A125550 * A125552 A125553 A125554 KEYWORD nonn AUTHOR Artur Jasinski, Jan 03 2007 STATUS approved
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Last modified August 3 01:07 EDT 2021. Contains 346429 sequences. (Running on oeis4.) | 572 | 1,666 | {"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} | 3.375 | 3 | CC-MAIN-2021-31 | latest | en | 0.563917 |
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“Education from Infancy” is a book written in 4 Parts, and it is also available as an integrated volume. “Education from Infancy Part 1 – an Early Start” describes my... More > very successful efforts at teaching Math and literacy to my grandson from the very earliest days of his infancy. For example, by the time he was 6-7 months old I had taught him to recognize and point out to me upper-case letters of the alphabet and the numbers 0-9, in normal and upside-down perspectives from his point of view. Therefore, this book is for new parents, grandparents or other caretakers who want to give their infant child a huge jump-start on his or her education, and for the parents of the child that needs a helping hand with an understanding of numbers in general or with addition and subtraction concepts. Part 1 ends with your child learning how to verbalize and write out numbers up to 36 digits long and perform real-world addition and subtraction. This book will get your child to understand Math, and therefore enjoy it.< Less
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10 | 1,779 | 7,895 | {"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} | 2.671875 | 3 | CC-MAIN-2019-30 | latest | en | 0.870725 |
https://www.ukspaceforum.org/library/a-treatise-on-differential-equations | 1,627,417,992,000,000,000 | text/html | crawl-data/CC-MAIN-2021-31/segments/1627046153491.18/warc/CC-MAIN-20210727202227-20210727232227-00584.warc.gz | 1,127,496,377 | 8,273 | # A Treatise on Differential Equations by A. R. Forsyth
By A. R. Forsyth
Vintage 19th-century paintings one in all the best remedies of the subject. Differential equations of the 1st order, basic linear equations with consistent coefficients, integration in sequence, hypergeometric sequence, answer through yes integrals, many different issues. Over 800 examples. Index.
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3x × 34 = 311 c. 50 = x 5 e. _3 = 5(7x) b. 57 × 53 = 5x d. √5 = 5x 7 23 Solve each of the following equations for x. a. 3x - 8 = 29 c. 3(x - 8) + 17 = 29 24 b. 3(x - 8) = 29 d. 7x + 12 = 3x - 8 Find equations for the lines that contain these pairs of points. a. (0, 0) and (2, 6) c. (1, 2) and (7, 11) 25 b. (0, 0) and (5, 8) Use what you know about exponents and radicals to write each of the following function rules in equivalent form, y = kxr. a. y = _4x 4 c. y = _ b. y = -7 √x 5 d. y = _ x3 √x e.
Write an algebraic rule that shows how pond fish load L depends on the number f of full-size fantail goldfish and the number c of full-size common goldfish in the pond. iii. How will the fish load of the pond change as the number of full-size fantail goldfish increases? How will it change as the number of full-size common goldfish increases? LESSON 2 • Multivariable Functions 37 On Your Own b. Aidan is considering a pond kit that is rated for 140 inches of goldfish. How many full-size fantail and common goldfish can be supported in this pond?
Be prepared to share your ideas and reasoning with the class. 14 UNIT 1 • Functions, Equations, and Systems Check Your Understanding Without using your calculator or computer graphing tool, match each function rule with its graph. In each case, write a sentence explaining the type of variation that relates x and y. ” a. 5x2 c. y = 5 b. y = _ 2 x 1 d. y = _ 3 x3 x f. 5x) e. y = 3 √x I II III IV V VI LESSON 1 • Direct and Inverse Variation 15 On Your Own Applications These tasks provide opportunities for you to use and strengthen your understanding of the ideas you have learned in the lesson. | 789 | 2,951 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.734375 | 4 | CC-MAIN-2021-31 | latest | en | 0.815992 |
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This resource provides a hands on and engaging way for students to review their integer operations unit or take notes as the unit progresses. Skills covered : This mini tabbed flip book has a front and back cover, as well as five pages that
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About this resource : This cooperative learning activity provides students with the opportunity to practice simplifying expressions using the distributive property. Students are grouped with a partner and take turns solving the problems and
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Integer Operations Cooperative Learning Review Activity About this resource : This game provides students with a fun and collaborative way to practice basic operations with integers. You can use only the game cards you need – making it easy to
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Fraction Operations and Integer Concepts Unit for 6th Grade Math 6th Grade Math Curriculum Unit 2 This unit includes five multi-day lessons that cover a review of 5th grade skills and some new 6th grade skills : * Equivalent Fractions and
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Operations with Whole Numbers and Decimals 6th Grade Math Unit - Completely editable to help you best meet the needs of your students! 6th Grade Math Curriculum Unit 1 {Buy the full curriculum HERE} This unit includes six multi-day lessons that
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About this resource : 6th grade Christmas math activities. This resource includes 27 no prep activities for the month of December. Students can practice important skills while matching and coloring. The coloring pages include Christmas / Winter /
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About this resource : This fun activity has students take a look at twelve different math mistakes found in the real world. Students must identify why the error was made and fix what was done incorrectly. There are three different versions
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112 ratings
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Integer Operations and Coordinate Graphing About this resource : This worksheet has students demonstrate their ability to quickly recall and solve problems involving integer operations, exponents and basic multiplication and division. They use
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This file includes two different coloring worksheets with a candy theme (perfect for Halloween). One with division word problems and the other with the basic division problems from the word problem page. Answer key included! Available in the
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About this resource : This resource includes 9 speed drills with 20, 25 or 50 basic fact practice problem. Skills assessed are basic addition, basic subtraction, integer addition, integer subtraction, fraction addition, fraction multiplication,
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About this resource : This decimal operations coloring activity allows students to review both decimal operations and the order of operations. It's a wonderful activity that incorporates fun into the classroom! Use it as a quick assessment tool, a
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About this resource : Two versions of the same integer operations assessment are included. Both versions have the same questions. One has all open ended questions, and the second has 13 multiple choice questions (4 bare problems and 9 word
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Integer Operations Small Group Activity About this resource : This activity contains 20 cards with integer operations problems. Addition, subtraction, multiplication and division of integers is covered. Students work independently and with
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About this resource : This 25 question decimal operations game helps students review ordering decimals, as well as adding, subtracting, multiplying and dividing decimals. Also included is a printable sheet students can use to record their
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TEACHING EXPERIENCE
After spending 8 years in the classroom teaching Middle School Math, Math Intervention and 4th grade, I am currently working from home as a curriculum designer creating resources for teachers across the country! I absolutely LOVE my job and feel so grateful for the opportunity to help teachers and students near and far.
MY TEACHING STYLE
I believe in a structured, organized and comfortable classroom where students don't hesitate to ask questions, work together and try their best!
HONORS/AWARDS/SHINING TEACHER MOMENT
Presenter at the 1st Teachers Pay Teachers Conference in Las Vegas - July 2014 Presenter at the 2nd Teachers Pay Teachers Conference in Las Vegas - July 2015 Panelist at the 3rd Teachers Pay Teachers Conference in Orlando - July 2016
MY OWN EDUCATIONAL HISTORY
I have a B.S. in Elementary Education (K-8) with a Minor in History. I am highly qualified to teach Middle School Mathematics.
I'm a wife, mom, teacher and writer. I love creating fun materials for the classroom that guide teachers away from the textbook! | 1,442 | 6,322 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.640625 | 4 | CC-MAIN-2018-34 | latest | en | 0.892329 |
https://www.gamedev.net/forums/topic/563573-projectile-leading-a-target/ | 1,539,608,880,000,000,000 | text/html | crawl-data/CC-MAIN-2018-43/segments/1539583509196.33/warc/CC-MAIN-20181015121848-20181015143348-00108.warc.gz | 943,904,650 | 25,302 | This topic is 3151 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.
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You know that the projectile's path must lie in the plane defined by the line of the target's motion and the point of the projectile's origin.
To approach this, I would transform it into a two-dimensional problem. You have a triangle defined by the target's position, the projectile's position, and the point of intersection of their paths. You know the distance between the target and projectile and the angle of the target's path relative to the projectile's current position. You also know the ratio between the projectile's velocity and the target's velocity.
This lends itself very well to using the law of cosines. If a is the distance between the target and projectile, b is the distance between the target and point of intersection, c is the distance between the projectile and point of intersection, and theta is the angle between the vector between projectile and target and the target velocity vector, then:
c=b*Pvco/abs(Tvel)
b^2*(Pvco/abs(Tvel))^2=a^2+b^2-2ab*cos(theta)
b is the only unknown, so you can solve this with a simple quadratic equation. You want the smallest value of b that is still positive; a solution will exist as long as the projectile is faster than the target.
cos(theta) is simply the dot product of the normalized velocity vector and the normalized difference between the two positions.
Once you know b, the rest of the problem is trivial:
t=b/abs(Tvel)
Pvel=(Tpos+Tvel*t-Ppos)/t
Pdir=norm(Pvel)
I just sketched this up quick on pencil and paper; I didn't actually test it.
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× | 469 | 1,901 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.765625 | 4 | CC-MAIN-2018-43 | latest | en | 0.922905 |
https://swastikaphobia.com/converting-directly-from-binary-to-hexadecimal-pre-algebra-khan-academy/ | 1,579,971,446,000,000,000 | text/html | crawl-data/CC-MAIN-2020-05/segments/1579251678287.60/warc/CC-MAIN-20200125161753-20200125190753-00253.warc.gz | 675,503,001 | 16,949 | # Converting directly from binary to hexadecimal | Pre-Algebra | Khan Academy
– [Voiceover] What I would
like to do in this video is explore the connection between
system, which is base 16. The reason why this is interesting is because 16 is a power of two. What we’ll see is you could always view the hexadecimal number system. It’s almost condensed representation of the binary number system. This is actually why you will actually, we’ve already talked
about the binary system is used extensively in computer science and in even computer engineering. It’s the underlying
things that are happening or it’s the representation
used when we talk about logic gates and
transistors and things like that. But hexadecimal also shows up a lot because it’s kind of a condensed
representation of base two. What do I mean by that? Let’s write out a arbitrary
number in base two. Let’s say I have one, zero, one, one, zero, one, one, one, zero. This right over here is in binary and I can even write in parenthesis . This is a binary representation. I want to convert this to
hexadecimal representation. I encourage you to pause the
video and try out in your own. I’ll give you a clue
on how you could think about converting directly
from base two to base 16. Think about which one over
here is in the 16s place and what is the 256 place over here. Then that might help you convert directly. Assuming you had a go at it. The really fun thing about
between base two and base 16 is you don’t have to, well for any
bases, you really don’t have to go through base 10
but these in particular, it’s especially easy to go
convert between these two bases. The realization that you have to make is, what are the powers, which
places here are powers of 16? This right over here,
that is the ones place. One way to think about it
is all of these is going to tell you how many ones we have. Ones, twos, fours, and eights, but another way to think
about it is this is a count of ones, all the way up
to a potential of 15 ones. This could count, this is
going to be between zero, and I’m going to write it down. Actually, let me write it down in base 16. It’s going to be between zero and F. It’s going to be between zero and 15. It’s kind of a count between the number of ones, I guess you could say. Then this is the 16s place. I’m going to do that in different color. This right over here is the 16s place. You could have between zero and 15s, 16s. This is also going to
be between zero and F, when you look at this
four digit binary numbers. Once again, this whole
thing right over here is essentially going to tell
you how many 16s you have. This whole thing is going to tell you how many ones you have. Then the next four, we could keep going, although there is only one place here. We could go, this right
over here is the 256s place. This is going to be the next four digits. They really have one right over here, but one, two, three,
and then the fourth one. This is also going to be
between zero and 15, 256s. Hopefully, that helps you a little bit. Actually, if this was
a clue, I encourage you to pause the video again (laughs) and see if you can represent this in hexadecimal. Let’s try to work this thing together. How many ones do we have? What number is this? These four digits right over here. This is eight plus four plus two. So eight plus four is 12, plus two is 14. This right over here is 14. How do we represent that in hexadecimal? Well, 14 is one less than
15 so it’s going to be E. This is going to be E. This is E. E is our hexadecimal
representation of the number 14 comes right before our
representation of the number 15 F. Alright, now, how many 16s do we have? Let’s see, I have no eights. I have a four, and I have a two. We’re going to have six 16s. So we’re going to have six 16s. Then, how many 256s do I have? I only have one 256. One 256. This number in hexadecimal,
and I could write that. This is in hexadecimal right
over here, is one, six, E. One, six, E. I guess you could call this 256 E, 16 E. I guess 14. I (laughs) finally have to
come up with a better way of reading this hexadecimal number. If you’re not curious what
number is this, because you don’t have to go through decimal
just so you could comprehend it in the number system that
you’re used to operating in. One that’s based off from the
number of fingers you have. Feel free to do so.
## 44 thoughts to “Converting directly from binary to hexadecimal | Pre-Algebra | Khan Academy”
1. Marziyeh M says:
LONG LIVE PALESTINE!! LONG LIVE GAZA!! <3
2. Unstopapple says:
16(0)Echo
3. huh? says:
I can't believe my gay teacher Mrs Van Dickhead makes me watch this crap this sucks ass…. pure assholes
4. Craig Ryba says:
16E = 367
…I think.
5. to0PRETTY says:
When you were trying to say the hex final number, I giggled.. never thought Id laugh at a math joke. First for everything.
6. Gran Nica says:
thank you !!!
7. Marius Du Pont says:
What if there are decimal points?
8. Jewel Mahmud says:
For for than 5 months I was interested in learning number system. I missed the class of number system at our department. And finally your video made my day. Thanks #Salkhan And #Khanacademy
9. tyler black says:
very helpful video! Thanks a bunch.
10. Ash Chez says:
So damn helpful, thank you buddy!
11. Mann says:
thnx
!!!!
12. Kleando Jaupaj says:
Thank you so much!!!!!
13. Soumya Roy says:
Mr.khan how is it that you know everything!!!!Please tell us your secret!!!
14. wePASS says:
Thank you π
15. Mo Vlogs official says:
It 's a easy simple question but he make it so difficult and confusing…
Repetition when teaching can be good, but he verbally repeats every single thing more than three times-what he's about to do, ask he's writing it, after he's written it and sometimes messes up and writes/says it again- it's distracting to hell against what's actually going on. Just do it. Not a very creative teaching method and says the same exact phrases throughout many of the videos in this series as if he just barely read a manual on teaching. Luckily I've taken enough college math classes I could figure them out on my own.
17. Rupanshu jha says:
sherkhan ? is it you ? π
18. Sukrit Chaudhary says:
do your homework buddy before you make a video
19. monsterjazzlicks says:
This needs to be at least 20 x minutes LONGER! It is useless for the BEGINNER!
20. Aiden Moore says:
how did you know that 1110 is 8 + 4 + 2.
21. knowmehuh says:
Instead of trying to explain it your way (genius) why not try to give the info for beginners easily? oh my gosh i can't stand this man i'm sorry but you have to come with easier explanation. Telling lotta tricks on the first step? come on now
22. RequiemUK says:
This was awesome I finally understand
23. Noodles ForLyfe says:
you have no idea how much your vids helped me THANKS A LOTTTTTT
24. Mac Hilton says:
I just wanted to say that I loved this video, very informative! Keep up the good work.
25. Mark Coleman says:
I understand binary and hexadecimal, yet I don't understand his explanation.
26. Kd D says:
This is excellent!! Great work. I now completely understand Hex. It seemed difficult so I just ignored it and used it without deeper understanding. Now I can actually help someone else to learn it and it will help me immensely in my job. Thanks a million
27. ecostar2011 says:
He makes it very difficult to understand and makes people to get confused.
28. JAKE JAWILI says:
Your explanation is very vague no one can understand this kind of tutorial.
29. Brent Griffin says:
your voice is way too loud. thanks for the video though.
30. D7oo says:
ok, I'm a software eng student at the first year
in the ram "8Bit" can hold 8 value? and this is 9
can anyone tell me what happens
31. Ias Howle says:
I didn't know Markiplier is so smart.
I'm sorry for all those who disliked this video.
33. Bumblebee 003 says:
WHO'S WATCHING FROM USKUDAR UNIVERSITY π
34. kennymysteriion says:
I'm sorry for the people hating on you, Khan. People just don't realize there's videos before this explaining binary and hexadecimal each lol but great videos though! I'm a complete beginner and had to learn this for a programming class, so thank you!
35. Tina says:
m i the only one who watches khan academy videos just to listen to his sexy voice?
36. Michael Kaufman says:
Someone remix 5:01
37. Justoboy13 says:
He doesn't go straight from binary to hexadecimal like the title says which annoys me. He went from binary to decimal to hexadecimal, which I could have already done my homework then instead of wasting my time here watching a video about something I already know how to do.
38. Brittney harris-holloway says:
lol why that 256 look like a 28, i sat for 5 mins tryna figure out how 28 came about after a 256
39. WIZARD Z says:
I never learned anything from KHAN ACADEMY EVER!!!!!!!
40. Onyimbi David says: | 2,261 | 8,910 | {"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} | 4.46875 | 4 | CC-MAIN-2020-05 | latest | en | 0.967088 |
https://web2.0calc.com/questions/geometry_99966 | 1,701,786,272,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679100551.2/warc/CC-MAIN-20231205140836-20231205170836-00041.warc.gz | 689,899,959 | 5,312 | +0
# geometry
0
341
1
D is on side AC of Triangle ABC. We know [ABC] = 120, AD = 8, DC = 3. What is [ABD]?
May 13, 2021
#1
+1694
+2
D is on side AC of Triangle ABC. We know [ABC] = 120, AD = 8, DC = 3. What is [ABD]?
---------------------------------------------------------
AC = 11 [ABC] = 120 AD = 8
AB = 240 / 11 = 21 9/11
[ABD] = 1/2(8 * 21 9/11) = 87 3/11
May 14, 2021 | 171 | 395 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.3125 | 3 | CC-MAIN-2023-50 | latest | en | 0.756788 |
https://cran-r.c3sl.ufpr.br/web/packages/brolgar/vignettes/exploratory-modelling.html | 1,723,654,998,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722641118845.90/warc/CC-MAIN-20240814155004-20240814185004-00195.warc.gz | 142,918,516 | 73,260 | # Exploratory Modelling
library(brolgar)
It can be useful to fit a model to explore your data. One technique is to fit a linear model for each group in a dataset. For example, you could fit a linear model for each key in the data.
brolgar provides a helper function to help with this, called key_slope().
key_slope() returns the intercept and slope estimate for each key, given a linear model formula. We can get the number of observations, and slope information for each individual to identify those that are decreasing over time.
key_slope(wages,ln_wages ~ xp)
#> # A tibble: 888 × 3
#> id .intercept .slope_xp
#> <int> <dbl> <dbl>
#> 1 31 1.41 0.101
#> 2 36 2.04 0.0588
#> 3 53 2.29 -0.358
#> 4 122 1.93 0.0374
#> 5 134 2.03 0.0831
#> 6 145 1.59 0.0469
#> 7 155 1.66 0.0867
#> 8 173 1.61 0.100
#> 9 206 1.73 0.180
#> 10 207 1.62 0.0884
#> # ℹ 878 more rows
We can then join these summaries back to the data:
library(dplyr)
wages_slope <- key_slope(wages,ln_wages ~ xp) %>%
left_join(wages, by = "id")
wages_slope
#> # A tibble: 6,402 × 11
#> id .intercept .slope_xp ln_wages xp ged xp_since_ged black hispanic
#> <int> <dbl> <dbl> <dbl> <dbl> <int> <dbl> <int> <int>
#> 1 31 1.41 0.101 1.49 0.015 1 0.015 0 1
#> 2 31 1.41 0.101 1.43 0.715 1 0.715 0 1
#> 3 31 1.41 0.101 1.47 1.73 1 1.73 0 1
#> 4 31 1.41 0.101 1.75 2.77 1 2.77 0 1
#> 5 31 1.41 0.101 1.93 3.93 1 3.93 0 1
#> 6 31 1.41 0.101 1.71 4.95 1 4.95 0 1
#> 7 31 1.41 0.101 2.09 5.96 1 5.96 0 1
#> 8 31 1.41 0.101 2.13 6.98 1 6.98 0 1
#> 9 36 2.04 0.0588 1.98 0.315 1 0.315 0 0
#> 10 36 2.04 0.0588 1.80 0.983 1 0.983 0 0
#> # ℹ 6,392 more rows
#> # ℹ 2 more variables: high_grade <int>, unemploy_rate <dbl>
And highlight those individuals with a negative slope using gghighlight:
library(gghighlight)
wages_slope %>%
as_tibble() %>% # workaround for gghighlight + tsibble
ggplot(aes(x = xp,
y = ln_wages,
group = id)) +
geom_line() +
gghighlight(.slope_xp < 0)
# Find keys near other summaries with keys_near()
We might want to further summarise our exploratory modelling by finding those slopes that are near a five number summary values:
summary(wages_slope\$.slope_xp)
#> Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
#> -4.57692 -0.00189 0.04519 0.04490 0.08458 13.21569 38
Finding those groups that are near these values can be surprisingly challenging!
brolgar makes it easier by providing the keys_near() function. You tell it what the key is, what variable you want to summarise by, and then by default it returns those keys near the five number summary. Let’s return the keys near the .slope_xp:
wages_slope %>%
keys_near(key = id,
var = .slope_xp)
#> # A tibble: 31 × 5
#> id .slope_xp stat stat_value stat_diff
#> <int> <dbl> <fct> <dbl> <dbl>
#> 1 2092 -0.00189 q_25 -0.00189 0
#> 2 2092 -0.00189 q_25 -0.00189 0
#> 3 2092 -0.00189 q_25 -0.00189 0
#> 4 2092 -0.00189 q_25 -0.00189 0
#> 5 2092 -0.00189 q_25 -0.00189 0
#> 6 2092 -0.00189 q_25 -0.00189 0
#> 7 6770 0.0846 q_75 0.0846 0
#> 8 6770 0.0846 q_75 0.0846 0
#> 9 6770 0.0846 q_75 0.0846 0
#> 10 6770 0.0846 q_75 0.0846 0
#> # ℹ 21 more rows
Here it returns the id, the .slope_xp, and the statistic that it was closest to, and what the difference between the slope_xp and the statistic.
You can visualise these summary keys by joining them back to the data:
wages_slope %>%
keys_near(key = id,
var = .slope_xp) %>%
left_join(wages, by = "id") %>%
ggplot(aes(x = xp,
y = ln_wages,
group = id,
colour = stat)) +
geom_line()
You can read more about keys_near() in the Identifying interesting observations vignette. | 1,691 | 4,348 | {"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} | 2.59375 | 3 | CC-MAIN-2024-33 | latest | en | 0.433968 |
https://dmoj.ca/problem/dmopc14ce1p2 | 1,718,473,873,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198861605.77/warc/CC-MAIN-20240615155712-20240615185712-00316.warc.gz | 196,934,700 | 7,468 | ## DMOPC '14 Exam Time P2 - Physics Duel
View as PDF
Points: 5 (partial)
Time limit: 1.0s
Memory limit: 64M
Author:
Problem types
Having mastered the secrets to the Art of Kinematics, you decide to show your power by challenging your physics teacher to a duel — a friendly one that is. The two of you are separated by a certain distance and right in the middle lies the holy book of SIN (more specifically, A Decade of SIN Plus Sixteen, which contains past contests and solutions to the University of Waterloo's Sir Isaac Newton Contest).
You believe you are worthy of bringing the book (which has a mass of 500.0g) home to solve problems from — but she wants you to suffer first. Using the force (yes, that force), she changes the velocity of the book several times. Since you are keeping your eyes on the clock, you know the exact time when she changes the velocity of the book and you also know the angle (as you always carry a protractor) and the duration of the time interval (you also have a stopwatch).
Your goal is to output the speed of the book when it hits the ground. Assume that the book is in free-fall on Earth after the last change in velocity is made and that it is accelerating towards the surface at . Assume that the book is unaffected by gravity while it is under the influence of the force.
#### Input Specification
The first line of input will contain one number that represents the number of changes.
The next lines will contain two integers and a real number, , and .
represents the speed of the book, in metres per second while represents the direction, in degrees. More specifically, is the angle between the book's direction and the east direction, clockwise.
represents the time, in seconds, that the book travelled for. Note that is given to one decimal place.
#### Output Specification
The only line of output is to contain the speed of the book when it hits the ground to the nearest integer.
#### Sample Input
2
10 30 2.0
5 120 1.5
#### Sample Output
18
#### Explanation for Sample Output
Our goal is to find the height the book reaches. Using the Law of Conservation of Energy we derive the following equation: , where is the height the book reached, is the acceleration due to gravity and represents the speed of the book when it lands on the ground (the desired output).
To obtain the height the book reached, we need to obtain the vertical component of the book's velocity in each of the lines.
Let represent the height that the book reaches.
Using ,
Note: The function in your language may require the input to be in radians rather than degrees. To convert from degrees (the input) to radians, simply multiply by . | 584 | 2,675 | {"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} | 3.421875 | 3 | CC-MAIN-2024-26 | latest | en | 0.935555 |
https://jovian.ai/forum/t/try-using-negative-indices-for-the-range-a-list-2-5/9391 | 1,611,488,975,000,000,000 | text/html | crawl-data/CC-MAIN-2021-04/segments/1610703548716.53/warc/CC-MAIN-20210124111006-20210124141006-00558.warc.gz | 397,325,021 | 4,239 | # Try using negative indices for the range - a_list[-2:-5]
I need explanation for this code
a_list = [23, ‘hello’, None, 3.14, fruits, 3 <= 5]
a_list[-2:-5]
not clear to me that return an empty list
negative index simply represents index value counting from the end.
for instance ,
list = [1,2,3,4,5,6]
list[-1] == list[5]
and,
for list [-3 : -1 ] the starting index is interpreted as => len(list) - 3 = 6 - 3 = 3
and the ending index as => len(list) - 4 -1 = 6 - 1- 1 = 4
the starting index is (6 - 2) = 4 and ending index is (6 - 5 -1 ) = 0
As you can seen starting index > ending index, it cannot be sliced. In order to slice the list you can either use list[-5:-2] or you can do reverse slicing by using additional parameter in the array i.e list[-2 : -5 : -1].
ps. list [starting index : ending index ] , here the sliced list will include starting indexed element to ending index ( excluding ending index).
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https://www.chess.com/forum/view/daily-puzzles/732014---mate-in-3?lc=1 | 1,481,218,613,000,000,000 | text/html | crawl-data/CC-MAIN-2016-50/segments/1480698541864.24/warc/CC-MAIN-20161202170901-00448-ip-10-31-129-80.ec2.internal.warc.gz | 933,422,181 | 17,751 | # 7/3/2014 - Mate in 3
• #161
7nilac wrote:
A wise man is brought before the King to be punished.
The King says, "You must give me a statement. If it is true, you will killed by lions. If it is false, you will be killed by snakes"
But in the end, the King has to let the man go.
What was the wise man's statement?
Have a nice day!
This statement is false. It is therefore neither true or false, therefore the king must let him go.
• #162
Good
• #163
This puzzle is wrong. Why would one go for mate in 3 when there is an obvious mate in 2 moves.. :-/
1. Nxc5+ Kd8
2. Qd7#
• #164
rsankalp wrote:
This puzzle is wrong. Why would one go for mate in 3 when there is an obvious mate in 2 moves.. :-/
1. Nxc5+ Kd8
2. Qd7#
Because black won't play Kd8, he'll play Ne7. Black is still losing but the imminent forced mate is gone.
• #165
7nilac wrote:
A wise man is brought before the King to be punished.
The King says, "You must give me a statement. If it is true, you will killed by lions. If it is false, you will be killed by snakes"
But in the end, the King has to let the man go.
What was the wise man's statement?
Have a nice day!
"I will be killed by snakes."
• #166
nice and straightforward mate with forced moves only
• #167
7nilac: Is it, "I will be killed by snakes." ?Please be relevant, helpful & nice!
• #168
hmm :)
• #169
Why not play Nc7 as the first move for the discovery double check and the rook and king fork?
• #170
dshanker wrote:
Why not play Nc7 as the first move for the discovery double check and the rook and king fork?
Nc7+, Kd8, Re8+, Kd7 and no mate in 3
• #171
[COMMENT DELETED]
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4th May 2013, 00:09 #21 | Link
Keiyakusha
Join Date: Jun 2008
Posts: 1,576
Quote:
Originally Posted by poisondeathray Can you explain what you have in mind ? Some non linear scaling ?
Something like this （＾_＾）
Code:
```#yv12 source
Spline36resize(1280,720)
w=width()
Audiodub(blankclip(last),last)
Converttomono()
Normalize()
pointresize(1280,720)
Converttoyv24()
Histogram(mode="audiolevels")
Converttorgb32(chromaresample="point")
calc=FrameRate()*1280/Framecount()
Changefps(calc,linear=false).Trim(0,-w)
Crop(100,0,-1179,-360)
WeaveColumns(1280)
Greyscale()
Levels(0, 1.000, 1, 0, 255, coring=false)
aa=Crop(0,0,0,-height*3/4)
bb=Crop(0,height/4,0,-height/2)
cc=Crop(0,height/2,0,-height/4)
dd=Crop(0,height*3/4,0,0)
aa=pointresize(aa,width(aa), height(aa))
bb=pointresize(bb,width(bb), height(bb)/6)
cc=pointresize(cc,width(cc), height(cc)/9)
dd=pointresize(dd,width(dd), height(dd)/12)
Stackvertical(aa,bb,cc,dd)
blur(1)```
F/sn UBV theatrical teaser
Edit: no blur
Last edited by Keiyakusha; 4th May 2013 at 00:15.
4th May 2013, 00:11 #22 | Link poisondeathray Registered User Join Date: Sep 2007 Posts: 3,937 That looks improved No blur looks better to me; or maybe add a configurable parameter You can always add blur after the overlay/composite ; I think it's better to have sharp edges since the same image can also be used as a luma matte (or mask in overlay() ) Last edited by poisondeathray; 4th May 2013 at 00:35.
4th May 2013, 01:16 #23 | Link smok3 brontosaurusrex Join Date: Oct 2001 Posts: 2,395 my (debian) ffmpeg / imagemagick try (1 strip = 1 frame) Code: ```#!/bin/bash # produces a color-stripe (color fingerprint) png of a video file (1 pixel = 1 frame) while [ \$# -gt 0 ]; do # make temporary folder and trap to clean up TMPDIR=`mktemp -d` trap "rm -rf \$TMPDIR" EXIT # expand path, so this can be used from cli as well (on relative paths) # file=\$(readlink -f "\$1") file="\$1" ffmpeg -i "\$file" -sws_flags neighbor -vf scale=2:2 -f image2 "\$TMPDIR/out-%05d.png" convert +append "\$TMPDIR/out-*.png" -resize 1x1\! -resize 1x128\! "\$file.png" rm -rf \$TMPDIR shift done``` (didn't bother with audio and could not figure out how to pipe ffmpeg to convert, improvements welcome) examples: http://shrani.si/f/16/OU/3fUvCjIb/shakira-loca.png http://shrani.si/f/2Z/Mh/2eV7odGN/psy.png __________________ certain other member Last edited by smok3; 4th May 2013 at 20:12.
4th May 2013, 02:17 #24 | Link Keiyakusha 契約者 Join Date: Jun 2008 Posts: 1,576 smok3 Yeah, I mentioned batch-scripted imagemagick before. But we also need to make that result match to the given video horizontally, attach to the bottom and make it reveal itself over time like a slider. And this is a bit more complicated... ok, back to the audio. New update. Not sure If I can make adjustable height as instead of proper nonlinear scaling I just chained few usual resamplers, and simulating this "feather"... some bicubicresize probably can be replaced to pointresize with no harm but with speedup... not sure. Edit: or actually this is super simple? just need to set any kind of height in last bicubicresize call? Hmm... Code: ```#1280x720 yv12 input with audio. nothing else tested. w=width() AudioDub(BlankClip(last,pixel_type="YV24",width=1280,height=720),last) Converttomono().Normalize() Histogram(mode="audiolevels").Converttorgb32() calc=FrameRate()*w/Framecount() Changefps(calc,linear=false).Trim(0,-w) Crop(100,0,-1179,-0188) Greyscale().Levels(0,1.000,64,0,255,coring=false) WeaveColumns(w).Greyscale() e=Crop(0,0,0,-height*3/4) f=Crop(0,height/4,0,-height/2) g=Crop(0,height/2,0,-height/4) h=Crop(0,height*3/4,0,0) e=bicubicresize(e,width(e),height(e)/2) f=bicubicresize(f,width(f),height(f)/6) g=bicubicresize(g,width(g),height(g)/9) h=bicubicresize(h,width(h),height(h)/12) Stackvertical(e,f,g,h) bicubicresize(width,48) bicubicresize(width,6).addborders(0,1,0,0) bicubicresize(width,48)``` F/sn UBV theatrical teaser. This is constant music though, trailer for american movie probably will look more "uneven" like that thing on youtube. Or maybe not. Also I wonder how ugly it will look when overlayed... Last edited by Keiyakusha; 4th May 2013 at 02:37.
4th May 2013, 04:33 #25 | Link Keiyakusha 契約者 Join Date: Jun 2008 Posts: 1,576 ok, here is function for video AND audio combined. All standard resolutions as input should work. Probably needs some tweaking though, to make it look more like that thing on YT. I wanted waveform to be around 30% of the video fingerprint height. Not sure if it is right or I failed basic math, or maybe I did some other mistake. Code: ```function fingerprint(clip source, int "fph"){ w=width(source) v=crop(source,8,8,-8,-8) v=bicubicresize(v,640,360) calc=FrameRate(v)*w/Framecount(v) v=Changefps(v,calc,linear=false).Trim(0,-w) v=converttorgb32(v).bicubicresize(4,4).blur(0.65).bilinearresize(2,2) a=Crop(v,0,0,-1,-1) b=Crop(v,1,0,0,-1) c=Crop(v,0,1,-1,0) d=Crop(v,1,1,0,0) x=Overlay(a,b,mode="blend",opacity=0.5) y=Overlay(c,d,mode="blend",opacity=0.5) v=Overlay(x,y,mode="blend",opacity=0.5) v=pointresize(v,1,fph) v=WeaveColumns(v,w).Converttoyv12() wf=AudioDub(BlankClip(source,pixel_type="YV24",width=1280,height=720),source) wf=Converttomono(wf).Normalize() wf=Histogram(wf,mode="audiolevels").Converttorgb32() wf=Changefps(wf,calc,linear=false).Trim(0,-w) wf=Crop(wf,100,0,-1179,-0188) wf=Greyscale(wf).Levels(0,1.000,64,0,255,coring=false) wf=WeaveColumns(wf,w) e=Crop(wf,0,0,0,-height(wf)*3/4) f=Crop(wf,0,height(wf)/4,0,-height(wf)/2) g=Crop(wf,0,height(wf)/2,0,-height(wf)/4) h=Crop(wf,0,height(wf)*3/4,0,0) e=bicubicresize(e,width(e),height(e)/2) f=bicubicresize(f,width(f),height(f)/6) g=bicubicresize(g,width(g),height(g)/9) h=bicubicresize(h,width(h),height(h)/12) wf=Stackvertical(e,f,g,h) wf=bicubicresize(wf,w,48) wf=bicubicresize(wf,w,6).addborders(0,1,0,0) wf=bicubicresize(wf,w,fph*30/100).addborders(0,fph-fph*30/100,0,0) v=Overlay(v,wf,mode="Add",opacity=0.333) bg=blankclip(width=w,height=fph) v=StackVertical(source,v) Function ovl(clip c1, clip c2, int xx, int yy) { Overlay(c1, c2 , xx , yy) } v=Animate(v,0,source.framecount+1,"ovl", bg,0,source.height, bg,source.width,source.height) return v }``` fingerprint(fph=128) Looks like this. Last edited by Keiyakusha; 4th May 2013 at 04:43.
4th May 2013, 09:12 #26 | Link
smok3
brontosaurusrex
Join Date: Oct 2001
Posts: 2,395
Quote:
Yeah, I mentioned batch-scripted imagemagick before. But we also need to make that result match to the given video horizontally, attach to the bottom and make it reveal itself over time like a slider. And this is a bit more complicated...
Yeah, ill skip that part, but if you have a (working) ffmpeg>convert piping solution don't be shy to post.
__________________
certain other member
11th May 2013, 17:10 #27 | Link wonkey_monkey Formerly davidh***** Join Date: Jan 2004 Posts: 1,810 Coming soon... From the Man of Steel trailer: More info and a plugin soon.
6th June 2013, 19:56 #28 | Link wonkey_monkey Formerly davidh***** Join Date: Jan 2004 Posts: 1,810 Whoops, never got around to providing this. First you'll need the plugin from here. Then you can use this function to apply it (probably bad to give the function the same name as the filter, but whatever): Code: ```function fingerprint(clip a, int h) { rgb=a.converttorgb32 resized=rgb.bicubicresize(a.width,h) fingerprinted=resized.fingerprint stack=stackvertical(rgb,fingerprinted.bicubicresize(rgb.width,fingerprinted.height)) return stack }``` You'll get gaps if you seek around in the video without playing it in sequence first, but that also means it doesn't have to preload the clip. It forces the clip to RGB32 with the default matrix (rec601) so you'll need to bear that in mind if you want to convert it back to the original format. David
7th June 2013, 00:49 #29 | Link Sparktank 47.952fps@71.928Hz Join Date: Mar 2011 Posts: 903 Thanks for the plugin, davidhorman. Interesting take on the fingerprint. --- I've found a Windows program that can generate a favorable waveform, but it's only a matter of finding a decent way to normalize the audio. It requires a physical WAV/MP3 file to work with and produces a PNG. Depending what approach you take to normalize or level out the audio without it peaking, you'll get very different waveforms generated. You can set the WxH dimensions for the PNG but if the audio peaks, the waveform will disappear off the picture. Maybe use SoX to apply compand to each channel and then downmix to mono and normalize? I want the lowest point of the wave form to not be at the center of the X-axis. About 1/3 to 1/2 would be nice to make it appear larger as a waveform. And without it peaking beyond the given dimensions of the PNG frame. I'll find the link to the Windows app. I believe there's a python extension for it or a PHP extension. Also will post several examples of what I'm currently doing with the generated waveforms and video fingerprints. ALSO, for full feature length films (much longer than trailers!), I got some error about nonlinear access? I can't remember, but I just added it to the Keiyakusha/poisondeathray fingerprint script and it was able to handle full length films and allow seeking at any point in VirtualDub (quite a bit of time to load the whole project lol). Updates and progress coming soon once I get things sorted. __________________ Win10 (x64) build 18362| GPU Caps Viewer 1.42.4.0 NVIDIA GeForce GTX 1060 3GB (GP106) 3071MB/GDDR5 | (r435_95-4)NTSC | DVD: R1 | BD: AIntel Xeon X5660 @2.80GHz
10th June 2013, 17:30 #30 | Link StainlessS HeartlessS Usurer Join Date: Dec 2009 Location: Over the rainbow Posts: 7,104 David, Using this Code: ```Avisource("D:\avs\test.avi")#.Trim(0,-2*1280) function fingerprint(clip a, int h) { rgb=a.converttorgb32 resized=rgb.bicubicresize(a.width,h) fingerprinted=resized.fingerprint stack=stackvertical(rgb,fingerprinted.bicubicresize(rgb.width,fingerprinted.height)) return stack } Last.fingerprint(128)``` I get, "Iinvalid arguments to function fingerprint". changing to Code: ```Avisource("D:\avs\test.avi")#.Trim(0,-2*1280) function fingerprintB(clip a, int h) { rgb=a.converttorgb32 resized=rgb.bicubicresize(a.width,h) fingerprinted=resized.fingerprint stack=stackvertical(rgb,fingerprinted.bicubicresize(rgb.width,fingerprinted.height)) return stack } Last.fingerprintB(128)``` "There is no function named fingerprint". How should it be called (and yes, probably a bad idea to have same name function as plugin, as user function name overrides plugin_name/builtin_Avisynth_name). @Keiyakusha, you've made "fph" an optional argument, without a default. EDIT: I'm also seeing a date of 11 May 2013 for the Fingerprint.dll ? EDIT: Oops, thats the day you made first post on it. EDIT: I seem to recall a plugin called WarpResize. __________________ I sometimes post sober. StainlessS@MediaFire ::: AND/OR ::: StainlessS@SendSpace "Some infinities are bigger than other infinities", but how many of them are infinitely bigger ??? Last edited by StainlessS; 10th June 2013 at 17:53.
11th June 2013, 11:42 #31 | Link wonkey_monkey Formerly davidh***** Join Date: Jan 2004 Posts: 1,810 I've only recently moved over to Avisynth 2.6. Do you have 2.5.8? Maybe I did something wrong in compiling it... David
11th June 2013, 12:02 #32 | Link StainlessS HeartlessS Usurer Join Date: Dec 2009 Location: Over the rainbow Posts: 7,104 Nope, I'm using 2.6a4 almost exclusively. I know you believe you are a bit messy and dont like to reveal your source, but if you would like me to take a peek I'll be happy to. PM me a link if you like. I've done a number of 2.6 plugs and they seem to work OK. I had myself started out doing a Fingerprint plugin, but discarded it what I saw that you had posted one already (had only just spent about 1/2 hour on it so was far from doing anything). EDIT: Nice job on the fingerprint strip you posted, looks great. __________________ I sometimes post sober. StainlessS@MediaFire ::: AND/OR ::: StainlessS@SendSpace "Some infinities are bigger than other infinities", but how many of them are infinitely bigger ??? Last edited by StainlessS; 11th June 2013 at 12:05.
14th June 2013, 02:12 #33 | Link Sparktank 47.952fps@71.928Hz Join Date: Mar 2011 Posts: 903 David, I'm using the same AVS StainlessS is using and can't get your Fingerprint to run. It crashes instantly in VirtualDub with something about a "kernal" crash. Hopefully you and StainlessS can find something. It would be fun to use both forms of the fingerprint. __________________ Win10 (x64) build 18362| GPU Caps Viewer 1.42.4.0 NVIDIA GeForce GTX 1060 3GB (GP106) 3071MB/GDDR5 | (r435_95-4)NTSC | DVD: R1 | BD: AIntel Xeon X5660 @2.80GHz
14th June 2013, 15:49 #35 | Link
wonkey_monkey
Formerly davidh*****
Join Date: Jan 2004
Posts: 1,810
Quote:
Originally Posted by Sparktank It crashes instantly in VirtualDub with something about a "kernal" crash.
How long in frames is your clip?
15th June 2013, 00:21 #36 | Link
Sparktank
47.952fps@71.928Hz
Join Date: Mar 2011
Posts: 903
Quote:
Originally Posted by davidhorman How long in frames is your clip?
@23.976, 244010 frames.
2:49:37.242 (H:MM:SS.sss) total run length of The Hobbit: An Unexpected Journey.
__________________
Win10 (x64) build 18362| GPU Caps Viewer 1.42.4.0
NVIDIA GeForce GTX 1060 3GB (GP106) 3071MB/GDDR5 | (r435_95-4)
NTSC | DVD: R1 | BD: A
Intel Xeon X5660 @2.80GHz
15th June 2013, 16:19 #37 | Link wonkey_monkey Formerly davidh***** Join Date: Jan 2004 Posts: 1,810 I was lazy and left resizing of the clip to AviSynth rather than doing it in-plugin. So it's probably AviSynth complaining about a) being given a 244010-pixel wide clip or b) being asked to resize said clip.
15th June 2013, 23:15 #38 | Link IanB Avisynth Developer Join Date: Jan 2003 Location: Melbourne, Australia Posts: 3,171 Probably running out of memory. YV12 244010 x 480 clip is 167Mb per frame! Resize works with that, but you cannot do much else.
16th June 2013, 01:00 #39 | Link Sparktank 47.952fps@71.928Hz Join Date: Mar 2011 Posts: 903 Oh, I misread what you meant. I thought you were asking the total runtime of the movie in frames. The frame width is 1920x800, cropped. Here's what the basic script looks like before adding any of the fingerprint functions. Code: ```SetMemoryMax(1280) SetMTMode(3,4) DirectShowSource("L:\1080p (Remux)\The Hobbit.mkv").KillAudio() SetMTMode(2) Crop(0,140,0,-140) SetMTMode(1) Distributor() Return(last)``` __________________ Win10 (x64) build 18362| GPU Caps Viewer 1.42.4.0 NVIDIA GeForce GTX 1060 3GB (GP106) 3071MB/GDDR5 | (r435_95-4)NTSC | DVD: R1 | BD: AIntel Xeon X5660 @2.80GHz
16th June 2013, 04:12 #40 | Link IanB Avisynth Developer Join Date: Jan 2003 Location: Melbourne, Australia Posts: 3,171 Where are people getting the crazy idea that a big SetMemoryMax is ever a good idea. I have searched the forum numerous times looking for any fud and misinformational posts and I do not find any, all I find are the occasional post advising to turn it down. and lots of posts with people using insanely high values and having problems. SetMemoryMax just sets the size of the Avisynth frame cache! It does not control any other memory usage! The frame cache only needs to be just large enough to hold the temporal requirements of the script. If a script has no temporal requirements, i.e. a frame that is required more than once in some part of the script then the cache is completely useless and may prevent some other memory usage from being able to malloc the memory that it needs to work. A 1920x1080 YV12 video frame is ~3meg, as RGB32 it is 8meg, you can hold 64 such frames in 512meg. YV12 720x480 frames are only 0.5meg you can hold 1024 in 512 meg. It takes some resources to manage the frame cache so doing a SetMemoryMax(2048) for a SD video and having 4000 odd buffers in play is just stupid and will actually slow the script processing down a little bit. Advise :- SetMemoryMax, Turn it down!
Tags fingerprint, trailers, waveform
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Doom9.org - Archive - Top | 5,345 | 17,944 | {"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-2019-43 | latest | en | 0.734398 |
https://calculator.academy/cylindrical-shell-calculator/ | 1,701,178,825,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679099514.72/warc/CC-MAIN-20231128115347-20231128145347-00450.warc.gz | 187,919,276 | 51,391 | Calculate the volume and surface area of a shell using this cylindrical shell calculator. Enter the inner radius, out radius, and length of the shell into the calculator below.
## Cylindrical Shell Formula
The following formulas are used to calculate cylindrical shell values.
V = (R^2 - r^2) * L * PI
• Where V is volume
• R is the outer radius
• r is the inner radius
• L is the length/height
The following formula can be used to calculate the total surface area of a shell:
A = 2*PI*(R+r)*(R-r+L)
• Where A is the surface area
• r is the inner radius
• R is the outer radius
• L is the height
## Cylindrical Shell Definition
A cylindrical shell is defined as any hollowed-out cylinder that contains an inner diameter and an outer diameter. This is also considered a tube.
## How to calculate a cylindrical shell?
Calculating the values of a cylindrical shell are as easy as using the above equation. The only values you need are the inner radius, outer radius, and length.
## FAQ
What is a cylindrical shell?
A cylindrical shell is defined as any hollowed-out cylinder that contains an inner diameter and outer diameter. This is also considered a tube. | 267 | 1,168 | {"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} | 3.3125 | 3 | CC-MAIN-2023-50 | latest | en | 0.881884 |
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Can anyone offer insight on an abstract math problem?
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8th October 2010, 11:46 AM #1 diyAudio Member Join Date: Dec 2005 Location: west lafayette Can anyone offer insight on an abstract math problem? Hello members of DIYAudio, I am a bit stumped on a mathematical problem. Recently, I've become interested in polyhedrons. However, I am having a bit of trouble with their analysis. Consider a given dodecahedron. If we consider the solid to be of uniform density, the centroid will occur at (0,0,0) and the distance from the centroid to all of the vertices will be constant. However, the distance from the centroid to other points on the surface will vary. Since the dodecahedron is symmetrical, we can restrict the problem to a single pentagon on the surface. I would like to plot a 2 dimensional function (y=f(x)), where "x" represents radius and "y" represents frequency. For the dodecahedron, the domain of "x" (ie radius) will be continuous from a vertex to the center of the pentagon. The domain of "y" will be continuous from 0-->1 (ie it will be normalized). I would like to extend this analysis to assymetrical polyhedron (ex. the diminished rhombicosidodecahedron. In that particular case, the centroid will be displaced and the individual polygons will not be seperable. Would the solution simply be analogous to a fourier transform over the surface? Could anyone offer insight on this? Thanks, Thadman __________________ "It is a profound and necessary truth that the deep things in science are not found because they are useful; they are found because it was possible to find them."
8th October 2010, 12:48 PM #2 diyAudio Member Join Date: Dec 2005 Location: west lafayette disregard the above post. The problem is much simpler than I initially expected. __________________ "It is a profound and necessary truth that the deep things in science are not found because they are useful; they are found because it was possible to find them."
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All times are GMT. The time now is 07:45 AM. | 716 | 3,012 | {"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 | 3 | CC-MAIN-2016-44 | longest | en | 0.921375 |
https://www.mapleprimes.com/questions/238232-Wrong-Minimal-Polynomials | 1,723,651,353,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722641118845.90/warc/CC-MAIN-20240814155004-20240814185004-00100.warc.gz | 688,873,965 | 41,092 | # Question:Wrong minimal polynomials?
## Question:Wrong minimal polynomials?
Maple 2024
Consider the following exact algebraic number
> restart;
> kernelopts('version'):
> Physics:-Version():
>
>
memory used=0.97MiB, alloc change=12.00KiB, cpu time=31.00ms, real time=27.00ms, gc time=0ns
(1)
>
(2)
>
memory used=70.25GiB, alloc change=48.00MiB, cpu time=23.63m, real time=21.81m, gc time=3.18m
(3)
>
(4)
I would like to find its minimal polynomial (without a priori knowledge).
According to the documentation,
if expr is an exact algebraic number, and n and acc are not given, then `PolynomialTools:-MinimalPolynomial(expr)` will call `evala/Minpoly` to compute an exact minimal polynomial of expr. If a name is not specified for the variable x, then _X will be used.
Regretfully, it is easy to see that the minimal polynomial of cannot be the returned . And when I invoke evala@Minpoly directly, the result is still not correct (and this evaluation takes a rather long time).
Another help page mentions that:
the call `mp := evala(Minpoly(expr, _X))` computes the monic minimal polynomial of a in the variable _X over the field of rational numbers (or multivariate rational functions); the resulting polynomial will not contain any algebraic numbers or functions.
However, as `type(mp, polynom(rational, _X))` gives false, we know that mp cannot be the desired minimal polynomial of either.
So, what is the proper way to compute the minimal polynomial of in Maple?
Code:
```use alpha=1-(1/2)/(1-(RootOf(16*_Z*(_Z*(2*_Z*(_Z*(8*_Z*(_Z*(_Z*(_Z*(32*_Z*(8*_Z-33)+1513)-812)-13)+267)-1469)-330)+811)+279)+345,index=2)-1/2)**2) in
expr:=(1+alpha)*sqrt(1-alpha**2)+(3+4*alpha)/12*sqrt(3-4*alpha**2)+2*(1+alpha)/3*sqrt(2*(1+alpha)*(1-2*alpha))+(1+2*alpha)/6*sqrt(2*((1-alpha)**2-3*alpha**2))
end:
CodeTools:-Usage(PolynomialTools:-MinimalPolynomial(expr));```
Of note, the minimal polynomial of an algebraic number is the unique irreducible monic polynomial of smallest degree with rational coefficients such that and whose leading coefficient is 1
| 626 | 2,076 | {"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-2024-33 | latest | en | 0.609433 |
https://francinebavay.info/relationship-between-and/relationship-between-gravity-and-the-speed-of-light.php | 1,571,491,584,000,000,000 | text/html | crawl-data/CC-MAIN-2019-43/segments/1570986693979.65/warc/CC-MAIN-20191019114429-20191019141929-00021.warc.gz | 505,658,953 | 9,752 | # Relationship between gravity and the speed of light
### Speed of gravity - Wikipedia
Gravity and the Speed of Light It refers to the relationship between the amount of matter in the Universe and the gravitational pull that all. So in the presence of gravity the speed of light becomes relative (variable Finally, there is no difference between the effects of g-forces experienced from these. It simply is the maximum speed that light and gravity travel at. . the only special speed, since it describes the relation between space and time.
### Speed of Light in Gravity
The consequence of this is that static fields either electric or gravitational always point directly to the actual position of the bodies that they are connected to, without any delay that is due to any "signal" traveling or propagating from the charge, over a distance to an observer. This remains true if the charged bodies and their observers are made to "move" or notby simply changing reference frames.
This fact sometimes causes confusion about the "speed" of such static fields, which sometimes appear to change infinitely quickly when the changes in the field are mere artifacts of the motion of the observer, or of observation. In such cases, nothing actually changes infinitely quickly, save the point of view of an observer of the field.
For example, when an observer begins to move with respect to a static field that already extends over light years, it appears as though "immediately" the entire field, along with its source, has begun moving at the speed of the observer.
This, of course, includes the extended parts of the field. However, this "change" in the apparent behavior of the field source, along with its distant field, does not represent any sort of propagation that is faster than light.
## Does Gravity Travel at the Speed of Light?
Newtonian gravitation[ edit ] Isaac Newton 's formulation of a gravitational force law requires that each particle with mass respond instantaneously to every other particle with mass irrespective of the distance between them.
In modern terms, Newtonian gravitation is described by the Poisson equationaccording to which, when the mass distribution of a system changes, its gravitational field instantaneously adjusts.
Therefore, the theory assumes the speed of gravity to be infinite. This assumption was adequate to account for all phenomena with the observational accuracy of that time. It was not until the 19th century that an anomaly in astronomical observations which could not be reconciled with the Newtonian gravitational model of instantaneous action was noted: Based on Newton's force law he considered a model in which the gravitational field is defined as a radiation field or fluid.
Changes in the motion of the attracting body are transmitted by some sort of waves. This velocity was used by many in the 19th century to criticize any model based on a finite speed of gravity, like electrical or mechanical explanations of gravitation.
If a charged particle is moving at a constant velocity, it exerts a force that points toward its present position, not its retarded position, even though electromagnetic interactions certainly move at the speed of light.
### Why Does Gravity Travel at the Speed of Light? - D-brief
Here, as in general relativity, subtleties in the nature of the interaction "conspire" to disguise the effect of propagation delay. It should be emphasized that in both electromagnetism and general relativity, this effect is not put in ad hoc but comes out of the equations.
Also, the cancellation is nearly exact only for constant velocities. If a charged particle or a gravitating mass suddenly accelerates, the change in the electric or gravitational field propagates outward at the speed of light. Since this point can be confusing, it's worth exploring a little further, in a slightly more technical manner. Consider two bodies—call them A and B—held in orbit by either electrical or gravitational attraction.
As long as the force on A points directly towards B and vice versa, a stable orbit is possible.
If the force on A points instead towards the retarded propagation-time-delayed position of B, on the other hand, the effect is to add a new component of force in the direction of A's motion, causing instability of the orbit. This instability, in turn, leads to a change in the mechanical angular momentum of the A-B system. But total angular momentum is conserved, so this change can only occur if some of the angular momentum of the A-B system is carried away by electromagnetic or gravitational radiation.
• Relative Speed of Light
• Speed of gravity
Now, in electrodynamics, a charge moving at a constant velocity does not radiate. Technically, the lowest-order radiation is dipole radiation, and the radiated power depends on the second time derivative of the electric dipole moment; two time derivatives give acceleration.
So, to the extent that A's motion can be approximated as motion at a constant velocity, A cannot lose angular momentum. For the theory to be consistent, there must therefore be compensating terms that partially cancel the instability of the orbit caused by retardation. This is exactly what happens; a calculation shows that the force on A points not towards B's retarded position, but towards B's "linearly extrapolated" retarded position. It depends on where I am and where you are it depends on locations.
So in the presence of gravity the speed of light becomes relative variable depending on the reference frame of the observer. This does not mean that photons accelerate or decelerate; this is just gravity causing clocks to run slower and rulers to shrink.
Recalling the very famous second postulate of Special Relativity by Einstein From Newton's second law: The other factor besides acceleration is gravity. Einstein emphasized in his paper in For example, an observer outside gravitational fields measures the speed of light locally in his location at At the same time an observer freefalling into that black hole zero-g measures the speed of light locally in his location at If he tries to resist his freefall into that black hole by firing his rockets for example he will not measure the speed of light locally anymore at Again when he looks towards the black hole he sees the speed of light there much slower; when he looks away from the black hole he sees the speed of light there much faster.
In any case, freefalling or not, he will never see the speed of light outside gravitational fields at Finally, there is no difference between the effects of g-forces experienced from these rockets and the effects of g-forces experienced when standing on planets, stars In the presence of gravity the speed of light becomes relative.
To see the steps how Einstein theorized that the measured speed of light in a gravitational field is actually not a constant but rather a variable depending upon the reference frame of the observer: | 1,352 | 6,967 | {"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} | 3.234375 | 3 | CC-MAIN-2019-43 | latest | en | 0.940929 |
https://www.coursehero.com/file/96571/d-X-np-1-p-Binomialnp-X-successes-in/ | 1,521,625,069,000,000,000 | text/html | crawl-data/CC-MAIN-2018-13/segments/1521257647600.49/warc/CC-MAIN-20180321082653-20180321102653-00275.warc.gz | 772,017,183 | 26,822 | {[ promptMessage ]}
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# D x np 1 p binomialnp x successes in
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Unformatted text preview: ,p) X = # successes in sample of n Uniform U( a, b ) Normal N(mean, stdev) Two main statistics: X = number of successes in a sample and related to it ... One main statistic: X = sample mean ^ p = propn of successes in sample 1. a. an observational study b. i. Age: quantitative, explanatory, continuous; ii. Internet Use: categorical, response, discrete c. i. Approximately symmetric, unimodal, approximately bell-shaped ii. 15 years iii. 28/200 for 14% d. Overall mean = 42 = (?)(170) + (56)(30) ? = (8400 1680)/170 = 39.5 years 200 e. i. 68 12 = 56 years ii. IQR = 65 49 = 16 years iii. Q1 1.5(IQR) = 49 1.5(16) = 25 years iv. Q3 v. 28 2. a. P...
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Ask a homework question - tutors are online | 320 | 1,035 | {"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-2018-13 | latest | en | 0.727355 |
https://nrich.maths.org/679/solution | 1,556,264,960,000,000,000 | text/html | crawl-data/CC-MAIN-2019-18/segments/1555578762045.99/warc/CC-MAIN-20190426073513-20190426095513-00434.warc.gz | 499,043,351 | 5,563 | ### Forgotten Number
I have forgotten the number of the combination of the lock on my briefcase. I did have a method for remembering it...
### Human Food
Sam displays cans in 3 triangular stacks. With the same number he could make one large triangular stack or stack them all in a square based pyramid. How many cans are there how were they arranged?
### Hot Pursuit
I added together the first 'n' positive integers and found that my answer was a 3 digit number in which all the digits were the same...
# Sam Again
##### Age 11 to 14 Challenge Level:
You can make good use of a spreadsheet or of algebra to solve this problem. As well as solutions to Hannah's problem, solutions are invited to Santa's problem using methods which work equally as well for large numbers as for 21.
Congratulations to Jamesof Hethersett High School, Norfolk and to Helen, Charis, Lyndsay, Christiane, Charlotte, Bellaand Rachel, Year 10, Mount School York. Some said that either the reindeer were extremely hungry or there are more reindeer in Santa's employ than we are led to believe (someone did suggest 'Reindeer Express' along the lines of the Pony Express of history!) Here is Helen's solution:
To find how many layers high the pyramid is:
$$231 {\rm (cm)} / 11 {\rm (cm)} = 21 {\rm \ layers\ high.}$$
Each layer is a consecutive square number and the square numbers from $1^2$ to $21^2$ are:
1, 4, 9, 16. 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441
All these added together gives 3311.
To find out how many cans in the triangular based pyramid, you add up the triangle numbers from the 1st to the 21st:
1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190, 210, 231
This equals 1771 cans.
The reindeer ate 3311 - 1771 = 1540 cans in one meal. There are 1771 cans left so there are enough to feed the reindeer another meal with 231 cans remaining.
James also solved Katherine's problem as follows. He wrote down all the triangular numbers smaller than 64 and then, using trial and improvement, James found two solutions:
$\begin{eqnarray} \\ T_5 + T_6 + T_7 &=& 15 + 21 + 28 = 64 \\ T_2 + T_3 + T_{10} &=& 3 + 6 + 55 = 64. \end{eqnarray}$
Well done Jacqui, Year 8, Mount School York for your solution to Nisha's problem. There are at least three ways of arranging 136 cans into four $T-$ stacks.
$\begin{eqnarray} \\ T_p + T_q + T_r + T_s &=& 136 \\ T_5 + T_6 + T_9 + T_{10} &=& 15 + 21 + 45 + 55 = 136 \\ T_3 + T_4 + T_5 + T_{14} &=& 6 + 10 + 15 + 105 = 136 \\ T_3 + T_7 + T_8 + T_{11} &=& 6 + 28+ 36 + 66 = 136. \end{eqnarray}$ | 807 | 2,598 | {"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} | 4.46875 | 4 | CC-MAIN-2019-18 | longest | en | 0.946455 |
https://chargersgame.org/what-is-the-quotient-6x4-15x3-2x2-10x-4-%C3%B7-3x2-2/ | 1,669,693,030,000,000,000 | text/html | crawl-data/CC-MAIN-2022-49/segments/1669446710685.0/warc/CC-MAIN-20221129031912-20221129061912-00046.warc.gz | 203,084,846 | 16,282 | # What is the quotient: (6×4 – 15×3 – 2×2 – 10x – 4) ÷ (3×2 + 2)?
(6x^4 – 15x^3 – 2x^2 – 10x – 4) ÷ (3x^2 + 2)
= (6x^4 – 15x^3 + 4x^2 – 6x^2 – 10x – 4) ÷ (3x^2 + 2)
= (6x^4 + 4x^2 – 15x^3 – 10x – 6x^2 – 4) ÷ (3x^2 + 2)
= 2x^2(3x^2 + 2) – 5x(3x^2 + 2) – 2(3x^2 + 2) ÷ (3x^2 + 2)
= (3x^2 + 2)(2x^2 – 5x – 2) ÷ (3x^2 + 2)
= 2x^2 – 5x – 2 Ans. | 260 | 340 | {"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-2022-49 | latest | en | 0.647234 |
https://www.blackhatworld.com/seo/10-to-xxxx-a-day-method-with-potential-any-advice-can-help.910509/ | 1,524,146,626,000,000,000 | text/html | crawl-data/CC-MAIN-2018-17/segments/1524125936969.10/warc/CC-MAIN-20180419130550-20180419150550-00220.warc.gz | 765,783,131 | 17,400 | # [\$10 to xxxx a day]Method with potential! Any advice can help!
Discussion in 'Making Money' started by cojocusd, Jan 23, 2017.
1. ### cojocusdNewbie
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I want to share with you a method who could work with little patience and some few minutes of your time!
So let s start.
This method is about Sport betting. You can easily earn from \$10 up to xxxx a day with low to 0 risk, depends on your budget.
Well let's say you have \$100 and you want to earn \$10 a day from this money.
Simple math \$10/day=>30 days = \$300. For some people this amount of money is more than enough for others is just a shit but let s go back to the method.
You will analise some games football or tenis or whatever. My opinion is go with football.
You have to go to flashscore find a match where the teams will score at least 1 goal maybe 2.
My advice is to find some match from secondary leagues or something like that. Where the teams are scoring much more.
Let s say this example. As you can see the teams are scoring alot. Now go to your bet site find the match and put that : "+0.5 goals all the match". Mean in 90 minutes at least 1 goal will be scored.
In this case you will have something like "Odd: 1.05 or 1.1". So you will pay \$100 and get back 105 or 110! Of course this is just an example you can study more games and play with other tips not goals.But this is my example.
Btw.The method is to play \$100 with 1.1 odds! This will return you \$10 for every win. As i said at the begging if you are searching and spending like 15-30 minutes a day finding a match you can earn easy \$10!
I hope this method will help you to make some bucks in order to start something big or why not make a living from betting! Happy earning!
If i miss somehting you can leave a comment or add some tips or twist and make it a real income! Enjoy!
Remeber, betting is not just luck!
2. ### MollowbassRegular Member
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And what happens when unfortunately both team wont score due to certain circumstances. It happens. Or do you think, well if it happens less then 1 time per 11 bets, you always have a profit?
3. ### eridonvevo77Regular Member
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This method works if you bet 1.3/1.4 odds nearly the end of 1st half..
4. ### Asif WILSON KhanExecutive VIPJr. VIP
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• Thanks x 2
5. ### VeeGeeNRegular Member
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Better odds creating a tipster website manually looking from people who do this for a hobby. They put a lot more effort in. Add the adverts and sportsbook offers emailed to you.. Create a few facebook pages post the football goals and funny moments... 15% of each bet for the lifetime of their account.
Sounds better then risking money on goals everyday when you can create your own goals..
6. ### dolomite310Regular Member
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This is terrible advice. If people wanted to lose their money this would be a binary options forum. Instead, most people are here because they want to grow their funds while using calculated risks.
7. ### insomnijakRegular Member
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Worst thread of the day
Seriously, this should be deleted. It is either ignorant or malicious.
8. ### Spike1337Registered Member
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I was playing a lot and and the percent of winning from betting is veeeeeeeeeeeeeeery low, I mean 0,000000000000000000000000000001 percent or maybe less, and only way to win as I found was to bet on NBA that one team wouldn't win all quarters,it has like 1.05 odds. OP you can see on flashscore how many times 1 team won every quarters of the game, I don't mean GSW or Cavs don't bet on them some other teams, if you are betting, this will help you.
• Thanks x 1
9. ### Spike1337Registered Member
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Oooooh I finishedwith betting I'm betting for 10 years and I lost like 50K \$ so I'm not playing anymore and i suggest you too, I knew any statistics about NBA and football but I was still loosing on last minute goals
10. ### knowing25Elite Member
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I always avoid myself to make money from betting and gambling etc...
11. ### Subhom SarkarRegular Member
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thank you, thank you so much, finally found a method. can i bribe these players with \$50?
12. ### stunaBANNEDBANNEDJr. VIP
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Nice Share..Thanks..
13. ### chemo38Newbie
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I believe this is why online gambling is against the law in the USA.
14. ### NeozinRegistered Member
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Are you f*cking kidding me?
15. ### sparksparkNewbie
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It's similar to gambling.
Sigh
16. ### McgeezaxNewbie
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If you want money from betting just go with the matched betting method. Basically with your method you win 10\$ with the risk of losing 100\$, for one bet lost you have to win 10 to get back your money, not very efficient.
If you want to make money and have 100\$ to lose, better to buy a domain/hosting and some seo/affiliate/dropshipping ebook.
17. ### Charlie98172Newbie
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Thank you for sharing.
18. ### frizenkingRegular Member
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So we should bet the whole 100\$ every time?
And be sure we will loose at least once and that's it.
19. ### TozzyRegular Member
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This is total bullshit trust me, you won't get anywhere.
The profit for total '0.5 or greater' bet is usually next to zero. Yes it seems like most of your bets will win but with this only one loss shall ruin a lot of successful bets.
Sorry but if it was that easy bookies would go bankrupt.
Joined:
Jan 28, 2017
Messages:
29 | 1,709 | 6,235 | {"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} | 2.828125 | 3 | CC-MAIN-2018-17 | latest | en | 0.935776 |
http://www.jiskha.com/display.cgi?id=1175206982 | 1,498,423,152,000,000,000 | text/html | crawl-data/CC-MAIN-2017-26/segments/1498128320582.2/warc/CC-MAIN-20170625203122-20170625223122-00097.warc.gz | 572,902,789 | 3,743 | posted by .
The cost of producing a number of items x is given by C=mx+b, inwhich b is the fixed cost and m is the variable cost (the cost of producing one more item).
(a) If the fixed cost is \$40 and the variable cost is \$10, write the cost equation.
Could someone help me please with this problem ASAP!!
How do I graph this/ Could you explain how I do this as well?
This is algebra. You have all the parts for the cost function. C=10.*X + 40.
This is a simple line. Starts at 40 on the y-axis and rises 10 for every x. | 136 | 526 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.25 | 3 | CC-MAIN-2017-26 | latest | en | 0.928965 |
https://chemistry.stackexchange.com/questions/13653/balancing-redox-equation?noredirect=1 | 1,586,258,708,000,000,000 | text/html | crawl-data/CC-MAIN-2020-16/segments/1585371700247.99/warc/CC-MAIN-20200407085717-20200407120217-00211.warc.gz | 391,136,382 | 31,813 | Balancing redox equation
So I had these two reactions that confused me .. I tried the standard way of balancing it (Putting oxygen number everywhere, +1,+2,-2 etc.) and then go on with it but it didn't work
So anyways here are the 2 reactions: $$\ce{3 Cu + 8HNO3-> 3Cu(NO3)2 + 2NO + 4H2O}$$ $$\ce{3Ag + 4HNO3 -> 3AgNO3 + NO + 2H2O}$$
I've no idea how do you get those coefficients (numbers).. Please, is there an easy way to do it (perhaps it has to do with electrons added/given? ) and if so - where do I start?
There are a few basic principles that are useful to keep in mind when you want to balance a redox equation.
1) OILRIG - Oxidation Is Loss, Reduction Is Gain (of electrons)
Let's look at the basics of the first equation: $$\ce{Cu + HNO3-> Cu(NO3)2} + ?$$
On the left hand side we have Cu(0) metal and N(V), on the right hand side we have Cu(II) ion and N(V), so from OILRIG we know that the copper is being oxidised... but we know from OILRIG we have to put the electrons from the Cu(0) somewhere...
2) Hydrogen ions are always +1, and oxygen ions are always (there are a few exceptions but this is a good general rule) -2
... So the only thing that can change is the nitrogen. The nitrogen must be being reduced.
Nitrogen actually has a large number of possible oxidation states, taking any value between -3 and +5, so how do we decide which one it goes to in this case? This depends on the temperature and the concentration of the acid. We can probably assume room temperature and bench concentration of acid (otherwise conditions need to be specified), and that the nitrogen isn't going to gain 5 electrons and become nitrogen gas, which means that we are going to form an oxide. Of the oxides, the most thermally stable is NO (nitrogen is in oxidation state +2 here).
What does that look like now?
$$\ce{Cu + HNO3-> Cu(NO3)2 + NO}$$
To balance the electron transfers, we need 3 Cu(O) going to Cu(II) to donate 6 electrons for 2 N(V) to go to N(II). Balancing for electrons and nitrogens, we now have:
$$\ce{3Cu + 8HNO3-> 3Cu(NO3)2 + 2NO}$$
Ok, now we need to look at balancing oxygens and hydrogens.
3) Use water if you can to balance oxygen and hydrogen. If not, start looking at hydroxide or hydrogen ions.
Here we need to somehow account for 8 hydrogens and 8x3 - 3x3x2 + 2 = 4 oxygens... That's 4 water molecules, so we finally have the answer you provided at the start!
$$\ce{3Cu + 8HNO3-> 3Cu(NO3)2 + 2NO + 4H2O}$$
• Good explanation; I would add why one would use water to balance oxygen and hydrogen over hydroxide or hydronium ion (if that is the case, and in what conditions). – Dissenter Jun 19 '14 at 16:04 | 761 | 2,653 | {"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} | 3.234375 | 3 | CC-MAIN-2020-16 | latest | en | 0.936871 |
http://forums.wolfram.com/mathgroup/archive/2006/Aug/msg00830.html | 1,527,190,752,000,000,000 | text/html | crawl-data/CC-MAIN-2018-22/segments/1526794866772.91/warc/CC-MAIN-20180524190036-20180524210036-00638.warc.gz | 108,126,143 | 9,031 | Re: Re: Numerical evaluation is Mathematica bottleneck?!
• To: mathgroup at smc.vnet.net
• Subject: [mg69107] Re: Re: Numerical evaluation is Mathematica bottleneck?!
• From: "Jens-Peer Kuska" <kuska at informatik.uni-leipzig.de>
• Date: Wed, 30 Aug 2006 06:33:17 -0400 (EDT)
• Organization: Uni Leipzig
• References: <ed0sb8\$src\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com
```Hi,
and there is only the unreadable form below ??
usual I prefer equations in the traditional
mathematical
way -- because from you original question it is
clear
that one should use NDSolve[] directly, or build a
SparseMatrix[] object and not the discretisation
you
give below.
Regards
Jens
"gregorc" <gregor.cernivec at fe.uni-lj.si> schrieb
im Newsbeitrag news:ed0sb8\$src\$1 at smc.vnet.net...
| Hello,
|
| The problem consists of three coupled nonlinear
equations: the Poisson
| equation and the countiniuty equations for
electrons and holes. The
| countiniuty equations consist of
convection-diffusion type equations for
| electrons and hole current and the
generation-recombination terms.
|
| The Poisson equation for non-uniform mesh at
node 2:
|
| FV[2]=(2*(-((-V[[1]] + V[[2]])/h[[1]]) +
(-V[[2]] +
| V[[3]])/h[[2]]))/(h[[1]] + h[[2]])-(q*(nt[2] +
n[[2]] + NA[[2]] -
| ND[[2]] - p[[2]]-pt[2]))/eps[[2]]
|
| The electron and hole currents between nodes 1-2
and 2-3 and the
| countinuity equations, respectively:
|
| Jn[1]=(Dn[[1]]*(-(B[(V[1] -
V[2])/UT[[1]]]*n[[1]]) + B[(-V[1] +
| V[2])/UT[[1]]]*n[[2]]))/h[[1]]
| Jn[2]=(Dn[[2]]*(-(B[(V[2] -
V[3])/UT[[2]]]*n[[2]]) + B[(-V[2] +
| V[3])/UT[[2]]]*n[[3]]))/h[[2]]
| FJn[2]=-2/(h[[2]]+h[[1]])*(Jn[1]-Jn[2])-R+GL
|
| Jh[1]=(Dp[[1]]*(B[(-V[1] +
V[2])/UT[[1]]]*p[[1]] - B[(V[1] -
| V[2])/UT[[1]]]*p[[2]]))/h[[1]]
| Jh[2]=(Dp[[2]]*(B[(-V[2] +
V[3])/UT[[2]]]*p[[2]] - B[(V[2] -
| V[3])/UT[[2]]]*p[[3]]))/h[[2]]
| FJh[2]=2/(h[[2]]+h[[1]])*(Jp[1]-Jp[2])-R+GL
|
| ,where V[[2]] is the calculation variable for
the electrical potential
| at node 2, n[[2]] and p[[2]] are the calculation
varibles for electron
| and hole concentrations, respectively. The rest
is material data, built
| in and/or trapped charge,
recombination-generation terms, which might be
| also set to zero (R,GL) and constants. B is the
Bernoulli function,
| which has to be approximated with Taylor series
to avoid singularity
| with argument 0 - zero field (V[[1]]=V[[2]]).
h[[1]], h[[2]]... is the
| discretization step.
|
| Functions:FJn[2], FV[2], FJh[2]
|
variables:X={n[[1]],V[[1]],p[[1]],n[[2]],V[[2]],p[[2]],n[[3]],V[[3]],p[[3]]}
|
| The Jacobian:
|
| JFV=Map[D[FV[2],#]&,X]
| JFJn=Map[D[FJn[2],#]&,X]
| JFJp=Map[D[FJp[2],#]&,X]
|
| Functions and the coresponding Jacobians are
compiled:
|
|
JFVnum=Compile[{{n,_Real,1},{V,_Real,1},{p,_Real,1},{consts},...},Evaluate[JFV]].
|
| Numerical evaluation:
|
|
mat. data}]
|
| ,where var`n=Partition[n,3,1] and same for the V
and p and the rest of
| the material data and constants.
|
| The numerical function is Threaded over the
overlapping triplets of
| calculation variables and data. When the
numerical function and the
| coresponding jacobians are calculated, the
sparse array is formed with
| the SparseArray function and the system is
solved with the LinearSolve.
| The majority of the computational time takes the
| compiled function on the partitioned data and
varibles. The functions
| and jacobians are compiled for sure, since I
have checked it with
| compiled_function[[-3]], which returns all real
numbers.
|
| Regards,
|
| gregor.
|
| Jens-Peer Kuska wrote:
|
| >Hi,
| >
| >the C/C++ version may be faster -- or not, it
depend on
| >your programming skills and the numerical
methods you are
| >using.
| >But as long as you don't tell more about the
problem and
| >how you have solved it in Mathematica, there is
| >
| >Regards
| > Jens
| >
| >gregorc wrote:
| >
| >
| >>Dear mathgroup members,
| >>
| >>I am solving a non-linear semiconductor PDE
problem with finite
| >>difference discretization. The Compiled
algebraic equation and its
| >>Jacobian take as input central point and two
| >>they are Threaded over the whole mesh. A
LinearSolve and some damping
| >>schemes are used to obtain next step towards
the solution. Typical mesh
| >>is about 300 points and the solution is
usually found in 7 iterations,
| >>which takes about 7 seconds of computational
time.This is already too
| >>slow, but since I plan to solve the problem in
2D this is much too
| >>slow!!! The bottleneck is the numerical
evaluation of the compiled
| >>equation and its Jacobian. I am thinking of
using MathLink and write the
| >>numerical evaluation routine in C++, which
would take a list of data and
| >>return evaluated function and the Jacobian.
| >>
| >>Is this the right way? Could the link itself
be a timing bottleneck? Any
| >>other suggestions?
| >>
| >>Regards,
| >>
| >>Gregor
| >>
| >>
| >>
| >
| >
| >__________ NOD32 1.1727 (20060826) Information
__________
| >
| >This message was checked by NOD32 antivirus
system.
| >http://www.eset.com
| >
| >
| >
| >
| >
|
```
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http://forums.wolfram.com/mathgroup/archive/2000/Apr/msg00404.html | 1,527,342,580,000,000,000 | text/html | crawl-data/CC-MAIN-2018-22/segments/1526794867417.75/warc/CC-MAIN-20180526131802-20180526151802-00293.warc.gz | 110,358,649 | 7,205 | Re:NestWhile
• To: mathgroup at smc.vnet.net
• Subject: [mg23265] Re:NestWhile
• From: "Alan W.Hopper" <awhopper at hermes.net.au>
• Date: Sat, 29 Apr 2000 22:05:07 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com
```Dear mathgroup ,
Concerning my query before Easter, about a version 3 equivalent to
NestWhile.
Thanks to Hartmut Wolf, Daniel Reeves, Andrzej Kozlowski, and
Jens-Peer Kuska
for their solutions.
And I received an e-mail from Eric Bynum of Wolfram Technical Support,
with code
which appropriately utilizes both Nest and While. Thanks also, Eric.
Here is Eric's Mathematica 3 Keith Sequence solution ;
In[1]:=
V3KeithSequence[n_Integer?Positive] :=
Module[{d = IntegerDigits[n], l, counter, lis},
l = Length[d];
counter = 1;
While[Nest[Append[#, Plus @@ Take[#, -l]] &, d, counter][[-1]] <
n,
counter++;
lis = Nest[Append[#, Plus @@ Take[#, -l]] &, d, counter]];
lis
]
In[5]:=
V3KeithSequence[197]
Out[5]=
{1, 9, 7, 17, 33, 57, 107, 197}
Where as before, 1+9+7=17, 9+7+17=33, etc., ending again with 197.
Alan Hopper
awhopper at hermes.net.au
```
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• Next by thread: join/problem | 416 | 1,250 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.546875 | 3 | CC-MAIN-2018-22 | latest | en | 0.721458 |
rachar.com | 1,638,226,799,000,000,000 | text/html | crawl-data/CC-MAIN-2021-49/segments/1637964358847.80/warc/CC-MAIN-20211129225145-20211130015145-00204.warc.gz | 61,518,084 | 5,531 | # Hard Work and Knowledge gives way to Attitude, Bullshit and Ass Kissing
I don’t know where this next little ditty came from, I was looking through my notes on my iPhone, that were copied from my Palm Trio, that was copied from my Palm Pilot. According to the date it was 1,490 days ago that I copied this from Who-Knows-Where? If anyone knows the original author let me know and I’ll give them credit.
The closest I have come to hearing this in the wild is one of the sayings, my Papa has used: Old Age and Treachery will beat Youth and Exuberance.
HERE WE GO:
Hard Work and Attitude, Giving More Than 100%
From a strictly mathematical viewpoint it goes like this…
What Makes 100%? What does it mean to give MORE than 100%? Ever wonder about those people who say they are giving more than 100%? We have all been to
those meetings where someone wants you to give over 100%. How about achieving 103%?
So what makes up 100% in life?
Here’s a little mathematical formula that might help you answer these questions:
If:
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z is represented as:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
Then…
H-A-R-D-W-O-R-K = 8+1+18+4+23+15+18+11 = 98%
and
K-N-O-W-L-E-D-G-E = 11+14+15+23+12+5+4+7+5 = 96%
But…
A-T-T-I-T-U-D-E = 1+20+20+9+20+21+4+5 = 100%
And..
B-U-L-L-S-H-I-T = 2+21+12+12+19+8+9+20 = 103%
AND look how far ass-kissing will take you…
A-S-S-K-I-S-S-I-N-G = 1+19+19+11+9+19+19+9+14+7 = 127%
So, one can then conclude with mathematical certainty that while Hard Work and Knowledge will get you close, and Attitude will get you there, Bullshit and Ass
Kissing will put over the top.
Lets try:
Old Age and Treachery = 15+12+4+1+14+4+20+18+5+1+3+8+5+18+25 = 153
Youth and Exuberance = 25+5+21+20+8+1+14+4+5+24+21+2+5+18+1+14+3+5 = 206
This goes to prove that if you don’t have Youth and Exuberance working for you then Old Age and Treachery will win over all others.
Always have Fun
G
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posted by .
how do i simplify -9/2x^-3/2??? please help i dun need a answer necessary just an explanation is fine :)
• Math -
IS THERE ANYONE WHO CUD HELP PLEASE
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lonlcjy.web.app | 1,721,245,176,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763514801.32/warc/CC-MAIN-20240717182340-20240717212340-00562.warc.gz | 330,306,641 | 7,038 | Lectures on quantum mechanics... - LIBRIS
A notation that does this very nicely was invented by the physicist P. A. M. Dirac for quantum physics — but we can use it anywhere. The notation chooses to enclose the vector symbol in a surround marker rather than putting an arrow over it. Dirac chose the 3. Prof.
Partly relativity theory was a symbol of theoretical physics, as such,. Let us call an a priori strategy deterministic if all pµ are Dirac measures. math-symbol was introduced), anecdotes and quotations can enliven the class even mathematical framework, group theory, in modern particle physics. The text is a result. of literature C.3 Dirac Notation .
## Rarita – Schwinger ekvation - Rarita–Schwinger equation
X. Wave plain equation for body text (Credit: Stellario Cama) Fysik Och Matematik,. Sparad från Calculus Symbols - Math Poster The Dirac equation predicted. av R Khamitova · 2009 · Citerat av 12 — Conservation laws for Maxwell-Dirac equations with dual Ohm's law The symbol Di denotes the total differentiation with respect to the variable xi: Di = xi + ui α. The introduction of shift into the Dirac equation is due to the argument that the in the K-G equation usually the quantity mc is replaced by another symbol like µ.
### Sagittarius
a '+! (b '). The Dirac Equation explicitely describes fermions with an intrinsic spin, and if you wanted to persue an equation which is void of spin, the Klein-Gorden Equation would satisfy.
(13) 3 Free particle solutions of the Dirac equa-tion Dirac equation is the relativistic extension to Shrodinger's equation.
Elinore
Resistive Memory 550, I. definitions of Commonly Used Symbols 555, II. of the density of States in the Conduction, v. derivation of Fermi—dirac Statistics 566, vI. H.263, MPEG-4 Visual (including DivX, XviD), H.264/AVC, Dirac. insertion of 370 mathematical symbols with only one click, a structure Diophantine equation sub. Dirac delta function sub. Diracs deltafunktion; se Dirac function.
Dirac’s equation is a relativistic wave equation which explained that for all half-spin electrons and quarks are parity inversion (sign inversion of spatial coordinates) is symmetrical. The equation was first explained in the year 1928 by P. A. M. Dirac. 2019-02-16 An online LaTeX editor that's easy to use. No installation, real-time collaboration, version control, hundreds of LaTeX templates, and more. Transforming the Dirac Equation: iµ⇤ µ⇥ mc ⇥ =0 ⇥ iµ⇤ µ⇥ mc ⇥ =0 iµ ⇤x⇥ ⇤xµ ⇤ ⇥ (S⇥) mc (S⇥)=0 S is constant in space time, so we can move it to the left of the derivatives iµS ⇤x⇥ ⇤xµ ⇤ ⇥ ⇥ mc (S⇥)=0 Now slap S-1 from both sides Since these equations must be the same, S must satisfy i The free-particle Dirac equation is derived.
This is a DIGITAL ( av J Kungsman · 2014 — well as some of the interpretational problems of the Dirac equation. generated by the eigenvalues of the principal symbol of D at the current This book explains and develops the Dirac equation in the context of general relativistic quantum mechanics in a range of spacetime dimensions. It clarifies the av T Ohlsson · Citerat av 1 — where the coe cient nq"#(B) of each symbol ^q. "#. should be Using the Dirac equation (i @ m q) q = 0, the Lagrangian (4.23) can be reduced. to. Lint 'i.
The outer product is represented within Dirac notations as $\ket{\psi} \bra{\phi}$, and sometimes called ketbras because the bras and kets occur in the opposite order as brakets. The outer product is defined via matrix multiplication as $\ket{\psi} \bra{\phi} = \psi \phi^\dagger$ for quantum state vectors $\psi$ and $\phi$. The Dirac operator is clearly a rst-order di erential operator.
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### Ett slags modernism i vetenskapen: Teoretisk fysik i Sverige
Dirac, Paul Adrien Maurice, Great Britain, Cam and which has made her ñame a symbol of the idealistic. Plats: Room 3721, Department of Mathematics, KTH Musard Balliu: ENCOVER: Symbolic Exploration for Information Flow Security. 28. maj Maria J. Esteban: Critical magnetic fields for the Dirac-Coulomb operator. 16. okt.
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### F¨ORORD INNEHÅLL - Matematiska institutionen
LATEX Mathematical Symbols The more unusual symbols are not defined in base LATEX (NFSS) and require \usepackage{amssymb} 1 Greek and Hebrew letters α \alpha κ \kappa ψ \psi z \digamma ∆ \Delta Θ \Theta Dirac’s equation is a relativistic wave equation which explained that for all half-spin electrons and quarks are parity inversion (sign inversion of spatial coordinates) is symmetrical. The equation was first explained in the year 1928 by P. A. M. Dirac. 2021-04-12 · A modified Dirac equation can be used to approximately describe protons and neutrons, which are not elementary particles (they are made up of quarks), but have a net spin of ½. Another modification of the Dirac equation, called the Majorana equation, is thought to describe neutrinos — also spin-½ particles. J. L. Martin (see references below) has identified four virtues of Dirac notation. It is concise. There are a small number of basic elements to Dirac’s notation: bras, kets, bra-ket pairs, ket-bra products, and the completeness relation (continuous and discreet).
## 3.3 Bindningsenergier - Relativitetsteori - MATH.SE
metaphor": mind/emo6onal state shows up as sign/symbol in various conduct, lågenergiska kvasipartiklar i grafen beskrivs av masslösa Dirac fermioner 12 . bg beroende av Ic (symbol) och normalstatningsmotståndet R n (linje) för V tg In equation (5), we introduce a parameter α to compensate for the aspect ratio List of recurrent acronyms and symbols. ALD. Atomic layer its entity can be modelled with Poisson's equation.
När det finns en kurshemsida visas en hus-symbol som leder till In particular we treat the Dirac equation for spin 1/2 particles in details. När det finns en kurshemsida visas en hus-symbol som leder till In particu-lar we treat the Dirac equation for spin 1/2 particles in details. Köp boken The Many Faces of Maxwell, Dirac and Einstein Equations av Jr The exercises with solutions, thecomprehensive list of mathematical symbols, and En graf för att förtydliga att Diracs deltafunktion är derivatan till Heavisidefunktionen. Diracs delta-funktion (även kallad Dirac-pulsen eller enhetsimpuls eller Melvyn Bragg and guests discuss the theoretical physicist Dirac (1902-1984), to physics, beyond predicting anti-particles as he did in his Dirac Equation. | 1,752 | 6,597 | {"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} | 2.8125 | 3 | CC-MAIN-2024-30 | latest | en | 0.812608 |
https://brexitbunker.uk/2022/11/08/why-body-mass-index-doesnt-say-anything-about-whether-youre-healthy-2/ | 1,669,975,038,000,000,000 | text/html | crawl-data/CC-MAIN-2022-49/segments/1669446710900.9/warc/CC-MAIN-20221202082526-20221202112526-00252.warc.gz | 177,945,986 | 19,236 | # Why Body Mass Index doesn’t say anything about whether you’re healthy
Am I slim or too fat? And if so, how overweight am I? In order to estimate your own weight, it is useful and common to calculate the Body Mass Index (BMI). This indicates whether you are underweight, normal weight or just (severely) overweight.
However, BMI says nothing about whether you are actually healthy. Because even slim people can have internal fat deposits and as a result suffer from the classic obesity diseases such as diabetes, high blood pressure and cardiovascular problems.
## What is Body Mass Index?
BMI is based on values from the World Health Organization (WHO) and is calculated based on height in relation to weight. It indicates whether the resulting value corresponds to a healthy balance (from a medical point of view).
There are masks for adults over 18 on the internet where you enter your values and the result is displayed. But you can also calculate it yourself: body weight (in kilograms) divided by height (in meters) squared. First, multiply your height by itself: 1.70 (meters) x 1.70 (meters) = 2.89. Then divide your weight by this value, so about 65 (kilogram): 2.89. The value – in this case 22.5 – is your BMI.
So a person who is 170 centimeters tall and weighs 65 kilos has a BMI of 22.5 – and is therefore in the absolute middle of the normal weight range. Anyone who is 185 centimeters tall and weighs 80 kilograms has a BMI of 23.4 – also a good normal value.
According to the WHO, there are six weight classes: under 18.5 means underweight, between 18.5 and 24.9 you are normal weight, between 25 and 29.9 you are overweight, from a BMI of 30 there are three different degrees of obesity (obesity) .
“Based on the mentioned weight classes, it is quick and easy to assess in the first step whether the body fat percentage is too high. The good thing about BMI is that it is so easy to calculate and provides a good initial orientation,’ says ecotrophologist Veronika Albers from the nutritional advice platform Oviva.
You can use the app to get prophylactic advice, help with intolerances, but also get help to lose weight – and it even works with a prescription; the doctor only has to prescribe it, then the app or advice is free or, depending on the insurance company, includes a personal contribution. Around 60 specialists work at Oviva, who provide support via chat or phone. Veronika Albers is one of them.
## Why is BMI not meaningful?
In short, the body mass index describes whether the kilos you carry with you are appropriate, too much or too little for our size. However, it says nothing about how the kilos are distributed – and that is precisely the main point of the criticism. Another is that BMI does not differentiate between fat and muscle. “Athletic people can have an increased BMI value without being overweight,” says Veronika Albers.
Muscle weighs more than fat. Nevertheless, an athlete with a high BMI is usually a very healthy person, whereas a slim person with an optimal BMI may be sick due to internal fat deposits that are not visible from the outside.
“We don’t know what it looks like inside the body,” says Albers. “We can only find out from laboratory values and a visit to the doctor. One result could be elevated liver values, which can be an indication of fatty liver.”
We don’t feel a fatty liver for a long time – too long. Because when the symptoms appear, it’s almost too late. Cirrhosis of the liver can occur, which can be fatal. Warning signs of fatty liver are fatigue, a feeling of pressure in the right upper part of the abdomen, flatulence, a feeling of fullness and nausea. “But there can also be problems with the pancreas or the stomach, which is why precise diagnostics are required,” says Veronika Albers.
Internal obesity, which is not visible, occurs if you eat unhealthy and do little exercise. You can still burn well, so you don’t get fat, but the excess calories are stored in the liver as fat.
It’s like this: If we snack a lot in between, wolf down our meals, eat too many carbohydrates, we automatically eat more than is good for us and than our body actually needs. The excess energy is then stored.
In short, you can have a BMI in the green but still be internally fat and even sick. Then you are thin and fat at the same time.
## What are skinny fat people?
As is so often the case, the term comes from English: thin outside, fat inside, abbreviated as the abbreviation TOFI, in German: thin outside, thick inside. “Internal obesity develops over years, it’s insidious,” says ecotrophologist Veronika Albers. “An unhealthy diet and lack of exercise, which results in muscle breakdown, plays a decisive role. However, our muscles are the burners, they use a lot of energy and prevent obesity.”
Those who are classically fat usually have a round stomach (men) or a strong hip and buttock area (women). Fat is visible. But when the liver is fatty, you don’t see it. “The stored fat wraps around the liver so that it can no longer function properly, even though it is our most important detoxification organ,” says Veronika Albers. “However, important conversion and degradation processes also take place in the liver, without which our metabolism cannot function properly.”
You can imagine it as a room where the walls move towards you. “There is a functional limitation of the liver, which in the end can even die out. This cannot be reversed and is really dangerous,” warns the expert. “Because we cannot live without a liver, it cannot be replaced by medicine, only by a transplant.” Without a liver, for example, we would not be able to take medicine because it ensures that the active ingredients do not cause harm in the body.
## How do I know if I am healthy?
Aside from the lab results mentioned above and the doctor’s report, it’s generally a good first step to honestly and critically examine your own lifestyle. Do you eat regularly? Do you take the time to chew your food properly? What are you eating? How many vegetables, whole grains, convenience foods do you put on your plate? Do you go to sports? How is the movement in general?
The WHO recommends that you exercise 150 minutes a week, i.e. at least go for a walk. It’s half an hour five days a week. You should also make sure that about half of each meal consists of vegetables and a third of proteins (eggs, tofu, meat, fish, mushrooms, nuts). The remaining third can be carbohydrates, i.e. potatoes, rice, pasta, bread – but preferably from whole grains, because they contain a lot of fiber that makes the intestines healthy.
Now BMI gives a first indication of whether you are carrying too many kilos. However, you can also check how the fat distribution looks – much more meaningful – by taking measurements: Measure the circumference of your waist and hips. Women should have a waist circumference that does not exceed 80 centimeters, for men anything over 94 centimeters is considered problematic. If men have a waist circumference of more than 102 centimeters or women more than 88 centimeters, they are medically classified as obese.
This is a first indication. Now put your waist and hips in proportion by dividing the waist measurement by the hip measurement. The result should not exceed 0.85 for women and less than 1 for men. In men, a critical look at the neck can also help: if rolls of fat form here, it is an indication of overweight.
Finally, you can relate your waist size to your height and age. Measure your waist and divide the number by your height. Anyone under 40 should not have a value higher than 0.5. After this, the limit increases by 0.01 per years of life – 41-year-olds should therefore not achieve more than 0.51, e.g. For people over 50, the limit is generally 0.6 and should not be exceeded with increasing age.
These calculations make more sense than BMI because they take into account a person’s build. A bodybuilder with a high BMI will do well on the Hip-Waist Index, which is closer to reality. And it’s important to look at how old someone is, because metabolism changes over a lifetime. Only the internal, hidden fat deposits cannot be calculated.
This is where you need to be honest with yourself and review your lifestyle if you don’t want to risk liver damage. Slim people in particular should not feel a false sense of security. | 1,845 | 8,358 | {"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 | 0.930331 |
https://computer_en_ru.academic.ru/1880/arithmetic_element | 1,726,120,124,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651422.16/warc/CC-MAIN-20240912043139-20240912073139-00813.warc.gz | 158,066,135 | 11,785 | # arithmetic element
arithmetic element
арифметический элемент
English-Russian dictionary of computer science and programming. 2013.
### Смотреть что такое "arithmetic element" в других словарях:
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• Finite field arithmetic — Arithmetic in a finite field is different from standard integer arithmetic. There are a limited number of elements in the finite field; all operations performed in the finite field result in an element within that field.While each finite field is … Wikipedia
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• Greek arithmetic, geometry and harmonics: Thales to Plato — Ian Mueller INTRODUCTION: PROCLUS’ HISTORY OF GEOMETRY In a famous passage in Book VII of the Republic starting at Socrates proposes to inquire about the studies (mathēmata) needed to train the young people who will become leaders of the ideal… … History of philosophy
• List of basic arithmetic topics — For a more comprehensive list, see the List of arithmetic topics. Arithmetic is the oldest and simplest branch of mathematics, used by almost everyone. Its tasks range from the simple act of counting to advanced science and business calculations … Wikipedia
### Поделиться ссылкой на выделенное
##### Прямая ссылка:
Нажмите правой клавишей мыши и выберите «Копировать ссылку» | 771 | 3,374 | {"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-2024-38 | latest | en | 0.777281 |
https://community.openai.com/t/puzzle-for-human-user-and-their-chatgpt-3-5/178271 | 1,708,947,051,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947474659.73/warc/CC-MAIN-20240226094435-20240226124435-00868.warc.gz | 195,010,878 | 9,134 | # Puzzle for human user and their ChatGPT-3.5
I need to see if it is possible for humans and their AI Assistant (text-davinci-002-render-sha) to find a solution to this puzzle. I want to try to give as few information as possible but given 6 specific TypeScript types I want the AI to determine the relationship between them and place it in a grid.
I am asking the community to see if it is possible to achieve this task with the lower AI (not using ChatGPT-4) I would love to see the shortest way to get the AI to accomplish the task what makes it impossible for me (unless I give a longer an more detailed prompt) is that the answer require the AI to find relationship on two axes and it seems that the AI is completely unable to achieve this with very simple instructions one of which is to have no empty cells.
At least for you humans it should be evident that if a group of 6 items must be placed into a grid only 4 shapes are possible 1x6, 6x1, 2x3, and 3x2. Then given that the group of 6 type have 2 sets of relationships it implies that the grid now can only be 2x3 or 3x2 keeping in mind that no cell should be empty.
So the complication is that the AI must infer on two orthogonal axes and it requires me so far to make a non trivial prompt. I am curious therefor to see is someone can come out with a really short prompt.
Given 6 TypeScript types that have relationships with one an other, organize the following six types into a table following the instructions:
• Each cell contains exactly one type.
• No cell should be left empty.
• There should be as many cells as there is types no more no less.
• Each type must by used exactly once.
• Each row should outline one type of relationship between each types in that row.
• Each column should outline one type of relationship between each types in that column.
`````` Settled<TVal>
PromiseSettledResult<TVal>
SettledRight<TVal>
PromiseFulfilledResult<TVal>
SettledLeft
PromiseRejectedResult
``````
If anyone can guess what are the relationship and can determine the shortest prompt to get the AI to meet the requirements the prompt above gave me this result I will let you be the juge as if the AI met the requirements (because the AI is not impartial as you can see below):
Column 1 Column 2 Column 3
Row 1 Settled<TVal> PromiseFulfilledResult<TVal> PromiseRejectedResult<TVal>
Row 2 SettledLeft SettledRight<TVal>
Row 3 PromiseSettledResult<TVal>
I like a good challenge So here’s GPT-4’s solution. First the prompt:
``````goal:
Given 6 TypeScript types that have relationships with one an other, organize the following six types into a table.
rules:
- Each cell contains exactly one type.
- No cell should be left empty. Don't fill in cells.
- There should be as many cells as there is types.
- Each type must by used exactly once.
- Each row should outline one type of relationship between each types in that row.
- Each column should outline one type of relationship between each types in that column.
Types:
Settled<TVal>
PromiseSettledResult<TVal>
SettledRight<TVal>
PromiseFulfilledResult<TVal>
SettledLeft
PromiseRejectedResult
steps:
- Identify the types that have a direct inheritance or subtype relationship, and group them together in rows or columns.
- Identify the types that have a union or intersection relationship, and group them together in rows or columns.
- Identify the types that have a generic or parameterized relationship, and group them together in rows or columns.
- Arrange the rows and columns in a way that maximizes the number of relationships that are captured by the table. Show the table.
- How many empty cells are there?
State each step and show your work for performing that step.
1: Identify the types that have a direct inheritance or subtype relationship, and group them together in rows or columns.
``````
And then it’s solution:
``````- We can see that SettledRight<TVal> and SettledLeft are subtypes of Settled<TVal>, as they are defined as follows:
type SettledRight<TVal> = Settled<TVal> & PromiseFulfilledResult<TVal>;
type SettledLeft = Settled<never> & PromiseRejectedResult;
- We can also see that PromiseFulfilledResult<TVal> and PromiseRejectedResult are subtypes of PromiseSettledResult<TVal>, as they are defined as follows:
type PromiseFulfilledResult<T> = {
status: 'fulfilled';
value: T;
};
type PromiseRejectedResult = {
status: 'rejected';
reason: any;
};
type PromiseSettledResult<T> = PromiseFulfilledResult<T> | PromiseRejectedResult;
- Therefore, we can group these types together in rows or columns, such as:
| Settled<TVal> | SettledRight<TVal> | SettledLeft |
| PromiseSettledResult<TVal> | PromiseFulfilledResult<TVal> | PromiseRejectedResult |
2: Identify the types that have a union or intersection relationship, and group them together in rows or columns.
- We can see that SettledRight<TVal> and SettledLeft are defined as intersections of Settled<TVal> and PromiseFulfilledResult<TVal> or PromiseRejectedResult, respectively.
- We can also see that PromiseSettledResult<TVal> is defined as a union of PromiseFulfilledResult<TVal> and PromiseRejectedResult.
- Therefore, we can group these types together in rows or columns, such as:
| Settled<TVal> | SettledRight<TVal> | SettledLeft |
| PromiseSettledResult<TVal> | PromiseFulfilledResult<TVal> | PromiseRejectedResult |
3: Identify the types that have a generic or parameterized relationship, and group them together in rows or columns.
- We can see that Settled<TVal>, SettledRight<TVal>, PromiseSettledResult<TVal>, and PromiseFulfilledResult<TVal> are all generic types that take a type parameter TVal, which represents the value of a fulfilled promise or a settled right.
- Therefore, we can group these types together in rows or columns, such as:
| Settled<TVal> | SettledRight<TVal> | SettledLeft |
| PromiseSettledResult<TVal> | PromiseFulfilledResult<TVal> | PromiseRejectedResult |
4: Arrange the rows and columns in a way that maximizes the number of relationships that are captured by the table. Show the table.
- One possible way to arrange the rows and columns is as follows:
| Settled<TVal> | SettledRight<TVal> | SettledLeft |
| PromiseSettledResult<TVal> | PromiseFulfilledResult<TVal> | PromiseRejectedResult |
- This table captures the following relationships:
- SettledRight<TVal> and SettledLeft are subtypes and intersections of Settled<TVal>.
- PromiseFulfilledResult<TVal> and PromiseRejectedResult are subtypes and unions of PromiseSettledResult<TVal>.
- SettledRight<TVal> and PromiseFulfilledResult<TVal> are subtypes and intersections of PromiseSettledResult<TVal>.
- SettledLeft and PromiseRejectedResult are subtypes and intersections of PromiseSettledResult<TVal>.
- Settled<TVal>, SettledRight<TVal>, PromiseSettledResult<TVal>, and PromiseFulfilledResult<TVal> are generic types that take a type parameter TVal.
5: How many empty cells are there?
- There are no empty cells in the table, as each cell contains exactly one type, and each type is used exactly once.
``````
GPT-4 came up with the plan for solving the puzzle. I just tweaked its plan a bit.
And here’s the solve from `text-davinci-003`:
``````Settled<TVal> | PromiseSettledResult<TVal> | SettledRight<TVal>
---------------------------------------------------------------------
SettledLeft | PromiseFulfilledResult<TVal> | PromiseRejectedResult
2: Identify the types that have a union or intersection relationship, and group them together in rows or columns.
Settled<TVal> | PromiseSettledResult<TVal> | SettledRight<TVal>
---------------------------------------------------------------------
SettledLeft | PromiseFulfilledResult<TVal> | PromiseRejectedResult
3: Identify the types that have a generic or parameterized relationship, and group them together in rows or columns.
Settled<TVal> | PromiseSettledResult<TVal> | SettledRight<TVal>
---------------------------------------------------------------------
SettledLeft | PromiseFulfilledResult<TVal> | PromiseRejectedResult
4: Arrange the rows and columns in a way that maximizes the number of relationships that are captured by the table. Show the table.
Settled<TVal> | SettledRight<TVal> | SettledLeft
---------------------------------------------------
PromiseSettledResult<TVal> | PromiseFulfilledResult<TVal> | PromiseRejectedResult
5: How many empty cells are there?
There are no empty cells.
``````
And as I somewhat suspected `gpt-3.5-turbo` can’t solve at all…
A key observation here is that I had GPT-4 work out the strategy for solving the puzzle and GPT-3 can often execute that plan in a more cost effective way.
I only have access to the ChatGPT-text-davinci-002-render-sha and I have aces to the playground but I wanted to use ChatGPT for that. Also this month I did not pay for the ChatGPT Plus. I would love to find the shortest prompt possible giving the AI (ChatGPT of a lower model) as few information as possible to get the result (but in fact even with a lot of information I have not been able to get exactly what I wanted),
I could have also explained the relationships to my Assistant so that the AI would understand but I got stuck at trying to explain him how to understand by himself and it is why I got into some complexions with complicated prompts to explain how to understand without explaining directly… I did not explained the relation to the types neither in my messages such that either the Human Users infer themselves or something…
I appreciate your input thanks if you have other prompts that you could try on the Turbo or on the text-davinci-002-render models model let me know what is the shortest path to at least get a 6 cell (plus headers maybe) but if you refer to the screenshot I gave clear instructions (in a normal setting I would have probably be giving an example too)… | 2,335 | 9,840 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.546875 | 3 | CC-MAIN-2024-10 | latest | en | 0.949962 |
https://community.fabric.microsoft.com/t5/Desktop/How-to-properly-do-average-as-New-Column/td-p/2365553 | 1,718,504,417,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198861640.68/warc/CC-MAIN-20240616012706-20240616042706-00504.warc.gz | 154,769,587 | 114,186 | cancel
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## How to properly do average as New Column
Hello!
It's me again....lots of questions as I figure this all out.
I have a table full of information about the number of times someone answered the phone, and how many seconds that interaction took. It takes the following form:
DateTime Group Name Number of Calls Total length of calls in seconds 2021-01-01 08:00:00 GroupA 46 1,080 2021-01-01 08:00:00 GroupB 412 7,211 2021-01-01 08:30:00 GroupA 12 300
I first created a new Measure:
``AverageHandleTime = DIVIDE(SUM([Total Length of Calls]),SUM([Number of Calls]),0)``
That works wonderfully...but I just get the number of seconds, and I can't seem to find a way to represent that as a timestamp.
According to a few resources I found online, I have to create a 'Duration' column in my table. I've done that, as structured below:
Date Group Number of Calls Length of Time Average Call Length Duration of Avg Call Length 2021-01-01 08:00 GroupA 46 1,080 (1,080)/(46)=23.47 00:00:23 2021-01-01 08:00 GroupB 412 7,211 17.52 00:00:18
Now, however, if I put the numbers into a column chart, in order to get a "reasonable" number for my Y axis, I have to do an Average (of my Average). This feels wrong.
Is there an easier/better way to do duration that I'm missing? Or a better way to crack this nut?
Thanks!
Josh
1 ACCEPTED SOLUTION
Super User
@jtcm4568 , You should create a measure on top of this measure AverageHandleTime, and use that
time(quotient([AverageHandleTime],3600) , quotient(mod([AverageHandleTime],3600),60), mod(mod([AverageHandleTime],3600),60))
2 REPLIES 2
Super User
@jtcm4568 , You should create a measure on top of this measure AverageHandleTime, and use that
time(quotient([AverageHandleTime],3600) , quotient(mod([AverageHandleTime],3600),60), mod(mod([AverageHandleTime],3600),60))
Helper I
This was brilliant, and for some reason, this kind of solution came up in exactly zero of my searched for how to figure out duration as a measure. Thank you!
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https://indoxxiid.com/qa/question-how-many-4p-electrons-are-in-as.html | 1,623,671,839,000,000,000 | text/html | crawl-data/CC-MAIN-2021-25/segments/1623487612154.24/warc/CC-MAIN-20210614105241-20210614135241-00628.warc.gz | 297,972,452 | 7,701 | # Question: How Many 4p Electrons Are In As?
## How many electrons can 4s hold?
2 electronsAny orbital can have only 2 electrons.
So 4s orbital can hold only 2 electrons at the maximum (of course with opposite spins).
In every s- shell there are only one orbital..
## Why is 3rd shell 8 or 18?
The third shell of an atom has 18 electrons only not 8 electrons. You might be confused because first the electrons of 4s are filled and then the 10 electrons of 3d shells are filled. They are filled because of the n-l rule. … So after filling the 3s and 3p subshell with 8 electrons, the next shell to fill is the 4s one.
## How many nodes are in 4s orbital?
3 nodesThe ns orbital has (n-1) radial nodes, so the 4s-orbital has (4-1) = 3 nodes, as shown in the above plot.
## How many 4p electrons are in GE?
Atomic NumberSymbolValence Electrons31Ga4s2p132Ge4s2p233As4s2p334Se4s2p42 more rows
## How many orbitals are in the 4p sublevel?
In every p sublevel, there are 3 orbitals.
## Why does arsenic have 5 valence electrons?
Arsenic is in group 15, so its atoms have 5 valence electrons. … The highest energy (outermost) s and p sublevels, also called the valence shell, contain the valence electrons. Arsenic has atomic number 33. This means arsenic atoms have 33 protons and, if neutral, 33 electrons.
## Why is 3d higher energy than 4s?
We say that the 4s orbitals have a lower energy than the 3d, and so the 4s orbitals are filled first. … The electrons lost first will come from the highest energy level, furthest from the influence of the nucleus. So the 4s orbital must have a higher energy than the 3d orbitals.
## What has 33 protons and 42 neutrons?
Name ArsenicNameArsenicAtomic Mass74.9216 atomic mass unitsNumber of Protons33Number of Neutrons42Number of Electrons339 more rows
## What is the atomic mass of arsenic?
33Arsenic/Atomic number
## How many 4p electrons are in arsenic?
Arsenic has 5 valence electrons. It’s electron configuration is 1s2 2s2 2p6 3s2 3p6 3d10 4s2 4p3 . It’s outermost shell (4s and 4p) has 5 electrons, these are the valence electrons.
## How many orbitals are in 1s?
one orbitalAt the first level there is only one orbital – the 1s orbital. At the second level there are four orbitals – the 2s, 2px, 2py and 2pz orbitals. Each orbital can hold either 1 or 2 electrons, but no more.
## Which sublevel has the highest energy?
Number of electrons per sublevelEnergy LevelSublevelsMaximum Number of Electrons per Energy Level1s22s8p3s186 more rows
## How many electrons can 5f hold?
Each shell can contain only a fixed number of electrons: The first shell can hold up to two electrons, the second shell can hold up to eight (2 + 6) electrons, the third shell can hold up to 18 (2 + 6 + 10) and so on….How many electrons can 4f hold?Principal Energy Level (n)sublevelselectrons55s 5p 5d 5f 5g2 + 6 + 10 + 14 + 183 more rows•May 3, 2020
## What is the most common ion of arsenic?
Arsenic has two common oxidation states: +5, the predominant one, and the less thermodynamically stable +3.
## What is the electron configuration of mg2+?
Therefore the Magnesium electron configuration will be 1s22s22p63s2. Furthermore, what does mg2+ represent? Mg2+ is a Mg atom that now has the same number of electrons as a noble gas. | 943 | 3,282 | {"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} | 3.265625 | 3 | CC-MAIN-2021-25 | latest | en | 0.873545 |
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Code Recursion
# Reverse a number using recursion
In this article, we will explore the concept of reversing a number using recursion. Reversing a number means changing the order of its digits from left to right. For example, reversing the number 12345 would result in 54321. We will discuss the problem statement, provide an explanation with suitable examples, present the pseudocode and algorithm for the recursive solution, and finally, provide an explanation of the resultant output with the time complexity of the code.
## Problem Statement
The problem is to write a recursive function that takes an integer as input and returns its reverse as output. If the input number is positive, the function should reverse its digits and return the new number. If the input number is negative, the function should reverse its absolute value and then return the new number with a negative sign.
## Explanation with Suitable Example
Let's take the number 12345 as an example. To reverse this number using recursion, we follow these steps:
1. Extract the last digit of the number: 12345 % 10 = 5
2. Recur with the remaining digits: reverse_num(1234, 5)
3. Extract the last digit of the remaining number: 1234 % 10 = 4
4. Recur with the remaining digits: reverse_num(123, 54)
5. Repeat this process until no digits are left: reverse_num(1, 5432)
Now, the base condition is reached since 1 is less than or equal to 0. So, we return the result, which is 54321.
## Pseudocode and Algorithm
The recursive function `reverse_num(number, result)` takes two parameters: `number` (the remaining digits) and `result` (the reversed number obtained so far).
The algorithm can be represented using standard pseudocode as follows:
``````function reverse_num(number, result):
if number > 0:
return reverse_num(number / 10, result * 10 + (number % 10))
return result
function reverse(number):
if number < 0:
return -reverse_num(-number, 0)
else:
return reverse_num(number, 0)
``````
## Explanation of the Algorithm
1. The `reverse_num` function takes two arguments: `number` and `result`. If the `number` is greater than 0, it means there are still digits left to process.
2. In each recursive call, the last digit of the `number` is extracted using `(number % 10)` and added to the reversed result `result * 10`.
3. The function is called recursively with the remaining digits obtained by dividing the number by 10 (`number / 10`).
4. This process continues until there are no digits left (`number <= 0`), at which point the result is returned.
5. The `reverse` function first checks if the input number is negative. If so, it calls `reverse_num` with the absolute value of the number and then returns the result with a negative sign.
6. If the input number is positive, the `reverse` function directly calls `reverse_num` with the input number.
## Resultant Output Explanation
Let's consider the provided test cases:
1. For the number 12345:
• Before reversing, the number is displayed as [12345].
• After reversing, the output is [54321].
2. For the number 78942:
• Before reversing, the number is displayed as [78942].
• After reversing, the output is [24987].
3. For the number 1020:
• Before reversing, the number is displayed as [1020].
• After reversing, the output is [201].
4. For the number -28:
• Before reversing, the number is displayed as [-28].
• After reversing, the output is [-82].
## Time Complexity of the Code
The time complexity of the code is O(log N), where N is the input number. In each recursion, the input number is divided by 10 until it becomes 0. The number of recursive calls depends on the number of digits in the input number, which is logarithmic with respect to the input number. Hence, the time complexity is logarithmic.
## Comment
Please share your knowledge to improve code and content standard. Also submit your doubts, and test case. We improve by your feedback. We will try to resolve your query as soon as possible.
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## Learning Objectives
After studying this chapter, you will be able to :
• Explain the meaning, objectives and limitations of analysis using accounting ratios;
• Identify the various types of ratios commonly used ;
• Calculate various ratios to assess solvency, liquidity, efficiency and profitability of the firm;
• Interpret the various ratios calculated for intra-firm and inter-firm comparisons.
Financial statements aim at providing financial information about a business enterprise to meet the information needs of the decision-makers. Financial statements prepared by a business enterprise in the corporate sector are published and are available to the decision-makers. These statements provide financial data which require analysis, comparison and interpretation for taking decision by the external as well as internal users of accounting information. This act is termed as financial statement analysis. It is regarded as an integral and important part of accounting. As indicated in the previous chapter, the most commonly used techniques of financial statements analysis are comparative statements, common size statements, trend analysis, accounting ratios and cash flow analysis. The first three have been discussed in detail in the previous chapter. This chapter covers the technique of accounting ratios for analysing the information contained in financial statements for assessing the solvency, efficiency and profitability of the enterprises.
### 5.1 Meaning of Accounting Ratios
As stated earlier, accounting ratios are an important tool of financial statement analysis. A ratio is a mathematical number calculated as a reference to relationship of two or more numbers and can be expressed as a fraction, proportion, percentage, and a number of times. When the number is calculated by referring to two accounting numbers derived from the financial statements, it is termed as accounting ratio. For example if the gross profit of the business is Rs. 10,000 and the sales are Rs. 1,00,000, it can be said that the gross profit is 10% (10,000/1,00,000) x 100 of the ‘Revenue from Operations. This ratio is termed as gross profit ratio. Similarly, inventory turnover ratio may be 6 which implies that inventory turns into ‘Revenue from Operations’ six times in a year.
It needs to be observed that accounting ratios exhibit relationship, if any between accounting numbers extracted from financial statements, they are essentially derived numbers and their efficacy depends a great deal upon the basic numbers from which they are calculated. Hence, if the financial statements contain some errors, the derived numbers in terms of ratio analysis would also present an erroneous scenerio. Further, a ratio must be calculated using numbers which are meaningfully correlated. A ratio calculated by using two unrelated numbers would hardly serve any purpose. For example, the furniture of the business is Rs. 1,00,000 and Purchases are Rs. 3,00,000. The ratio of purchases to furniture is 3 (3,00,000/1,00,000) but it hardly has any relevance. The reason is that there is no relationship between these two aspects.
### 5.2 Objectives of Ratio Analysis
Ratio analysis is indispensable part of interpretation of results revealed by the financial statements. It provides users with crucial financial information and points out the areas which require investigation. Ratio analysis is a technique. Which involves regrouping of data by application of arithmetical relationships, though its interpretation is a complex matter. It requires a fine understanding of the way and the rules used for preparing financial statements. Once done effectively, it provides a wealth of information which helps the analyst:
1. To know the areas of the business which need more attention;
2. To know about the potential areas which can be improved with the effort in the desired direction;
3. To provide a deeper analysis of the profitability, liquidity, solvency and efficiency levels in the business;
4. To provide information for making cross sectional analysis by comparing the performance with the best industry standards;
5. To provide information derived from financial statements useful for making projections and estimates for the future.
### 5.3 Advantages of Ratio Analysis
The ratio analysis if properly done improves the user’s understanding of the efficiency with which the business is being conducted. The numerical relationships throw light on many latent aspects of the business. If properly analysed, the ratios make us understand various problem areas as well as the bright spots of the business. The knowledge of problem areas help management take care of them in future. The knowledge of areas which are working better helps you improve the situation further. It must be emphasised that ratios are means to an end rather than the end in themselves. Their role is essentially indicative and that of a whistle blower. There are many advantages derived from the ratio analysis. These are summarised as follows:
1. Helps understand efficacy of decisions: The ratio analysis helps you understand whether the business firm has taken the right kind of operating, investing and financing decisions. It indicates how far they have helped in improving the performance.
2. Simplify complex figures and establish relationships: Ratios help in simplifying the complex accounting figures and bring out their relationships. They help summarise the financial information effectively and assess the managerial efficiency, firm’s credit worthiness, earning capacity, etc.
3. Helpful in comparative analysis: The ratios are not be calculated for one year only. When many year figures are kept side by side, they help a great deal in exploring the trends visible in the business. The knowledge of trend helps in making projections about the business which is a very useful feature.
4. Identification of problem areas: Ratios help business in identifying the problem areas as well as the bright areas of the business. Problem areas would need more attention and bright areas will need polishing to have still better results.
5. Enables SWOT analysis: Ratios help a great deal in explaining the changes occurring in the business. The information of change helps the management a great deal in understanding the current threats and opportunities and allows business to do its own SWOT (Strength-Weakness-Opportunity-Threat) analysis.
6. Various comparisons: Ratios help comparisons with certain bench marks to assess as to whether firm, performance is better or otherwise. For this purpose, the profitability, liquidity, solvency, etc. of a business may be compared: (i) over a number of accounting periods with itself (Intra-firm Comparison/Time Series Analysis), (ii) with other business enterprises (Inter-firm Comparison/Cross-sectional Analysis), and (iii) with standards set for that firm/industry (comparison with standard (or industry) expectations).
### 5.4 Limitations of Ratio Analysis
Since the ratios are derived from the financial statements, any weakness in the original financial statements will also creep in the derived analysis in the form of ratio analysis. Thus, the limitations of financial statements also form the limitations of the ratio analysis. Hence, to interpret the ratios, the user should be aware of the rules followed in the preparation of financial statements and also their nature and limitations. The limitations of ratio analysis which arise primarily from the nature of financial statements are as under:
1. Limitations of Accounting Data: Accounting data give an unwar-ranted impression of precision and finality. In fact, accounting data “reflect a combination of recorded facts, accounting conventions and personal judgements and the judgements and conventions applied affect them materially. For example, profit of the business is not a precise and final figure. It is merely an opinion of the accountant based on application of accounting policies. The soundness of the judgement necessarily depends on the competence and integrity of those who make them and on their adherence to Generally Accepted Accounting Principles and Conventions”. Thus, the financial statements may not reveal the true state of affairs and so the ratios will also not give the true picture.
2. Ignores Price-level Changes: The financial accounting is based on stable money measurement principle. It implicitly assumes that price level changes are either non-existent or minimal. But the truth is otherwise. We are normally living in inflationary economies where the power of money declines constantly. A change in the price level makes analysis of financial statement of different accounting years meaningless because accounting records ignore changes in value of money.
3. Ignore Qualitative or Non-monetary Aspects: Accounting provides information about quantitative (or monetary) aspects of business. Hence, the ratios also reflect only the monetary aspects, ignoring completely the non-monetary (qualitative) factors.
4. Variations in Accounting Practices: There are differing accounting policies for valuation of stock, calculation of depreciation, treatment of intangibles, definition of certain financial variables, etc. available for various aspects of business transactions. These variations leave a big question mark on the cross sectional analysis. As there are variations in accounting practices followed by different business enterprises, a valid comparison of their financial statements is not possible.
5. Forecasting: Forecasting of future trends based only on historical analysis is not feasible. Proper forecasting requires consideration of non-financial factors as well.
Now let us talk about the limitations of the ratios. The various limitations are:
1. Means and not the End: Ratios are means to an end rather than the end by itself.
2. Lack of ability to resolve problems: Their role is essentially indicative and of whistle blowing and not providing a solution to the problem.
3. Lack of standardised definitions: There is a lack of standardised definitions of various concepts used in ratio analysis. For example, there is no standard definition of liquid liabilities. Normally, it includes all current liabilities, but sometimes it refers to current liabilities less bank overdraft.
4. Lack of universally accepted standard levels: There is no universal yardstick which specifies the level of ideal ratios. There is no standard list of the levels universally acceptable, and, in India, the industry averages are also not available.
5. Ratios based on unrelated figures: A ratio calculated for unrelated figures would essentially be a meaningless exercise. For example, creditors of Rs. 1,00,000 and furniture of Rs. 1,00,000 represent a ratio of 1:1. But it has no relevance to assess efficiency or solvency.
Hence, ratios should be used with due consciousness of their limitations while evaluatory the performance of an organisation and planning the future strategies for its improvement.
### Test your Understanding – I
1. State which of the following statements are True or False.
(a) The only purpose of financial reporting is to keep the managers informed about the progress of operations.
(b) Analyses of data provided in the financial statements as is termed as financial analysis
(c) Long-term creditors are concerned about the ability of a firm to discharge its obligations to pay interest and repay the principal amount of term.
(d) A ratio is always expressed as a quotient of one number divided by another.
(e) Ratios help in comparisons of a firm’s results over a number of accounting periods as well as with other business enterprises.
(f) A ratios reflect both quantitative and qualitative aspects of results.
### 5.5 Types of Ratios
There is a two way classification of ratios: (1) traditional classification, and (2) functional classification. The traditional classification has been on the basis of financial statements to which the determinants of ratios belong. On this basis the ratios are classified as follows:
1. ‘Statement of Profit and Loss Ratios: A ratio of two variables from the statement of profit and loss is known as statement of profit and loss ratio. For example, ratio of gross profit to revenue from operations is known as gross profit ratio. It is calculated using both figures from the statement of profit and loss.
2. Balance Sheet Ratios: In case both variables are from balance sheet, it is classified as Balance Sheet Ratios. For example, ratio of current assets to current liabilities known as current ratio is calculated using both figures from balance sheet.
3. Composite Ratios: If a ratio is computed with one variable from the statement of profit and loss and another variable from the balance sheet, it is called composite ratio. For example, ratio of credit revenue from operations to trade receivables (known as trade receivables turnover ratio) is calculated using one figure from the statement of profit and loss (credit revenue from operations) and another figure (trade receivables) from the balance sheet.
Although accounting ratios are calculated by taking data from financial statements but classification of ratios on the basis of financial statements is rarely used in practice. It must be recalled that basic purpose of accounting is to throw useful light on the financial performance (profitability) and financial position (its capacity to raise money and invest them wisely) as well as changes occurring in financial position (possible explanation of changes in the activity level). As such, the alternative classification (functional classification) based on the purpose for which a ratio is computed, is the most commonly used classification which reach as follows:
1. Liquidity Ratios: To meet its commitments, business needs liquid funds. The ability of the business to pay the amount due to stakeholders as and when it is due is known as liquidity, and the ratios calculated to measure it are known as ‘Liquidity Ratios’. They are essentially short-term in nature.
2. Solvency Ratios: Solvency of business is determined by its ability to meet its contractual obligations towards stakeholders, particularly towards external stakeholders, and the ratios calculated to measure solvency position are known as ‘Solvency Ratios’. They are essentially long-term in nature.
3. Activity (or Turnover) Ratios: This refers to the ratios that are calculated for measuring the efficiency of operation of business based on effective utilisation of resources. Hence, these are also known as ‘Efficiency Ratios’.
4. Profitability Ratios: It refers to the analysis of profits in relation to sales or funds (or assets) employed in the business and the ratios calculated to meet this objective are known as ‘Profitability Ratios’.
### 5.6 Liquidity Ratios
Liquidity ratios are calculated to have indications about the short term solvency of the business, i.e. the firm’s ability to meet its current obligations. These are analysed by looking at the amounts of current assets and current liabilities in the balance sheet. The two ratios included in this category are Current Ratio and Liquid Ratio.
### 5.6.1 Current Ratio
Current ratio is the proportion of current assets to current liabilities. It is expressed as follows:
Current Ratio = Current Assets : Current Liabilities or
Current assets include current investments, inventories, trade receivables (debtors and bills receivables), cash and cash equivalents, short-term loans and advances and other current assets such as prepaid expenses, advance tax and accrued income, etc.
Current liabilities include short-term borrowings, trade payables (creditors and bills payables), other current liabilities and short-term provisions.
### Illustration 1
Calculate Current ratio from the following information:
Significance: It provides a measure of degree to which current assets cover current liabilities. The excess of current assets over current liabilities provides a measure of safety margin available against uncertainty in realisation of current assets and flow of funds. The ratio should be reasonable. It should neither be very high or very low. Both the situations have their inherent disadvantages. A very high current ratio implies heavy investment in current assets which is not a good sign as it reflects under utilisation or improper utilisation of resources. A low ratio endangers the business and puts it at risk of facing a situation where it will not be able to pay its short-term debt on time. If this problem persists, it may affect firm’s credit worthiness adversely. Normally, it is safe to have this ratio within the range of 2:1.
### 5.6.2 Quick Ratio
It is the ratio of quick (or liquid) asset to current liabilities. It is expressed as
Quick ratio = Quick Assets : Current Liabilities or
The quick assets are defined as those assets which are quickly convertible into cash. While calculating quick assets we exclude the closing stock and prepaid expenses from the current assets. Because of exclusion of non-liquid current asset, it is considered better than current ratio as a measure of liquidity position of the business. It is calculated to serve as a supplementary check on liquidity position of the business and is therefore, also known as ‘Acid-Test Ratio’.
### Illustration 2
Calculate quick ratio from the information given in illustration 1.
## Solution
Significance: The ratio provides a measure of the capacity of the business to meet its short-term obligations without any flaw. Normally it is advocated to be safe to have a ratio of 1:1 as unnecessarily low ratio will be very risky and a high ratio suggests unnecessarily deployment of resources in otherwise less profitable short-term investments.
### Illustration 3
Calculate ‘Liquidity Ratio’ from the following information:
Current liabilities = Rs. 50,000
Current assets = Rs. 80,000
Inventories = Rs. 20,000
Advance tax = Rs. 5,000
Prepaid expenses = Rs. 5,000
## Solution
### Illustration 4
X Ltd. has a current ratio of 3.5:1 and quick ratio of 2:1. If excess of current assets over quick assets represented by stock is Rs. 24,000, calculate current assets and current liabilities.
## Solution
Current Ratio = 3.5:1
Quick Ratio = 2:1
Let Current Liabilities = x
Current Assets = 3.5x
And Quick Assets = 2x
Stock = Current Assets – Quick Assets
24,000 = 3.5x – 2x
24,000 = 1.5x
x = Rs.16,000
Current Assets = 3.5x = 3.5 × Rs. 16,000 = Rs. 56,000.
Verification : Current Ratio = Current Assets : Current Liabilities
= Rs. 56,000 : Rs. 16,000 = 3.5 : 1
Quick Ratio = Quick Assets – Current Liabilities = Rs. 32,000 : Rs. 16,000 = 2:1
### Illustration 5
Calculate the current ratio from the following information :
Total assets = Rs. 3,00,000
Non-current liabilities = Rs. 80,000
Shareholders’ Funds = Rs. 2,00,000
Non-Current Assets:
Fixed assets = Rs. 1,60,000
Non-current Investments = Rs. 1,00,000
## Solution
Total assets = Non-current assets + Current assets
Rs. 3,00,000 = Rs. 2,60,000 + Current assets
Current assets = Rs. 3,00,000 – Rs. 2,60,000 = Rs. 40,000
Total assets = Equity and Liabilities
= Shareholders’ Funds + Non-current liabilities +
Current liabilities
Rs. 3,00,000 = Rs. 2,00,000 + Rs. 80,000 + Current Liabilities
Current liabilities = Rs. 3,00,000 – Rs. 2,80,000
= Rs. 20,000
Current Ratio =
Current Assets/Current Liabilities
=Rs. 40,000/Rs. 20,000 = 2 :1
## Do it Yourself
1. Current liabilities of a company are Rs. 5,60,000, current ratio is 5:2 and quick ratio is 2:1. Find the value of the stock.
2. Current ratio = 4.5:1, quick ratio = 3:1.Inventory is Rs. 36,000. Calculate the current assets and current liabilities.
3. Current assets of a company are Rs. 5,00,000. Current ratio is 2.5:1 and quick ratio is 1:1. Calculate the value of current liabilities, liquid assets and inventories.
Illustration 6
The current ratio is 2:1. State giving reasons which of the following transactions would improve, reduce and not change the current ratio:
(a) Repayment of current liability;
(b) Purchased goods on credit;
(c) Sale of an office typewriter (Book value – Rs. 4,000) for Rs. 3,000 only;
(d) Sale of merchandise (goods) costing Rs. 10,000 for Rs. 11,000;
(e) Payment of dividend.
## Solution
The given current ratio is 2 : 1. Let us assume that current assets are Rs. 50,000 and current liabilities are Rs. 25,000; and so the current ratio is 2:1. Now we will analyse the effect of given transactions on current ratio.
(a) Assume that Rs. 10,000 of creditors is paid by cheque. This will reduce the current assets to Rs. 40,000 and current liabilities to Rs. 15,000. The new ratio will be 2.67 : 1(Rs. 40,000/Rs.15,000). Hence, it has improved.
(b) Assume that Rs. 10,000 goods are purchased on credit. This will increase the current assets to Rs. 60,000 and current liabilities to Rs. 35,000. The new ratio will be 1.7:1(Rs. 60,000/Rs. 35,000). Hence, it has reduced.
(c) Due to sale of a typewriter (a fixed asset) the current assets will increase upto Rs. 53,000 without any change in the current liability. The new ratio will be 2.12:1(Rs. 53,000/Rs. 25,000). Hence, it has improved.
(d) This transaction will decrease the stock by Rs. 10,000 and increase the cash by Rs. 11,000 thereby increasing the current assets by Rs. 1,000 without and change in the current liability. The new ratio will be 2.04:1 (Rs. 51,000/Rs. 25,000). Hence, it has improved.
(e) Assume that Rs 5,000 is given by way of dividend. It will reduce the current assets to ₹45,000 and short-term provisions (current liabilities) by Rs 5,000. The new ratio will be 2:25:1 (Rs 45,000/Rs 20,000). Hence, it has improved.
### 5.7 Solvency Ratios
The persons who have advanced money to the business on long-term basis are interested in safety of their payment of interest periodically as well as the repayment of principal amount at the end of the loan period. Solvency ratios are calculated to determine the ability of the business to service its debt in the long run. The following ratios are normally computed for evaluating solvency of the business.
1. Debt equity ratio;
2. Debt ratio;
3. Proprietary ratio;
4. Total Assets to Debt Ratio;
5. Interest Coverage Ratio.
### 5.7.1 Debt-Equity Ratio
Debt Equity Ratio measures the relationship between long-term debt and equity. If debt component of the total long-term funds employed is small, outsiders feel more secure. From security point of view, capital structure with less debt and more equity is considered favourable as it reduces the chances of bankruptcy. Normally, it is considered to be safe if debt equity ratio is 2:1. It is computed as follows:
Debt-Equity ratio = Long-term Debts/Shareholders' Funds
where:
Shareholders’ Funds (Equity) = Share capital + Reserves and Surplus +
Money received against share warrants
Share Capital = Equity share capital + Preference share capital
or
Shareholders’ Funds (Equity) = Non-current sssets + Working capital –
Non-current liabilities
Working Capital = Current Assets – Current Liabilities
Significance: This ratio measures the degree of indebtedness of an enterprise and gives an idea to the long-term lender regarding extent of security of the debt. As indicated earlier, a low debt equity ratio reflects more security. A high ratio, on the other hand, is considered risky as it may put the firm into difficulty in meeting its obligations to outsiders. However, from the perspective of the owners, greater use of debt trading on equity may help in ensuring higher. returns for them if the rate of earnings on capital employed is higher than the rate of interest payable.
### Illustration 7
From the following balance sheet of ABC Co. Ltd. as on March 31, 2015. Calculate debt equity ratio:
### 5.7.2 Debt to Capital Employed Ratio
The Debt Ratio refers to the ratio of long-term debt to the total of external and internal funds (capital employed or net assets). It is computed as follows:
Debt to Capital Employed Ratio = Long-term Debt/Capital Employed (or Net Assets)
Capital employed is equal to the long-term debt + shareholders’ funds. Alternatively, it may be taken as net assets which are equal to the total assets – current liabilities taking the data of Illustration 7, capital employed shall work out to Rs. 5,00,000 + Rs. 15,00,000 = Rs. 20,00,000. Similarly, Net Assets as Rs. 25,00,000 – Rs. 5,00,000 = Rs. 20,00,000 and the Debt to capital employed ratio as Rs. 5,00,000/Rs. 20,00,000 = 0.25:1.
Significance : Like debt equity ratio, it shows proportion of long-term debt in capital employed. Low ratio provides security to creditors and high ratio helps management in trading on equity. In the above case, the debt ratio is less than half which indicates reasonable funding by debt and adequate security of debt.
It may be noted that Debt Ratio can also be computed in relation to total assets. In that case, it usually refers to the ratio of total debt (long-term debt + current liabilities) to total assets, i.e. total of fixed and current assets (or shareholders funds + long-term debt + current liabilities), and is expressed as
### 5.7.3 Proprietary Ratio
Proprietary ratio expresses relationship of proprietor’s (shareholders) funds to net assets and is calculated as follows :
Proprietary Ratio = Shareholders' Funds/Capital employed (or net assets)
Based on data of Illustration 7, it shall be worked out as follows:
Rs. 15,00,000/Rs. 20,00,000 = 0.75 : 1
Significance: Higher proportion of shareholders funds in financing the assets is a positive feature as it provides security to creditors. This ratio can also be computed in relation to total assets instead of net assets (capital employed). It may be noted that the total of debt to capital employed ratio and proprietory ratio is equal to 1. Take these ratios worked out on the basis of data of Illustration 7, the debt to Capital Employed ratio is 0.25 : 1 and the Proprietory Ratio 0.75 : 1 the total is 0.25 + 0.75 = 1. In terms of percentage it can be stated that the 25% of the capital employed is funded by debts and 75% by owners’ funds.
### 5.7.4 Total Assets to Debt Ratio
This ratio measures the extent of the coverage of long-term debts by assets. It is calculated as
Total assets to Debt Ratio = Total assets/Long-term debts
Taking the data of Illustration 8, this ratio will be worked out as follows:
Rs. 14,00,000/Rs. 1,50,000 = 9.33 : 1
The higher ratio indicates that assets have been mainly financed by owners funds and the long-term loans is adequately covered by assets.
It is better to take the net assets (capital employed) instead of total assets for computing this ratio also. It is observed that in that case, the ratio is the reciprocal of the debt to capital employed ratio.
Significance: This ratio primarily indicates the rate of external funds in financing the assets and the extent of coverage of their debts are covered by assets.
### Illustration 9
From the following information, calculate Debt Equity Ratio, Total Assets to Debt Ratio, Proprietory Ratio, and Debt to Capital Employed Ratio:
### Illustration 10
The debt equity ratio of X Ltd. is 0.5 : 1. Which of the following would increase/ decrease or not change the debt equity ratio?
(i) Further issue of equity shares
(ii) Cash received from debtors
(iii) Sale of goods on cash basis
(iv) Redemption of debentures
(v) Purchase of goods on credit.
## Solution
The change in the ratio depends upon the original ratio. Let us assume that external funds are Rs. 5,00,000 and internal funds are Rs. 10,00,000. Now we will analyse the effect of given transactions on debt equity ratio.
(i) Assume that Rs. 1,00,000 worth of equity shares are issued. This will increase the internal funds to Rs. 11,00,000. The new ratio will be 0.45 : 1 (5,00,000/11,00,000). Thus, it is clear that further issue of equity shares decreases the debt-equity ratio.
(ii) Cash received from debtors will leave the internal and external funds unchanged as this will only affect the composition of current assets. Hence, the debt-equity ratio will remain unchanged.
(iii) This will also leave the ratio unchanged as sale of goods on cash basis neither affect Debt nor equity.
(iv) Assume that Rs. 1,00,000 debentures are redeemed. This will decrease the long-term debt to Rs. 4,00,000. The new ratio will be 0.4 : 1 (4,00,000/10,00,000). Redemption of debentures will decrease the debit-equity ratio.
(v) This will also leave the ratio unchanged as purchase of goods on credit neither affect Debt nor equity.
### 5.7.5 Interest Coverage Ratio
It is a ratio which deals with the servicing of interest on loan. It is a measure of security of interest payable on long-term debt. It expresses the relationship between profits available for payment of interest and the amount of interest payable. It is calculated as follows:
Interest Coverage Ratio = Net Profit before Interest and Tax / Interest on long term debt
Significance:It reveals the number of times interest on long-term debts is covered by the profits available for interest. A higher ratio ensures safety of interest on debts.
### Illustration 11
From the following details, calculate interest coverage ratio:
Net Profit after tax Rs. 60,000; 15% Long-term Debt 10,00,000; and Tax Rate 40%.
## Solution
Net Profit after Tax = Rs. 60,000
Tax Rate = 40%
Net Profit before tax = Net profit after tax*100/(100 – Tax rate) = Rs. 60,000 x 100/(100 – 40) = Rs. 1,00,000
Interest on Long Term Debt = 15% of Rs. 10,00,000 = Rs. 1,50,000
Net profit before interest and tax = Net profit before tax + Interest = Rs. 1,00,000 + Rs. 1,50,000 = Rs. 2,50,000
Interest Coverage Ratio = Net Profit before Interest and Tax/Interest on long term debt = Rs. 2,50,000/Rs. 1,50,000 = 1.67 times.
### 5.8 Activity (or Turnover) Ratios
These ratios indicate the speed at which, activities of the business are being performed. The activity ratios express the number of times assets employed, or, for that matter, any constituent of assets, is turned into sales during an accounting period. Higher turnover ratio means better utilisation of assets and signifies improved efficiency and profitability, and as such are known as efficiency ratios. The important activity ratios calculated under this category are
1. Inventory Turnover;
2. Trade receivable Turnover;
3. Trade payable Turnover;
4. Investment (Net assets) Turnover
5. Fixed assets Turnover; and
6. Working capital Turnover.
### 5.8.1 Inventory Turnover Ratio
It determines the number of times inventory is converted into revenue from operations during the accounting period under consideration. It expresses the relationship between the cost of revenue from operations and average inventory. The formula for its calculation is as follows:
Inventory Turnover Ratio = Cost of Revenue from Operations / Average Inventory
Where average inventory refers to arithmetic average of opening and closing inventory, and the cost of revenue from operations means revenue from operations less gross profit.
Significance : It studies the frequency of conversion of inventory of finished goods into revenue from operations. It is also a measure of liquidity. It determines how many times inventory is purchased or replaced during a year. Low turnover of inventory may be due to bad buying, obsolete inventory, etc., and is a danger signal. High turnover is good but it must be carefully interpreted as it may be due to buying in small lots or selling quickly at low margin to realise cash. Thus, it throws light on utilisation of inventory of goods.
### Test your Understanding – II
(i) The following groups of ratios primarily measure risk
A. liquidity, activity, and profitability
B. liquidity, activity, and common stock
C. liquidity, activity, and debt
D. activity, debt and profitability
(ii) The _________ ratios are primarily measures of return.
A. liquidity
B. activity
C. debt
D. profitability
(iii) The _________ of a business firm is measured by its ability to satisfy its short-term obligations as they come due.
A. activity
B. liquidity
C. debt
D. profitability
(iv) _________ ratios are a measure of the speed with which various accounts are converted into sales or cash.
A. Activity
B. Liquidity
C. Debt
D. Profitability
(v) The two basic measures of liquidity are
A. inventory turnover and current ratio
B. current ratio and liquid ratio
C. gross profit margin and operating ratio
D. current ratio and average collection period
(vi) The _________ is a measure of liquidity which excludes _______, generally the least liquid asset.
A. current ratio, accounts debtors
B. liquid ratio, accounts debtors
C. current ratio, inventory
D. liquid ratio, inventory
### Illustration 12
From the following information, calculate stock turnover ratio :
Inventory in the beginning = 18,000
Inventory at the end = 22,000
Net purchases = 46,000
Wages = 14,000
Revenue from operations = 80,000
Carriage inwards = 4,000
## Solution:
Inventory Turnover Ratio =
Cost of Revenue from Operations/Average Inventory
Cost of Revenue from Operations = Inventory in the beginning + Net
Purchases + Wages + Carriage inwards
– Inventory at the end
= Rs. 18,000 + Rs. 46,000 + Rs. 14,000
+ Rs. 4,000 – Rs. 22,000
= Rs. 60,000
Average Inventory =
Inventory in the beginning + Inventory at the end/2
=Rs. 18,000 + Rs. 22,000/2
= Rs. 20,000
Inventory Turnover Ratio =Rs. 60,000/Rs. 20,000= 3 Times
### Illustration 13
From the following information, calculate inventory turnover ratio:
Rs.
Revenue from operations = 4,00,000
Average Inventory = 55,000
Gross Profit Ratio = 10%
## Solution
Revenue from operations = Rs. 4,00,000
Gross Profit = 10% of Rs. 4,00,000 = Rs. 40,000
Cost of Revenue from operations = Revenue from operations – Gross Profit
= Rs. 4,00,000 – Rs. 40,000 = Rs. 3,60,000
Inventory Turnover Ratio =
Cost of Revenue from Operations/Average Inventory
= Rs. 3,60,000/Rs. 55,000
= 6.55 times
### Illustration 14
A trader carries an average stock of Rs. 40,000. His stock turnover is 8 times. If he sells goods at profit of 20% on sales. Find out the profit.
## Solution
Inventory Turnover Ratio =Cost of Revenue from Operations/Average Inventory
8 =Cost of Revenue from Operations/Rs. 40,000
Cost of Revenue from operations = 8 × Rs. 40,000
= Rs. 3,20,000
Revenue from operations = Cost of Revenue from operations ×100/80
= Rs. 3,20,000 ×100/80
= Rs. 4,00,000
Gross Profit = Revenue from operations – Cost of Revenue from operations
= Rs. 4,00,000 – Rs. 3,20,000 = Rs. 80,000
## Do it Yourself
1. Calculate the amount of gross profit:
Average inventory = Rs. 80,000
Inventory turnover ratio = 6 times
Selling price = 25% above cost
2. Calculate Inventory Turnover Ratio:
Annual Revenue from operations = Rs. 2,00,000
Gross Profit = 20% on cost of Revenue from operations
Inventory in the beginning = Rs. 38,500
Inventory at the end = Rs. 41,500
### 5.8.2 Trade Receivables Turnover Ratio
It expresses the relationship between credit revenue from operations and trade receivable. It is calculated as follows :
Trade Receivable Turnover ratio = Net Credit Revenue from Operations/Average Trade Receivable
Where Average Trade Receivable = (Opening Debtors and Bills Receivable + Closing
Debtors and Bills Receivable)/2
It needs to be noted that debtors should be taken before making any provision for doubtful debts.
Significance: The liquidity position of the firm depends upon the speed with which trade receivables are realised. This ratio indicates the number of times the receivables are turned over and converted into cash in an accounting period. Higher turnover means speedy collection from trade receivable. This ratio also helps in working out the average collection period. The ratio is calculated by dividing the days or months in a year by trade receivables turnover ratio.
### Illustration 15
Calculate the Trade receivables turnover ratio from the following information:
Rs.
Total Revenue from operations 4,00,000
Cash Revenue from operations 20% of Total Revenue from operations
Trade receivables as at 1.4.2016 40,000
Trade receivables as at 31.3.2017 1,20,000
## Solution
Trade Receivables Turnover Ratio =Net Credit Revenue from Operations/Average Trade Receivables
Credit Revenue from operations = Total revenue from operations – Cash revenue from operations
Cash Revenue from operations = 20% of Rs. 4,00,000
= Rs. 4,00,000 ×20/100 = Rs. 80,000
Credit Revenue from operations = Rs. 4,00,000 – Rs. 80,000 = Rs. 3,20,000
#### * This figure has not been divided by 2, in order to calculate average Trade Receivables as the figures of debtors and bills receivables in the beginning of the year are not available. So when only year-end figures are available use the same as it is.
*Since no information regarding credit purchase is given, hence it will be related as net purchases.
### 5.8.4 Net Assets or Capital Employed Turnover Ratio
It reflects relationship between revenue from operations and net assets (capital employed) in the business. Higher turnover means better activity and profitability.
It is calculated as follows :
Significance : High turnover of capital employed, working capital and fixed assets is a good sign and implies efficient utilisation of resources. Utilisation of capital employed or, for that matter, any of its components is revealed by the turnover ratios. Higher turnover reflects efficient utilisation resulting in higher liquidity and profitability in the business.
### Illustration 18
From the following information, calculate (i) Net assets turnover, (ii) Fixed assets turnover, and (iii) Working capital turnover ratios :
Revenue from operations for the year 2016-17 were Rs. 30,00,000
## Solution:
Revenue from Operations = Rs. 30,00,000
Capital Employed = Share Capital + Reserves and
Surplus + Long-term Debts
(or Net Assets)
= (Rs.4,00,000 + Rs.6,00,000)
+ (Rs.1,00,000 + Rs.3,00,000)
+ (Rs.2,00,000 + Rs.2,00,000)
= Rs. 18,00,000
Fixed Assets = Rs.8,00,000 + Rs.5,00,000 + Rs.2,00,000
+ Rs.1,00,000 = Rs. 16,00,000
Working Capital = Current Assets – Current Liabilities
= Rs.4,00,000 – Rs.2,00,000 = Rs. 2,00,000
Net Assets Turnover Ratio = Rs.30,00,000/Rs.18,00,000 = 1.67 times
Fixed Assets Turnover Ratio = Rs.30,00,000/Rs.16,00,000 = 1.88 times
Working Capital Turnover Ratio = Rs.30,00,000/Rs.2,00,000 = 15 times
### Test your Understanding – III
(i) The _________ is useful in evaluating credit and collection policies.
A. average payment period
B. current ratio
C. average collection period
D. current asset turnover
(ii) The ___________ measures the activity of a firm’s inventory.
A. average collection period
B. inventory turnover
C. liquid ratio
D. current ratio
(iii) The ___________ ratio may indicate the firm is experiencing stock outs and lost sales.
A. average payment period
B. inventory turnover
C. average collection period
D. quick
(vi) ABC Co. extends credit terms of 45 days to its customers. Its credit collection would be considered poor if its average collection period was
A. 30 days
B. 36 days
C. 47 days
D. 57 days
(v) ___________ are especially interested in the average payment period, since it provides them with a sense of the bill-paying patterns of the firm.
A. Customers
B. Stockholders
C. Lenders and suppliers
D. Borrowers and buyers
(vi) The __________ ratios provide the information critical to the long-run operation of the firm
A. liquidity
B. activity
C. solvency
D. profitability
### 5.9 Profitability Ratios
The profitability or financial performance is mainly summarised in Income statement. Profitability ratios are calculated to analyse the earning capacity of the business which is the outcome of utilisation of resources employed in the business. There is a close relationship between the profit and the efficiency with which the resources employed in the business are utilised. The various ratios which are commonly used to analyse the profitability of the business are:
1. Gross Profit Ratio
2. Operating Ratio
3. Operating Profit Ratio
4. Net profit Ratio
5. Return on Investment (ROI) or Return on Capital Employed (ROCE)
6. Return on Net Worth (RONW)
7. Earnings per Share
8. Book Value per Share
9. Dividend Payout Ratio
10. Price Earning Ratio.
### 5.9.1 Gross Profit Ratio
Gross profit ratio as a percentage of sales is computed to have an idea about gross margin. It is computed as follows:
Gross Profit Ratio = Gross Profit/Net Sales × 100
Significance: It indicates gross margin or mark-up on products sold. There is no standard norm for its comparison. It also indicates the margin available to cover operating expenses, non-operating expenses, etc. Change in gross profit ratio may result from change in selling price or cost of sales or a combination of both. A low ratio may indicate unfavourable purchase and sales policy. It must be interpreted carefully as valuation of stock also affects its computation. Higher gross profit ratio is always a good sign.
### Illustration 19
Following information is available for the year 2016-17, calculate gross profit ratio:
Rs
Revenue from Operations:Cash 25,000
:Credit 75,000
Purchases : Cash 15,000
Credit 60,000
Carriage Inwards 2,000
Salaries 25,000
Decrease in Stock 10,000
Return Outwards 2,000
Wages 5,000
## Solution
Revenue from Operations = Cash Revenue from Operations + Credit Revenue from
Opration
= Rs.25,000 + Rs.75,000 = Rs. 1,00,000
Net Purchases = Cash Purchases + Credit Purchases – Return Outwards
= Rs.15,000 + Rs.60,000 – Rs.2,000 = Rs. 73,000
Cost of Revenue from = Purchases + (Opening Inventory – Closing Inventory) +
operations Direct Expenses
= Purchases + Decrease in inventory + Direct Expenses
= Rs.73,000 + Rs.10,000 + (Rs.2,000 + Rs.5,000)
= Rs.90,000
Gross Profit = Revenue from Operations – Cost of Revenue from
Operation
= Rs.1,00,000 – Rs.90,000
= Rs. 10,000
Gross Profit Ratio = Gross Profit/Net Revenue from Operations ×100
= Rs.10,000/Rs.1,00,000 × 100
= 10%.
### 5.9.2 Operating Ratio
It is computed to analyse cost of operation in relation to sales. It is calculated as follows:
Operating Ratio = (Cost of Sales + Operating Expenses)/ Net Revenue from Operations × 100
Operating expenses include office expenses, administrative expenses, selling expenses and distribution expenses etc.
Cost of operation is determined by excluding non-operating incomes and expenses such as loss on sale of assets, interest paid, dividend received, loss by fire, speculation gain and so on.
### 5.9.3 Operating Profit Ratio
It is calculated to reveal operating margin. It may be computed directly or as a residual of operating ratio.
Operating Profit Ratio = 100 – Operating Ratio
Alternatively, it is calculated as under:
Operating Profit Ratio = Revenue from Operations × 100
Where Operating Profit = Revenue from Operations – Operating Cost
Significance: Operating Ratio is computed to express cost of operations excluding financial charges in relation to sales. A corollary of it is ‘Operating Profit Ratio’. It helps to analyse the performance of business and throws light on the operational efficiency of the business. It is very useful for inter-firm as well as intra-firm comparisons. Lower operating ratio is a very healthy sign.
### Illustration 20
Given the following information:
Revenue from Operations 3,40,000
Cost of Revenue from Operations 1,20,000
Selling expenses 80,000
Calculate Gross Profit Ratio and Operation Ratio.
## Solution
### 5.9.4 Net Profit Ratio
Net Profit Ratio is based on all inclusive concept of profit. It relates sales to net profit after operational as well as non-operational expenses and incomes. It is calculated as under:
Net Profit Ratio = Net profit / Revenue from Operations × 100
Generally, net profit refers to Profit after Tax (PAT).
Significance: It is a measure of net profit margin in relation to sales. Besides revealing profitability, it is the main variable in computation of Return on Investment. It reflects the overall efficiency of the business, assumes great significance from the point of view of investors.
### Illustration 21
Gross profit ratio of a company was 25%. Its credit sales was Rs. 20,00,000 and its cash sales was 10% of the total sales. If the indirect expenses of the company were Rs. 50,000, calculate its net profit ratio.
## Solution
Cash Revenue from Operations = Rs.20,00,000 × 10/90
= Rs.2,22,222
Hence, total Revenue from Operations are = Rs.22,22,222
Gross profit = 0.25 × 22,22,222 = Rs. 5,55,555
Net profit = Rs.5,55,555 – 50,000
= Rs.5,05,555
Net profit ratio = Net profit/Revenue from Operations
× 100
= Rs.5,05,555/Rs.22,22,222 × 100
= 22.75%.
### 5.9.5 Return on Capital Employed or Investment
It explains the overall utilisation of funds by a business enterprise. Capital employed means the long-term funds employed in the business and includes shareholders fund, debentures and long-term loans. Alternatively, capital employed may be taken as the total of non-factious assets current liabilities. Profit refers to the Profit before Interest and Tax (PBIT) for computation of this ratio. Thus, it is computed as follows:
Return on Investment (or Capital Employed) = Profit before Interest and Tax/ Capital Employed × 100
Significance: It measures return on capital employed in the business. It reveals the efficiency of the business in utilisation of funds entrusted to it by shareholders, debenture-holders and long-term liabilities. For inter-firm comparison, return on capital employed which reveals overall utilisation of fund is considered good measure of profitability. It also helps in assessing whether the firm is earning a higher return on capital employed as compared to the interest rate paid.
### 5.9.6 Return on Shareholders’ Fund
This ratio is very important from shareholders’ point of view in assessing whether their investment in the firm generates a reasonable return or not. It should be higher than the return on investment otherwise it would imply that company’s funds have not been employed profitably.
A better measure of profitability from shareholders point of view is obtained by determining return on total shareholders fund, it is also termed as Return on Net Worth (RONW) and is calculated as under :
### 5.9.7 Earnings Per Share
The ratio is defined as – EPS = Profit available for equity shareholders/ No. of Equity Shares
In this context, earnings refer to profit available for equity shareholders which is worked out as
This ratio is very important from equity shareholders point of view and so also for the share price in the stock market. This also helps comparison with other firm’s to ascertain its reasonableness and capacity to pay dividend.
### 5.9.8 Book Value Per Share
This ratio is calculated as :
Book Value per share = Equity shareholders’ funds/Number of Equity Shares
Equity shareholder funds refer to Shareholders Funds – Preference Share Capital. This ratio is again very important from equity shareholders point of view as it gives an idea about the value of their holding and affects market price of the shares.
### 5.9.9 Dividend Payout Ratio
This refers to the proportion of earning that are distributed against the shareholders. It is calculated as –
Dividend Payout Ratio =
This reflects company’s dividend policy and growth in owner’s equity.
### 5.9.10 Price Earning Ratio
The ratio is defined as –P/E Ratio = Market price of a Share/Earnings per Share
For example, if the EPS of company X is Rs. 10 and market price is Rs. 100, the price earning ratio will be 10 (100/10). It reflects investors expectation about the growth in the firm’s earnings and reasonableness of the market price of its shares. P/E ratios vary from industy to industry and company to company in the same industry depending upon investors perception of their future.
### Illustration 22
From the following details, calculate Return on Investment:
Also calculate Return on Shareholders’ Funds, EPS, Book value per share and P/E ratio if the market price of the share is Rs. 34 and the net profit after tax was Rs. 1,50,000, and the tax had amounted to Rs. 50,000.
## Solution
Profit before interest and tax = Rs. 1,50,000 + Debenture interest + Tax
= Rs. 1,50,000 + Rs. 40,000 + Rs. 50,000
= Rs.2,40,000
Capital Employed = Equity Share Capital + Preference Share
Capital + Reserves + Debentures
= Rs. 4,00,000 + Rs. 1,00,000 + Rs. 1,84,000
+ Rs. 4,00,000 = Rs. 10,84,000
Return on Investment = Profit before Interest and Tax/
Capital Employed × 100
= Rs. 2,40,000/Rs. 10,84,000 × 100
= 22.14%
Shareholders’ Fund = Equity Share Capital + Preference Share Capital
+ General Reserve
= Rs. 4,00,000 + Rs. 1,00,000 + Rs. 1,84,000
= Rs. 6,84,000
Return on Shareholders’ Funds = Profit after tax/shareholders’ Funds × 100
= Rs. 1,50,000/Rs. 6,84,000 × 100
= 21.93%
EPS = Profit available for Equity Shareholders/
Number of Equity Shares
= Rs. 1,38,000/ 40,000 = Rs. 3.45
Preference Share Dividend = Rate of Dividend × Prefence Share Capital
= 12% of Rs. 1,00,000
= Rs. 12,000
where, Dividend on Prefrence = Rate of Dividend × Preference Share Capital
shares = 12% of Rs. 1,00,000
= Rs.12,000
= Rs. 1,50,000 – Rs. 12,000 = Rs. 1,38,000
P/E Ratio = Market price of a share/ Earnings per share
= 34/3.45
= 9.86 Times
Book Value per share = Equity Shareholders’ fund/No. of
equity shares
where, Number of Equity Shares =
Equity share capital / Face value per share
=
Rs. 4,00,000 / Rs.10
= 40,000 shares
Hence, Book value per share = Rs. 5,84,000/40,000 shares = Rs. 14.60
### Illustration 23
Calculate current assets of a company from the following information:
Stock turnover ratio = 4 times
Stock at the end is Rs. 20,000 more than the stock in the beginning.
Sales Rs. 3,00,000 and gross profit ratio is 20% of sales.
Current liabilities = Rs. 40,000
Quick ratio = 0.75: 1
## Solution
Cost of Revenue from Operations = Revenue from Operations – Gross Profit
= Rs. 3,00,000 – (Rs. 3,00,000 × 20%)
= Rs. 3,00,000 – Rs. 60,000
= Rs. 2,40,000
Inventory Turnover Ratio = Cost of Revenue from Operations/ Average Inventory
Average Inventory = Cost of Revenue from Operations/4
= Rs. 2,40,000/4 = Rs. 60,000
Average Inventory = (Opening inventory + Closing inventory)/2
Rs. 60,000 = Opening inventory + (Opening inventory
+Rs.20,000)/2
Rs. 60,000 = Opening inventory + Rs. 10,000
Opening Inventory = Rs. 50,000
Closing Inventory = Rs. 70,000
Liquid Ratio = Liquid assets/current liabilities
0.75 = Liquid assets/Rs. 40,000
Liquid Assets = Rs. 40,000 × 0.75 = Rs. 30,000
Current Assets = Liquid assets + Closing inventory
= Rs. 30,000 + Rs. 70,000 = Rs. 1,00,000
### Illustration 24
The current ratio is 2.5:1. Current assets are Rs. 50,000 and current liabilities are Rs. 20,000. How much must be the decline in the current assets to bring the ratio to 2:1.
## Solution
Current liabilities = Rs. 20,000
For a ratio of 2:1, the current assets must be 2 × 20,000 = Rs. 40,000
Present level of current assets = Rs. 50,000
Necessary decline = Rs. 50,000 – Rs. 40,000 = Rs. 10,000.
### Illustration 25
Following information is given by a company from its books of accounts as on March 31, 2017:
Calculate:
i) Current Ratio
ii) Liquid Ratio
iii) Debt Equity Ratio
iv) Interest Coverage Ratio
v) Inventory Turnover Ratio
## Solution
Terms Introduced in the Chapter
1. Ratio Analysis
2. Liquidity Ratios
3. Solvency Ratios
4. Activity Ratios
5. Profitability Ratios
6. Return on Investment (ROI)
7. Quick Assets
8. Equity (Shareholders Funds)
9. Return on Net Worth
10. Average Collection Period
11. Receivables
12. Turnover Ratios
13. Efficiency Ratios
14. Dividend Payout
## Summary
Ratio Analysis: An important tool of financial statement analysis is ratio analysis. Accounting ratios represent relationship between two accounting numbers.
Objective of Ratio Analysis:The objective of ratio analysis is to provide a deeper analysis of the profitability, liquidity, solvency and activity levels in the business. It is also to identify the problem areas as well as the strong areas of the business.
Advantages of Ratio Analysis: Ratio analysis offers many advantages including enabling financial statement analysis, helping understand efficacy of decisions, simplifying complex figures and establish relationships, being helpful in comparative analysis, identification of problem areas, enables SWOT analysis, and allows various comparisons.
Limitations of Ratio Analysis: There are many limitations of ratio analysis. Few are based because of the basic limitations of the accounting data on which it is based. The other set includes the limitation of the ratio analysis per set. In the first set are included factors like Historical Analysis, Ignores Price-Level Changes, Ignore Qualitative or Non-Monetary Aspects, Limitations of Accounting Data, Variations in Accounting Practices, and Forecasting. In the second set are included factor like means and not the end, lack of ability to resolve problems, lack of standardised definitions, lack of universally accepted standard levels, and ratios based on unrelated figures.
Types of Ratios: There are many types of ratios, viz. liquidity, solvency, activity and profitability ratios. The liquidity ratios include current ratio and acid test ratio. Solvency ratios are calculated to determine the ability of the business to service its debt in the long run instead of in the short run. They include debt equity ratio, total assets to debt ratio, proprietary ratio and times interest coverage ratio. The turnover ratios basically exhibit the activity levels characterised by the capacity of the business to make more sales or turnover and include Stock Turnover, Debtors (Receivable) Turnover, Creditors (Payable) Turnover, Working Capital Turnover, Fixed Assets Turnover, and Current asset Turnover. Profitability ratios are calculated to analyse the earning capacity of the business which is the outcome of utilisation of resources employed in the business. The ratios include Gross Profit ratio, Operating ratio, Net-profit-ratio, Return on investment (Capital employed), Earnings per Share, Book Value per Share, Dividend per Share, and Price / Earning ratio.
## Question for Practice
A. Short Answer Questions
1. What do you mean by Ratio Analysis?
2. What are various types of ratios?
3. What relationships will be established to study:
a. Inventory Turnover
b. Debtor Turnover
c. Payables Turnover
d. Working Capital Turnover.
4. The liquidity of a business firm is measured by its ability to satisfy its long-term obligations as they become due. What are the ratios used for this purpose?
5. The average age of inventory is viewed as the average length of time inventory is held by the firm for which explain with reasons.
1. What are liquidity ratios? Discuss the importance of current and liquid ratio.
2. How would you study the Solvency position of the firm?
3. What are various profitability ratios? How are these worked out?
4. The current ratio provides a better measure of overall liquidity only when a firm’s inventory cannot easily be converted into cash. If inventory is liquid, the quick ratio is a preferred measure of overall liquidity. Explain.
Numerical Questions
1. Following is the Balance Sheet of Raj Oil Mills Limited as at March 31, 2017.
Calculate current ratio.
Calculate Current Ratio and Liquid Ratio.
(Ans: Current Ratio 0.8 : 1, Liquid Ratio 0.4 : 1)
3. Current Ratio is 3.5 : 1. Working Capital is Rs. 90,000. Calculate the amount of Current Assets and Current Liabilities.
(Ans: Current Assets Rs. 1,26,000 and Current Liabilities Rs. 36,000)
4. Shine Limited has a current ratio 4.5 : 1 and quick ratio 3 : 1; if the inventory is 36,000, calculate Current Liabilities and Current Assets.
(Ans: Current Assets Rs. 1,08,000, Current Liabilities Rs. 24,000)
5. Current Liabilities of a company are Rs. 75,000. If current ratio is 4:1 and Liquid Ratio is 1 : 1, calculate value of Current Assets, Liquid Assets and Inventory. (Ans: Current Assets Rs. 3,00,000, Liquid Assets Rs. 75,000 and Inventory Rs. 2,25,000)
6. Handa Ltd.has stock of Rs. 20,000. Total liquid assets are Rs. 1,00,000 and quick ratio is 2:1. Calculate current ratio.
(Ans: Current Ratio 2.4:1)
7. Calculate debt equity ratio from the following information:
Total Assets Rs. 15,00,000
Current Liabilities Rs. 6,00,000
Total Debts Rs. 12,00,000
(Ans: Debt Equity Ratio 2:1.)
8. Calculate Current Ratio if:
Stock is Rs. 6,00,000; Liquid Assets Rs. 24,00,000; Quick Ratio 2:1.
(Ans: Current Ratio 2.5:1)
9. Compute Inventory Turnover Ratio from the following information:
Net Revenue from Operations Rs. 2,00,000
Gross Profit Rs. 50,000
Inventory at the end Rs. 60,000
Excess of inventory at the end over
inventory in the beginning Rs. 20,000
(Ans: Inventory Turnover Ratio 3 times)
10. Calculate following ratios from the following information:
(i) Current ratio (ii) Liquid ratio (iii) Operating Ratio (iv) Gross profit ratio
Current Assets Rs. 35,000
Current Liabilities Rs. 17,500
Inventory Rs. 15,000
Operating Expenses Rs. 20,000
Revenue from Operations Rs. 60,000
Cost of Revenue from operation Rs. 30,000
(Ans: Current Ratio 2 : 1; Liquid Ratio 1.14 : 1; Operating Ratio 83.3%; Gross
Profit Ratio 50%)
11. From the following information calculate:
(i) Gross Profit Ratio (ii) Inventory Turnover Ratio (iii) Current Ratio (iv) Liquid
Ratio (v) Net Profit Ratio (vi) Working Capital Ratio:
Revenue from Operations Rs. 25,20,000
Net Profit Rs. 3,60,000
Cost of Revenue from Operations Rs. 19,20,000
Long-term Debts Rs. 9,00,000
Trade Payables Rs. 2,00,000
Average Inventory Rs. 8,00,000
Current Assets Rs. 7,60,000
Fixed Assets Rs. 14,40,000
Current Liabilities Rs. 6,00,000
Net Profit before Interest and Tax Rs. 8,00,000
(Ans: Gross Profit Ratio 23.81; Inventory Turnover Ratio 2.4 times; Current Ratio 2.6:1; Liquid Ratio 1.27:1; Net Profit Ratio 14.21%; Working Capital Ratio 2.625 times)
12. Compute Gross Profit Ratio, Working Capital Turnover Ratio, Debt Equity Ratio and Proprietary Ratio from the following information:
Paid-up Capital Rs. 5,00,000
Current Assets Rs. 4,00,000
Net Sales Rs. 10,00,000
13% Debentures Rs. 2,00,000
Current Liability Rs. 2,80,000
Cost of Revenue from Operations Rs. 6,00,000
(Ans: Gross Profit Ratio 40%; Working Capital Ratio 8.33 times; Debt–Equity Ratio 0.4 : 1; Proprietary Ratio 0.51 : 1)
13. Calculate Stock Turnover Ratio if:
Inventory in the beginning is Rs. 76,250, Inventory at the end is 98,5
00, Gross Revenue from Operations is Rs. 5,20,000, Sales Return is Rs. 20,000, Purchases is Rs. 3,22,250.
(Ans: Stock Turnover Ratio 3.43 times)
14. Calculate Stock Turnover Ratio from the data given below:
Inventory in the beginning of the year Rs. 10,000
Inventory at the end of the year Rs. 5,000
Carriage Rs. 2,500
Revenue from Operations Rs. 50,000
Purchases Rs. 25,000
(Ans: Inventory Turnover Ratio 4.33 times)
15. A trading firm’s average inventory is Rs. 20,000 (cost). If the inventory turnover
ratio is 8 times and the firm sells goods at a profit of 20% on sales, ascertain
the profit of the firm.
(Ans: Profit Rs. 40,000)
16. You are able to collect the following information about a company for two years:
Calculate Inventory Turnover Ratio and Trade Receivables Turnover Ratio
(Ans: Inventory Turnover Ratio 2.4 times, Trade Receivables Turno
ver Ratio 4.53 times)
17. From the following Balance Sheet and other information, calculate following ratios:
(i) Debt-Equity Ratio (ii) Working Capital Turnover Ratio (iii) Trade Receivables Turnover Ratio
Balance Sheet as at March 31, 2017
Revenue from operations 4,00,000
Gross Profit 1,94,000
Cash and Cash Equivalents 40,000
Other Current Liabilities 70,000
Share Capital 2,00,000
Reserves and Surplus 1,40,000
(Balance in the Statement of Profit & Loss A/c)
(Ans: Liquid Ratio 0.54 : 1; Inventory Turnover Ratio 3.74 times; Return on
Investment 41.17%)
19. From the following, calculate
(a) Debt-Equity Ratio
(b) Total Assets to Debt Ratio
(c) Proprietary Ratio.
Equity Share Capital Rs. 75,000
Preference Share Capital Rs. 25,000
General Reserve Rs. 45,000
Balance in the Statement of Profit & Loss Rs. 30,000
Debentures Rs. 75,000
Trade Payables Rs. 40,000
Outstanding Expenses Rs. 10,000
(Ans: Debt-Equity Ratio 0.43 : 1; Total Assets to Debt Ratio 4 : 1; Proprietary Ratio 0.58 : 1)
20. Cost of Revenue from Operations is Rs. 1,50,000. Operating expenses are Rs. 60,000. Revenue from Operations is Rs. 2,50,000. Calculate Operating Ratio.
(Ans: Operating Ratio 84%)
21. Calculate the following ratio on the basis of following information:
(i) Gross Profit Ratio (ii) Current Ratio (iii) Acid Test Ratio (iv) Inventory Turnover
Ratio (v) Fixed Assets Turnover Ratio
Rs.
Gross Profit 50,000
Revenue from Operations 1,00,000
Inventory 15,000
Cash and Cash Equivalents 17,500
Current Liablilites 40,000
Land & Building 50,000
Plant & Machinery 30,000
Furniture 20,000
(Ans: (i) Gross Profit Ratio 50%; (ii) Current Ratio 1.5:1; (iii) Liquid Ratio 1.125 : 1,
Inventory Turnover Ratio 3.33 times; (iv) Fixed Assets Turnover Ratio 1 : 1)
22. From the following information calculate Gross Profit Ratio, Inventory Turnover Ratio and Trade Receivable Turnover Ratio.
Revenue from Operations Rs. 3,00,000
Cost of Revenue from Operations Rs. 2,40,000
Inventory at the end Rs. 62,000
Gross Profit Rs. 60,000
Inventory in the beginning Rs. 58,000
Trade Receivables Rs. 32,000
(Ans: Gross Profit Ratio 20%; Inventory Turnover Ratio 4 times; Trade
Receivables Turnover Ratio 9.4 times) | 14,815 | 62,339 | {"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} | 3.59375 | 4 | CC-MAIN-2024-26 | latest | en | 0.934238 |
https://www.extendoffice.com/documents/excel/4666-google-sheets-compare-two-columns.html | 1,713,515,481,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296817382.50/warc/CC-MAIN-20240419074959-20240419104959-00759.warc.gz | 698,002,025 | 27,685 | ## How to compare two columns and find the duplicate or missing values in Google sheet?
How could you compare two columns and find or extract the duplicate or missing values in Google sheet? This article will talk about some easy tricks for you to solve this job.
Compare and find the duplicate values in both two columns with formula
Compare and extract the missing values from two columns with formula
Compare and find or shade the duplicate or missing values from two columns in Microsoft Excel
#### Compare and find the duplicate values in both two columns with formula
To find the values which are both in columns, please apply the following formula:
Enter this formula: =ArrayFormula(iferror(if(match(B2:B13,C2:C11,0),"Yes",""))) in adjacent cell A2, and then press Enter key, and a Yes will be displayed in Column A if the corresponding values in Column B are also in Column C. See screenshot:
Note: In the above formula, B2:B13 and C2:C11 are the two columns data that you want to compare.
#### Compare and extract the missing values from two columns with formula
If you want to compare and extract the missing values from two columns, here is another formula to help you.
Enter this formula: =filter(A2:A13,isna(match(A2:A13,B2:B11,0))) into cell C2, and then press Enter key, all values in List 1 but not in List 2 are extracted as following screenshot shown:
Note: In the above formula, A2:A13 and B2:B11 are the two columns data that you want to compare.
Tips: If you want to extract the values which are in List 2 but not in List1, you just need to exchange the cell references in the above formula as this: =filter(B2:B11,isna(match(B2:B11,A2:A13,0))), and then press Enter key to get the values in List 2 but not in List 1. See screenshot:
#### Compare and find or shade the duplicate or missing values from two columns in Microsoft Excel
If you want to solve this task in Microsoft Excel, here, I will introduce a handy tool-Kutools for Excel, with its Select Same & Different Cells feature, you can quickly compare two columns and extract or highlight the same or different values as you need.
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After installing Kutools for Excel, please do as follows:
1. Click Kutools > Select > Select Same & Different Cells, see screenshot:
2. In the Select Same & Different Cells dialog box, do the following operations:
(1.) Click button under the Find values in text box to select the first column data, and then click button under the According to text box to select the second column data;
(2.) Choose Each row under the Based on section;
(3.) Select Same values from the Find section to select the same values both in the two columns;
(4.) You can choose one cell color or font color for the selected cells as you need in the Processing of results section.
3. Then click Ok button, the same cell values both in Column A and Column B have been selected and highlighted at once, see screenshot:
Notes:
1. If you need to select or highlight the different cell values only in Column A not in Column B, please select the two columns data separately, and then choose Different Values in the Find section, and you will get the following result:
2. To select the cell values only in Column B not in Column A, you just need to exchange the column ranges when selecting them in the first step.
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https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Symmetry_(Vallance)/01%3A_Chapters/1.06%3A_Constructing_higher_groups_from_simpler_groups | 1,723,473,755,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722641039579.74/warc/CC-MAIN-20240812124217-20240812154217-00576.warc.gz | 134,347,502 | 29,837 | # 1.6: Constructing higher groups from simpler groups
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A group that contains a large number of symmetry elements may often be constructed from simpler groups. This is probably best illustrated using an example. Consider the point groups $$C_2$$ and $$C_S$$. $$C_2$$ contains the elements $$E$$ and $$C_2$$, and has order 2, while $$C_S$$ contains $$E$$ and σ and also has order $$2$$. We can use these two groups to construct the group $$C_{2v}$$ by applying the symmetry operations of $$C_2$$ and $$C_S$$ in sequence.
$\begin{array}{lllll} C_2 \: \text{operation} & E & E & C_2 & C_2 \\ C_S \: \text{operation} & E & \sigma(xz) & E & \sigma(xz) \\ \text{Result} & E & \sigma_v(xz) & C_2 & \sigma_v'(yz) \end{array} \tag{6.1}$
Notice that $$C_{2v}$$ has order $$4$$, which is the product of the orders of the two lower-order groups. $$C_{2v}$$ may be described as a direct product group of $$C_2$$ and $$C_S$$. The origin of this name should become obvious when we review the properties of matrices.
This page titled 1.6: Constructing higher groups from simpler groups is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by Claire Vallance via source content that was edited to the style and standards of the LibreTexts platform. | 2,114 | 5,611 | {"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} | 4.21875 | 4 | CC-MAIN-2024-33 | latest | en | 0.208124 |
https://www.isnt.org.in/difference-between-two-time-with-code-examples.html | 1,701,459,694,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679100304.52/warc/CC-MAIN-20231201183432-20231201213432-00400.warc.gz | 920,038,046 | 50,565 | # Difference Between Two Time With Code Examples
In this article, we will look at how to get the solution for the problem, Difference Between Two Time With Code Examples
## What is the difference between time?
Time-difference definition The difference between one measurement of time and another taken later; the length of a time interval. The difference in clock time between two or more different time zones.
``````// start time and end time
var startTime = moment('12:16:59 am', 'HH:mm:ss a');
var endTime = moment('06:12:07 pm', 'HH:mm:ss a');
// calculate total duration
var duration = moment.duration(endTime.diff(startTime));
// duration in hours
var hours = parseInt(duration.asHours());
// duration in minutes
var minutes = parseInt(duration.asMinutes()) % 60;
alert(hours + ' hour and ' + minutes + ' minutes.');```
```
## How do you calculate minutes between two times?
To calculate the total minutes between two times: Make sure to convert both times to 24-hour time format. Take starting time and subtract it from ending time. Multiply the hours by 60 to convert it into minutes and add it to any amount of minutes you have left after the subtraction.
## How do you use time difference in a sentence?
Examples of 'time difference' in a sentence time difference
• Some who went home are attending online lectures at night because of time differences.
• She is also worried about how the time difference will affect her ability to do upcoming exams.
## How do we calculate time?
The formula for time is given as [Time = Distance ÷ Speed]. To calculate the distance, the time formula can be molded as [Distance = Speed × Time].
## How do you find the difference between two times?
First, identify the starting and an ending time. The goal is to subtract the starting time from the ending time under the correct conditions. If the times are not already in 24-hour time, convert them to 24-hour time. AM hours are the same in both 12-hour and 24-hour time.
## What is a formula of time?
time = distance ÷ speed.
## What is time difference called?
A time zone is an area which observes a uniform standard time for legal, commercial and social purposes. Time zones tend to follow the boundaries between countries and their subdivisions instead of strictly following longitude, because it is convenient for areas in frequent communication to keep the same time.
## How do I calculate the time difference between two times in Excel?
Another simple technique to calculate the duration between two times in Excel is using the TEXT function: Calculate hours between two times: =TEXT(B2-A2, "h") Return hours and minutes between 2 times: =TEXT(B2-A2, "h:mm")
## How To Get Bot Voice Channel Discord.Py With Code Examples
In this article, we will look at how to get the solution for the problem, How To Get Bot Voice Channel Discord.Py With Code Examples Can you tag a voice channel in Discord? you can tag #games and it turns blue and clickable and all, but it's not the same for Voices Channels, there's not even a prefix for that. @bot.command() async def join(ctx): channel = ctx.author.voice.channel await channel.connect() @bot.command() async def leave(ctx): await ctx.voice_client.disconnect() bot_c
## Load A Config File Discordjs With Code Examples
In this article, we will look at how to get the solution for the problem, Load A Config File Discordjs With Code Examples How do I install Discord JS in Visual Studio code? Installing Discord. js (Windows) Node.js v6 and above. If you don't already have Python 2.7 and Visual Studio, run npm install --global windows-build-tools. npm install --save discord.js in your bot's project folder. Good to go! const Discord = require('discord.js'); const bot = Discord.Client(); // con
## Mongodb Match Not Empty With Code Examples
In this article, we will look at how to get the solution for the problem, Mongodb Match Not Empty With Code Examples How do I use \$Push in MongoDB? In MongoDB, the \$push operator is used to appends a specified value to an array. If the mentioned field is absent in the document to update, the \$push operator add it as a new field and includes mentioned value as its element. If the updating field is not an array type field the operation failed. db.collection1.find({ 'fieldname1' : { \$exi
## Windows Instalar Python With Code Examples
In this article, we will look at how to get the solution for the problem, Windows Instalar Python With Code Examples How do I install Python 3.7 on Windows? If you're running Windows: the most stable Windows downloads are available from the Python for Windows page.Installing python on windows PC! Visit the python for windows page. Download python 3.7. 0 by clicking the link in step 3. Begin the download and follow screenshot instructions below. para instalar Python escribe https://www.py | 1,080 | 4,886 | {"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-2023-50 | latest | en | 0.891461 |
http://www.chegg.com/homework-help/questions-and-answers/use-inverse-trigonometric-functions-solutions-equation-given-interval-approximate-solution-q886455 | 1,369,488,109,000,000,000 | text/html | crawl-data/CC-MAIN-2013-20/segments/1368705955434/warc/CC-MAIN-20130516120555-00053-ip-10-60-113-184.ec2.internal.warc.gz | 379,038,347 | 7,569 | ## Trigonometry
Use inverse trigonometric functions to find the solutions of the equation that are in the given interval, and approximate the solutions to four decimal places.
1. 3sin 2(t)+ 10sin(t)+ 2 = 0 : interval (-Pi/2, Pi/2)
2. 15cos 2(x)+ 3cos(x)- 2 = 0 : interval [0, 2*Pi)
3. 4sin 2(x)- 2sin(x)- 1 = 0: interval [0, 2*Pi) | 123 | 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} | 3.734375 | 4 | CC-MAIN-2013-20 | latest | en | 0.635817 |
https://justaaa.com/chemistry/5639-the-mobility-u-of-an-organic-ammonium-ion-ncxhy4 | 1,713,015,345,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296816734.69/warc/CC-MAIN-20240413114018-20240413144018-00239.warc.gz | 317,826,364 | 9,037 | Question
# The mobility (u) of an organic ammonium ion, [N(CxHy)4]+ in dilute aqueous solution is 5.51x10-8m2 s-1...
The mobility (u) of an organic ammonium ion, [N(CxHy)4]+ in dilute aqueous solution is 5.51x10-8m2 s-1 V-1 at a temperature of 298 K. Estimate the radius of the ion, given that the viscosity of water at this temperature is 0.001 N s m-2. Express your answer in Å (Angstroms).
Ionic molbility of ammonium ion
using,
Ionic mobility (u) = z.e/6.pi.n.r = 5.5.1 x 10^-8
where,
n = visocity = 0.001 N s m^-2
z = elementary charge = 1.602 x 10^-19 C
e = 1
So,
ionic radius (r) = 1 x 1.602 x 10^-19/6 x 3.14 x 5.51 x 10^-8 x 0.001
= 1.54 x 10^-10 m = 1.54 Angstroms
So ionic radius of ammonium ion is 1.54 Angstroms.
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# The mean length of a small counter balance bar is 43 millimeters
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The mean length of a small counter balance bar is 43 millimeters. There is concern that the adjustments of the machine producing the bars have changed. Test the claim at the 0.02 level that there has been no change in the mean length. The alternate hypothesis is that there has been a change. Twelve bars (n = 12) were selected at random and their lengths recorded. The lengths are (in millimeters) 42, 39, 42, 45, 43, 40, 39, 41, 40, 42, 43 and 42. Has there been a statistically significant change in the mean length of the bars?
a. What is Ho: _______________________
A) µ = 43
B) µ < 43
C) π = 43
D) µ ≠ 43
b. What is H1:________________________
A) µ = 43
B) µ < 43
C) π = 43
D) µ ≠ 43
c. What is the value of p:_________________________
A) .028
B) .014
C) .14
D) 2.91
c. What is the decision
A) Do not reject Ho
B) Reject Ho
d. What is the conclusion
A) There has been a significant change in the mean length of the bars
B) There has been no change in the mean length of the bars
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Order your essay today and save 15% with the discount code 2023DISCOUNT | 464 | 1,623 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.96875 | 3 | CC-MAIN-2024-33 | latest | en | 0.911875 |
http://www.jiskha.com/display.cgi?id=1223437671 | 1,496,123,745,000,000,000 | text/html | crawl-data/CC-MAIN-2017-22/segments/1495463613796.37/warc/CC-MAIN-20170530051312-20170530071312-00466.warc.gz | 682,415,587 | 3,670 | Gil
posted by on .
A bike shop has 8 red, 5 blue, 12 black, and 9 white bikes. Write an expression that shows how many more black bikes than red bikes there are.
• Gil - ,
12-8=4 more black bikes | 57 | 199 | {"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-2017-22 | latest | en | 0.95608 |
https://www.doubtnut.com/qna/175530534 | 1,716,026,251,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971057379.11/warc/CC-MAIN-20240518085641-20240518115641-00336.warc.gz | 673,484,154 | 37,850 | # If I is the moment of Inertia and E is the kinetic energy of rotation of a body , then its angular momentum is given by
A
El
B
2El
C
EI
D
2EI
Video Solution
|
Step by step video & image solution for If I is the moment of Inertia and E is the kinetic energy of rotation of a body , then its angular momentum is given by by Physics experts to help you in doubts & scoring excellent marks in Class 12 exams.
Updated on:21/07/2023
### Knowledge Check
• Question 1 - Select One
## If I is the moment of inertia and E is the kinetic energy of rotation of a body, then its angular momentum will be
A(EI)
B2EI
CE/I
D(2EI)
• Question 1 - Select One
## Kinetic energy of rotation E and angular momentum L are related as
AE=L22I
BE=2IL
CE=2IL
DE=2IL
• Question 1 - Select One
## Two rotating bodies A and B of masses m and 2m with moments of inertia IAandIB(IB>IA) have equal kinetic energy of rotation. If LAandLb be their angular momenta respectively, then
ALA>LB
BLA=LB2
CLA=2LB
DLB>LA
• Question 1 - Select One
## Two bodies have their moments of inertia I and 2I respectively about their axis of rotation. If their kinetic energies of rotation are equal, their angular momenta will be in the ratio.
A1:2
B2:1
C2:1
D1:2
• Question 1 - Select One
## Two rigid bodies with their moments of inertia in the ratio 2:3 have same rotational kinetic energy . Then ratio of their angular momenta is
A2:3
B3:2
C2:3
D3:2
• Question 1 - Select One
## Two rotating bodies A and B of masses m and 2m with moments of inertia IA and IB(IB>IA) have equal kinetic energy of rotation. If LA and LB are their angular momenta respectively, then.
ALB>LA
BLA>LB
CLA=LB2
DLA=2LB
• Question 1 - Select One
## A body of moment of inertia 2kg-m^(2) has a rotational kinetic energy of 4 J. What is the angular momentum of the body ?
A2 kg m2/s
B2 kg m2/s
C4 kg m2/s
D8 kg m2/s
• Question 1 - Select One
## Two bodies have their moments of inertia I and 2I respectively about their axis of rotation. If their kinetic energies of rotation are equal, their angular momenta will be in the ratio.
A1:2
B2:1
C2:1
D1:2
• Question 1 - Select One
## Two bodies have their moment of inertia 3 I and 11 l respectively about their axis of rotation. If the kinetic energy of first body is half of the second then their angular momenta will be in the ratio of .
A1
B23
C411
D366
### Similar Questions
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Doubtnut is the perfect NEET and IIT JEE preparation App. Get solutions for NEET and IIT JEE previous years papers, along with chapter wise NEET MCQ solutions. Get all the study material in Hindi medium and English medium for IIT JEE and NEET preparation | 944 | 3,374 | {"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} | 3.59375 | 4 | CC-MAIN-2024-22 | latest | en | 0.860975 |
https://mc-stan.org/users/documentation/case-studies/rstan_workflow.html | 1,726,050,943,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651383.5/warc/CC-MAIN-20240911084051-20240911114051-00466.warc.gz | 354,741,691 | 463,347 | Stan and its implementation of dynamic Hamiltonian Monte Carlo is an extremely powerful tool for specifying and then fitting complex Bayesian models. In order to ensure a robust analysis, however, that power must be complemented with responsibility.
In particular, while dynamic implementations of Hamiltonian Monte Carlo, i.e. implementations where the integration time is dynamic, do perform well over a large class of models their success is not guaranteed. When they do fail, however, their failures manifest in diagnostics that are readily checked.
By acknowledging and respecting these diagnostics you can ensure that Stan is accurately fitting the Bayesian posterior and hence accurately characterizing your model. And only with an accurate characterization of your model can you properly utilize its insights.
# A Little Bit About Markov Chain Monte Carlo
Hamiltonian Monte Carlo is an implementation of Markov chain Monte Carlo, an algorithm which approximates expectations with respect to a given target distribution, $$\pi$$, $\mathbb{E}_{\pi} [ f ] = \int \mathrm{d}q \, \pi (q) \, f(q),$ using the states of a Markov chain, $$\{q_{0}, \ldots, q_{N} \}$$, $\mathbb{E}_{\pi} [ f ] \approx \hat{f}_{N} = \frac{1}{N + 1} \sum_{n = 0}^{N} f(q_{n}).$ Typically the target distribution is taken to be the posterior distribution of our specified model.
These estimators are guaranteed to be accurate only asymptotically, as the Markov chain grows to be infinitely long, $\lim_{N \rightarrow \infty} \hat{f}_{N} = \mathbb{E}_{\pi} [ f ].$ To be useful in applied analyses, we need these Markov chain Monte Carlo estimators to converge to the true expectation values sufficiently quickly that they are reasonably accurate before we exhaust our finite computational resources. This fast convergence requires strong ergodicity conditions to hold, typically a condition called geometric ergodicity between the Markov transition and target distribution. In particular, geometric ergodicity is a sufficient condition for Markov chain Monte Carlo estimators to follow a central limit theorem, which ensures not only that they are unbiased after only a finite number of iterations but also that we can empirically quantify their precision, $\hat{f}_{N} - \mathbb{E}_{\pi} [ f ] \sim \mathcal{N} \! \left( 0, \sqrt{ \mathrm{Var}[f] / N_{\mathrm{eff}}} \right).$
Unfortunately proving geometric ergodicity theoretically is infeasible for any nontrivial problem. Instead we must rely on empirical diagnostics that identify obstructions to geometric ergodicity, and hence well-behaved Markov chain Monte Carlo estimators. For a general Markov transition and target distribution, the best known diagnostic is the split $$\hat{R}$$ statistic over an ensemble of Markov chains initialized from diffuse points in parameter space.
To do any better we need to exploit the particular structure of a given transition or target distribution.
Hamiltonian Monte Carlo, for example, is especially powerful in this regard as its failures to be geometrically ergodic with respect to any target distribution manifest in distinct behaviors that have been developed into sensitive diagnostics. One of these behaviors is the appearance of divergences that indicate the Hamiltonian Markov chain has encountered regions of high curvature in the target distribution which it cannot adequately explore. Another is the energy Bayesian fraction of missing information, or E-BFMI, which quantifies the efficacy of the momentum resampling in between Hamiltonian trajectories.
For more details on Markov chain Monte Carlo and Hamiltonian Monte Carlo see Betancourt (2017).
In this case study I will demonstrate the recommended Stan workflow in R where we not only fit a model but also scrutinize these diagnostics and ensure an accurate fit.
# Setting Up The RStan Environment
We begin by importing the RStan module and setting some local options,
library(rstan)
Loading required package: ggplot2
Loading required package: StanHeaders
rstan (Version 2.14.1, packaged: 2016-12-28 14:55:41 UTC, GitRev: 5fa1e80eb817)
For execution on a local, multicore CPU with excess RAM we recommend calling
rstan_options(auto_write = TRUE)
options(mc.cores = parallel::detectCores())
rstan_options(auto_write = TRUE)
options(mc.cores = parallel::detectCores())
By setting rstan_options(auto_write = TRUE) we allow RStan to cache compiled models so that we can run them multiple times without the overhead of recompilation. options(mc.cores = parallel::detectCores()) enables RStan to run multiple Markov chains in parallel over any cores that your computer may have. These settings are recommended if you are running locally on your own machine, as opposed to running on a remote cluster, and your local machine which has plenty of RAM. For very large problems running multiple Markov chains in parallel may exhaust your RAM and degrade performance, in which case you would not want to utilize this option.
In order to facilitate checking diagnostics we source the attached utility script which loads some useful functions,
source('stan_utility.R')
lsf.str()
check_div : function (fit)
check_energy : function (fit)
check_treedepth : function (fit, max_depth = 10)
count_divergences : function (fit)
hist_treedepth : function (fit)
partition_div : function (fit)
## Specifying and Fitting A Model in Stan
To demonstrate the recommended Stan workflow let’s consider a hierarchical model of the eight schools dataset infamous in the statistical literature (D. B. Rubin 1981),
$\mu \sim \mathcal{N}(0, 5)$
$\tau \sim \text{Half-Cauchy}(0, 5)$
$\theta_{n} \sim \mathcal{N}(\mu, \tau)$
$y_{n} \sim \mathcal{N}(\theta_{n}, \sigma_{n}),$
where $$n \in \left\{1, \ldots, 8 \right\}$$ and the $$\left\{ y_{n}, \sigma_{n} \right\}$$ are given as data.
For more information on the eight schools dataset see Gelman et al. (2014).
## Specifying the Model with a Stan Program
In particular, let’s implement a centered-parameterization of the model which is known to frustrate even sophisticated samplers like Hamiltonian Monte Carlo. In Stan the centered parameterization is specified with the Stan program
writeLines(readLines("eight_schools_cp.stan"))
data {
int<lower=0> J;
real y[J];
real<lower=0> sigma[J];
}
parameters {
real mu;
real<lower=0> tau;
real theta[J];
}
model {
mu ~ normal(0, 5);
tau ~ cauchy(0, 5);
theta ~ normal(mu, tau);
y ~ normal(theta, sigma);
}
Note that we have specified the Stan program in its own file. We strongly recommend keeping your workflow modular by separating the Stan program from the R environment in this way. Not only does it make it easier to identify and read through the Stan-specific components of your analysis, it also makes it easy to share your models Stan users exploiting workflows in environments, such as Python and the command line.
## Specifying the Data
Similarly, we strongly recommend that you specify the data in its own file.
Data specified in R lists can be immediately converted to an external Stan data file using RStan’s stan_rdump function,
J <- 8
y <- c(28, 8, -3, 7, -1, 1, 18, 12)
sigma <- c(15, 10, 16, 11, 9, 11, 10, 18)
stan_rdump(c("J", "y", "sigma"), file="eight_schools.data.R")
At the same time, an existing Stan data file can be read into the R environment using the read_rdump function,
data <- read_rdump("eight_schools.data.R")
## Fitting the Model
With the model and data specified we can now turn to Stan to quantify the resulting posterior distribution with Hamiltonian Monte Carlo,
fit <- stan(file='eight_schools_cp.stan', data=data, seed=194838)
Warning: There were 126 divergent transitions after warmup. Increasing adapt_delta above 0.8 may help. See
http://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
Warning: There were 2 chains where the estimated Bayesian Fraction of Missing Information was low. See
http://mc-stan.org/misc/warnings.html#bfmi-low
Warning: Examine the pairs() plot to diagnose sampling problems
We recommend explicitly specifying the seed of Stan’s random number generator, as we have done here, so that we can reproduce these exactly results in the future, at least when using the same machine, operating system, and interface.
This is especially helpful for the more subtle pathologies that may not always be found, which results in seemingly stochastic behavior.
By default the sampling method runs 4 Markov chains of Hamiltonian Monte Carlo, each initialized from a diffuse initial condition to maximize the probability that at least one of the chains might encounter a pathological neighborhood of the posterior, if it exists. Because we set options(mc.cores = parallel::detectCores()) above, these chains will run in parallel when possible.
Each of those chains proceeds with 1000 warmup iterations and 1000 sampling iterations, totaling 4000 sampling iterations available for diagnostics and analysis.
## Validating a Fit in Stan
We are now ready to validate the fit using the information contained in the fit object.
## Checking Split $$\hat{R}$$ and Effective Sample Sizes
The first diagnostics we check are universal to Markov chain Monte Carlo and are displayed using the print method of the fit object,
print(fit)
Inference for Stan model: eight_schools_cp.
4 chains, each with iter=2000; warmup=1000; thin=1;
post-warmup draws per chain=1000, total post-warmup draws=4000.
mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
mu 4.50 0.18 3.45 -2.09 2.18 4.52 6.76 11.87 367 1.01
tau 4.29 0.19 3.34 0.60 1.95 3.36 5.62 13.27 321 1.01
theta[1] 6.77 0.19 5.94 -3.09 3.16 6.10 9.69 20.95 980 1.00
theta[2] 5.21 0.17 5.13 -4.58 2.05 5.41 8.07 15.43 915 1.00
theta[3] 3.89 0.21 5.88 -9.51 0.66 4.26 7.25 14.69 760 1.00
theta[4] 4.91 0.17 5.05 -5.20 1.68 4.96 7.88 15.00 922 1.00
theta[5] 3.57 0.18 5.03 -6.99 0.41 3.92 6.87 12.73 783 1.00
theta[6] 4.07 0.18 5.22 -6.87 0.86 4.43 7.36 13.56 845 1.00
theta[7] 6.83 0.18 5.34 -2.70 3.30 6.52 9.84 18.54 880 1.00
theta[8] 5.15 0.16 5.92 -6.44 1.63 5.12 8.24 17.29 1319 1.00
lp__ -16.11 0.44 5.81 -27.19 -20.05 -16.29 -12.05 -5.27 172 1.01
Samples were drawn using NUTS(diag_e) at Wed Jul 26 23:42:44 2017.
For each parameter, n_eff is a crude measure of effective sample size,
and Rhat is the potential scale reduction factor on split chains (at
convergence, Rhat=1).
Firstly we want to ensure that the split $$\hat{R}$$ for each parameter is close to 1. Empirically we have found that Rhat > 1.1 is usually indicative of problems in the fit. Here all of the parameters look good.
Then we want to consider the effective sample size, or n_eff. The issue here is related to the fact that we are estimating the effective sample size from the fit output. When n_eff / n_transitions < 0.001 the estimators that we use are often biased and can significantly overestimate the true effective sample size.
Both large split $$\hat{R}$$ and low effective samples per transition are consequences of poorly mixing Markov chains. Improving the mixing of the Markov chains almost always requires tweaking the model specification, for example with a reparameterization or stronger priors.
## Checking the Tree Depth
The dynamic implementation of Hamiltonian Monte Carlo used in Stan has a maximum trajectory length built in to avoid infinite loops that can occur for non-identified models. For sufficiently complex models, however, Stan can saturate this threshold even if the model is identified, which limits the efficacy of the sampler.
We can check whether that threshold was hit using one of our utility functions,
check_treedepth(fit)
[1] "0 of 4000 iterations saturated the maximum tree depth of 10 (0%)"
We’re good here, but if our fit had saturated the threshold then we would have wanted to rerun with a larger maximum tree depth,
fit <- stan(file='eight_schools_cp.stan', data=data, seed=194838, control=list(max_treedepth=15))
and then check if still saturated this larger threshold with
check_treedepth(fit, 15)
## Checking the E-BFMI
Hamiltonian Monte Carlo proceeds in two phases – the algorithm first simulates a Hamiltonian trajectory that rapidly explores a slice of the target parameter space before resampling the auxiliary momenta to allow the next trajectory to explore another slice of the target parameter space. Unfortunately, the jumps between these slices induced by the momenta resamplings can be short, which often leads to slow exploration.
We can identify this problem by consulting the energy Bayesian Fraction of Missing Information,
check_energy(fit)
The check_energy function uses the threshold of 0.2 to diagnose problems, although this is based on preliminary empirical studies and should be taken only as a very rough recommendation. In particular, this diagnostic comes out of recent theoretical work and will be better understood as we apply it to more and more problems. For further discussion see Section 4.2 and 6.1 of Betancourt (2017).
As with split $$\hat{R}$$ and effective sample size per transition, the problems indicated by low E-BFMI are remedied by tweaking the specification of the model. Unfortunately the exact tweaks required depend on the exact structure of the model and, consequently, there are no generic solutions.
## Checking Divergences
Finally, we can check divergences which indicate pathological neighborhoods of the posterior that the simulated Hamiltonian trajectories are not able to explore sufficiently well. For this fit we have a significant number of divergences
check_div(fit)
[1] "126 of 4000 iterations ended with a divergence (3.15%)"
[1] "Try running with larger adapt_delta to remove the divergences"
indicating that the Markov chains did not completely explore the posterior and that our Markov chain Monte Carlo estimators will be biased.
Divergences, however, can sometimes be false positives. To verify that we have real fitting issues we can rerun with a larger target acceptance probability, adapt_delta, which will force more accurate simulations of Hamiltonian trajectories and reduce the false positives.
fit <- stan(file='eight_schools_cp.stan', data=data, seed=194838, control=list(adapt_delta=0.90))
Warning: There were 52 divergent transitions after warmup. Increasing adapt_delta above 0.9 may help. See
http://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
Warning: There were 3 chains where the estimated Bayesian Fraction of Missing Information was low. See
http://mc-stan.org/misc/warnings.html#bfmi-low
Warning: Examine the pairs() plot to diagnose sampling problems
Checking again,
check_div(fit)
[1] "52 of 4000 iterations ended with a divergence (1.3%)"
[1] "Try running with larger adapt_delta to remove the divergences"
we see that while the divergences were reduced they did not completely vanish. In order to argue that divergences are only false positives, the divergences have to be completely eliminated for some adapt_delta sufficiently close to 1. Here we could continue increasing adapt_delta, where we would see that the divergences do not completely vanish, or we can analyze the existing divergences graphically.
If the divergences are not false positives then they will tend to concentrate in the pathological neighborhoods of the posterior. Falsely positive divergent iterations, however, will follow the same distribution as non-divergent iterations.
Here we will use the partition_div function of the stan_utility module to separate divergence and non-divergent iterations,
c_dark <- c("#8F272780")
green <- c("#00FF0080")
partition <- partition_div(fit)
div_params <- partition[[1]]
nondiv_params <- partition[[2]]
par(mar = c(4, 4, 0.5, 0.5))
plot(nondiv_params$'theta[1]', log(nondiv_params$tau),
col=c_dark, pch=16, cex=0.8, xlab="theta[1]", ylab="log(tau)",
xlim=c(-20, 50), ylim=c(-1,4))
points(div_params$'theta[1]', log(div_params$tau),
col=green, pch=16, cex=0.8) | 4,084 | 16,087 | {"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": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.140625 | 3 | CC-MAIN-2024-38 | latest | en | 0.869343 |
https://docs.scipy.org/doc/numpy-dev/reference/generated/numpy.convolve.html | 1,496,043,227,000,000,000 | text/html | crawl-data/CC-MAIN-2017-22/segments/1495463612036.99/warc/CC-MAIN-20170529072631-20170529092631-00205.warc.gz | 924,201,081 | 4,059 | # numpy.convolve¶
numpy.convolve(a, v, mode='full')[source]
Returns the discrete, linear convolution of two one-dimensional sequences.
The convolution operator is often seen in signal processing, where it models the effect of a linear time-invariant system on a signal [R17]. In probability theory, the sum of two independent random variables is distributed according to the convolution of their individual distributions.
If v is longer than a, the arrays are swapped before computation.
Parameters: a : (N,) array_like First one-dimensional input array. v : (M,) array_like Second one-dimensional input array. mode : {‘full’, ‘valid’, ‘same’}, optional ‘full’: By default, mode is ‘full’. This returns the convolution at each point of overlap, with an output shape of (N+M-1,). At the end-points of the convolution, the signals do not overlap completely, and boundary effects may be seen. ‘same’: Mode ‘same’ returns output of length max(M, N). Boundary effects are still visible. ‘valid’: Mode ‘valid’ returns output of length max(M, N) - min(M, N) + 1. The convolution product is only given for points where the signals overlap completely. Values outside the signal boundary have no effect. out : ndarray Discrete, linear convolution of a and v.
scipy.signal.fftconvolve
Convolve two arrays using the Fast Fourier Transform.
scipy.linalg.toeplitz
Used to construct the convolution operator.
polymul
Polynomial multiplication. Same output as convolve, but also accepts poly1d objects as input.
Notes
The discrete convolution operation is defined as
It can be shown that a convolution in time/space is equivalent to the multiplication in the Fourier domain, after appropriate padding (padding is necessary to prevent circular convolution). Since multiplication is more efficient (faster) than convolution, the function scipy.signal.fftconvolve exploits the FFT to calculate the convolution of large data-sets.
References
[R17] (1, 2) Wikipedia, “Convolution”, http://en.wikipedia.org/wiki/Convolution.
Examples
Note how the convolution operator flips the second array before “sliding” the two across one another:
>>> np.convolve([1, 2, 3], [0, 1, 0.5])
array([ 0. , 1. , 2.5, 4. , 1.5])
Only return the middle values of the convolution. Contains boundary effects, where zeros are taken into account:
>>> np.convolve([1,2,3],[0,1,0.5], 'same')
array([ 1. , 2.5, 4. ])
The two arrays are of the same length, so there is only one position where they completely overlap:
>>> np.convolve([1,2,3],[0,1,0.5], 'valid')
array([ 2.5])
numpy.conj
numpy.clip | 627 | 2,577 | {"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} | 2.8125 | 3 | CC-MAIN-2017-22 | longest | en | 0.826643 |
http://math.stackexchange.com/questions/140636/what-is-the-shortest-path-equation-between-2-points-on-a-cone?answertab=oldest | 1,462,460,855,000,000,000 | text/html | crawl-data/CC-MAIN-2016-18/segments/1461860127496.74/warc/CC-MAIN-20160428161527-00218-ip-10-239-7-51.ec2.internal.warc.gz | 186,189,746 | 18,339 | # What is the shortest path equation between 2 points on a cone?
What is the shortest path equation between 2 points (from A to B) on a cone surface?
$A= (x_1,y_1,z_1)$ and $B=(x_2,y_2,z_2)$ and cone equation is $x^2+y^2=r^2z^2$
I know that the shortest path is a line on the cone surface as shown below but I do not know how to convert it to 3D curve path equation.
-
Since you know it's a line on the unrolled surface, what you need is the transformation from that surface to the actual surface. Using $r$ for the slope of the cone seems a bit confusing; I'll take the liberty to rename that to $m$ and use $r$ for the distance from the origin as usual.
The opening angle of the cone is $\alpha=\arctan m$. The point $(r\cos\phi,r\sin\phi)$ on the unrolled surface corresponds to the point $(r\sin\alpha\cos(\lambda\phi),r\sin\alpha\sin(\lambda\phi),r\cos\alpha)$ on the cone, where the factor $\lambda$ between the angles in the plane and the angles on the cone is determined by the condition that the circles on the cone have $\sin\alpha$ times the length that they would have in the plane, so we need $\lambda=1/\sin\alpha$.
Now use the polar equation for a line,
$$r=\frac{r_0}{\sin(\phi-\phi_0)}\;,$$
to find the equation of the geodesic on the cone, parametrized by $\phi$:
$$\vec x(\phi)=\frac{r_0}{\sin(\phi-\phi_0)}\pmatrix{\sin\alpha\cos\frac\phi{\sin\alpha}\\\sin\alpha\sin\frac\phi{\sin\alpha}\\\cos\alpha}\;.$$
Here's a plot for $\alpha=\pi/10$, $r_0=1$, $\phi_0=0$.
P.S: Perhaps I should add that while your image of the cone rolled out on a plane shows the cone once, we can continue across the boundaries in your image and keep wrapping around the cone, with the angle on the cone always changing by $1/\sin\alpha$ times the change of $\phi$ in the plane. Since a line subtends exactly an angle of $\pi=(2\pi)/2$ with respect to the origin (unless it's a line through the origin, which would simply map to a straight line through the apex of the cone), every geodesic on the cone wraps around the cone exactly $1/(2\sin\alpha)$ times.
-
Some work is needed, I give just a start..
First, you should transpose the carthesian 3d coordinate on polar 2d coordinate for the projection of the cone on the plane. The distance is just the distance between the origin and the point on the cone so:
$$d=\sqrt{x^2+y^2+z^2}$$ For finding the angle you need to impose that a circle at $r^2z^2=1$ (that is long $2\pi$) mantain his lenght when transposed into an arc in polar coordinate ($=d*\alpha$). $$\theta=\frac{1}{\sqrt{1+r^2}}\arctan (y/x)+\theta_0$$
Now you need to introduce 2d cartesian coordinate on the projection, setting: $$X=d*\sin(\theta)$$ $$Y=d*\cos(\theta)$$
Now you should convert $(x,y,z)\rightarrow(X,Y)$, find the equation of the line in $(X,Y)$ and then do the inverse transformation $(X,Y)\rightarrow(x,y,z)$.
Some care are needed for chooing the angle $\theta_0$, the easier choice is putting one of the two point at $\theta=0$, and choosing what geodesic (there are a lot of them, take a look here). Analitically do the invertion don't seem easy, depends on what are you are interested on (finding the equation in $x,y,z$? finding the equation in polar 3d coordinate (that should be easier)? calculate the lenght of the geodesic(that can be done in 2d coordinate)?).
edit: take a look also at this PDF.
- | 955 | 3,354 | {"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} | 4.15625 | 4 | CC-MAIN-2016-18 | latest | en | 0.894643 |
https://nathanielpark.com/hisense-mini-uijded/parametrize-the-intersection-of-two-planes-1b8d59 | 1,723,003,328,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722640667712.32/warc/CC-MAIN-20240807015121-20240807045121-00415.warc.gz | 335,386,934 | 19,767 | # parametrize the intersection of two planes
And what we're going to do is have two parameters. Then since $x = 3y + 2$, we have that $t = 3y + 2$ and so $y = \frac{t}{3} - \frac{2}{3}$. Since this is a system of two equations and three unknowns, we know we can't solve it for a unique $(x,y,z)$. In order to parametrize a line, you need to know at least one point on the line, and the direction of the line. Plugged in z = 2 into the plane x 2 3 + y 2 + 2 5 = 1. Still contains (0,t,0) though. 2. So this is the x-z plane. Parametrization of lines. Generally speaking, the intersection of two surfaces in 3 dimensional space can be a bunch of complicated curves, even if the surfaces are fairly simple. ?, ???b??? 2. But here, … ?r=a\bold i+b\bold j+c\bold k??? Also by the intersection of x=0 and y=0 we get the line which is z-axis, similarly you can easily see that by the intersection of z=0 and y=0 we get line which is x-axis. Write a vector equation that represents this line. Use the following parametrization for the curve s generated by the intersection: s(t)=(x(t), y(t), z(t)), t in [0, 2pi) x = 5cos(t) y = 5sin(t) z=75cos^2(t) Note that s(t): RR -> RR^3 is a vector valued function of a real variable. I think you'd better stick with the normal and cross product method. By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy. To this point (in both Calculus I and Calculus II) we’ve looked almost exclusively at functions in the form $$y = f\left( x \right)$$ or $$x = h\left( y \right)$$ and almost all of the formulas that we’ve developed require that functions be in one of these two … I got $x(t)=\sqrt3cos(t)$ and $y(t)=sin(t)$. A segment S intersects P only i… How do you know how much to withold on your W2? Thanks for contributing an answer to Mathematics Stack Exchange! The normal vector to each plane will be orthogonal to the line of intersection (since the line lies in both planes). Now to get the parametric equations of the line, just break the vector equation of the line into the x, y, and z components. In this section we will take a look at the basics of representing a surface with parametric equations. When t = 0 we have x = 7 and when t = 1 we have x = 2.. The two normals are (4,-2,1) and (2,1,-4). Section 6-3 : Equations of Planes. The point x = p + s a + t b (in cyan) sweeps out all points in the plane as the parameters s and t sweep through their values. The parametric equations for the line of intersection are given by. In this case we can express y and z,and of course x itself, in terms of x on each of the two green curves, so we can "parametrize" the intersection curves by x: From the second equation we get y2 = 2 xz, and substituting into the first equations gives x2z - x (2 xz) = 4, or z = -4/ x2 -- from which we can see immediately that the z -values will be negative. We may as well put t = 1 at (2, 3) since that's a reasonable number.. Look at x and t first. with our vector equation ?? This type of intersection is called complete intersection. ), \begin{align} Then describe the projections of this curve on the three coordinate planes. Then describe the projections of this curve on the three coordinate planes. The next step is to parametrize the ellipse, and recall that the parametrization for the $z$ coordinate is $z(t) = 2$. Parameterization of Curves in Three-Dimensional Space. We would like a more general equation for planes. between two given points through a point and perpendicular to a given plane through a point and perpendicular to two given lines tangent to a curve r(t) at t= a given as the intersection of two planes Parametrize other simple curves (circles) Check whether lines intersect Take a limit (by taking the limit of each component) Now we’ll plug ???v??? MathJax reference. ?? Sometimes we can describe a curve as an equation or as the intersections of surfaces in $\mathbb{R}^3$, however, we might rather prefer that the curve is parameterized so that we can easily describe the curve as a vector equation.We will now look at some examples of parameterizing curves in $\mathbb{R}^3$. Notice that this parameterization involves two parameters, $$u$$ and $$v$$, because a surface is two-dimensional, and therefore two variables are needed to trace out the surface. \frac{5}{3} \cdot \frac{x^2}{3} + \frac{5}{3} \cdot y^2 &= \frac{5}{3} \cdot \frac{3}{5} \\ Use sine and cosine to parametrize the intersection of the cylinders x^2+y^2=1 and x^2+z^2=1 (use two vector-valued functions). We can find the vector equation of that intersection curve using these steps: Hi! If two planes intersect each other, the intersection will always be a line. Get more help from Chegg. Therefore the line of intersection can be obtained with the parametric equations $\left\{\begin{matrix} x = t\\ y = \frac{t}{3} - \frac{2}{3}\\ z = \frac{t}{12} - \frac{2}{3} \end{ma… How can I buy an activation key for a game to activate on Steam? Here we have$h = k = 0$,$a = \sqrt{\frac{9}{5}} = \frac{3}{\sqrt{5}}$, and$b = \sqrt{\frac{3}{5}}$. The parameterization should be at (7, 9) when t = 0 and should draw the line from right to left.. We're told that t = 0 should be (7, 9). Parametrize the line that goes through the points (2, 3) and (7, 9). This calculator will find out what is the intersection point of 2 functions or relations are. z = r ( t) 3. z=r (t)_3 z = r(t) . The projection of curve (A) onto the xy-plane is a vertical line, hence the corresponding projection is (ii). Subtract them and get x-z=0. Match the space curves … So one parameter is going to be the angle between our radius and the x-z plane. In the drawing below, we are looking right down the line of intersection, and we get an idea as to why the cross product of the normals of the red and blue planes generates a third vector, perpendicular to the normal vectors, that defines the direction of the line of intersection. Therefore, we can get the direction vector of the line by taking the cross product of the two planes’ normal vectors. x^{2}+y^{2}=9 \text { and } z=x+y Enroll in one of our FREE online STEM summer camps. ?, the cross product of the normal vectors of the given planes. in both equations, we get, To find the line of intersection, first find a point on the line, and the cross product of the normal vectors, Plugging ???x=2??? Derivation of curl of magnetic field in Griffiths. Answer to: Find a vector equation for the line of intersection formed by the intersection of the two planes 2x-y+z=5 and x+y-z=1. ?, we can say that, Therefore, the parametric equations for the line of intersection are. Where is the energy coming from to light my Christmas tree lights? The plane is determined by the point p (in red) and the vectors a (in green) and b (in blue), which you can move by dragging with the mouse. Does a private citizen in the US have the right to make a "Contact the Police" poster? The sphere is centered at the origin with a radius of sqrt(5) and the plane in perpendicular to the z-axis that runs through the origin, so the center of the circle is on the z-axis....at (0,0,1). Let me do that in the same color. For integrals containing exponential functions, try using the power for the substitution. Two cylinders of revolution can not have more than two common real generatrices. Example 1. Line of intersection of two planes FP3 Vectors Quickest way to find a point of intersection between two planes. Generate the vector function that describes the intersection curve using the formulas. (x13.5, Exercise 65 of the textbook) Let Ldenote the intersection of the planes x y z= 1 and 2x+ 3y+ z= 2. We will also see how the parameterization of a surface can be used to find a normal vector for the surface (which will be very useful in a couple of sections) and how the parameterization can be used to find the surface area of a surface. I got y 2 = 9 − 5 x 2 Then I substituted y 2 into the plane x 2 3 + 9 − 5 x 2 + 2 5 = 1 to solve for x 2. Get 1:1 help now from expert Calculus tutors Solve it … Parametrization of a plane. (b) A displaced circle. View Answer Parametrize the intersection of the surfaces y2 − z2 = x − 2, y2 + z2 = 9 Using t = y as the parameter (two vector functions are needed as in Example 3). Use sine and cosine to parametrize the intersection of the cylinders x^2+y^2=1 and x^2+z^2=1 (use two vector-valued functions). Popper 1 10. between two given points through a point and perpendicular to a given plane through a point and perpendicular to two given lines tangent to a curve r(t) at t= a given as the intersection of two planes Parametrize other simple curves (circles) Check whether lines intersect Take a limit (by taking the limit of each component) Parameterize the line of intersection of the planes$x = 3y + 2$and$y = 4z + 2$by letting$x = t$. so the parametric equation is$\mathbf{\{\sqrt3cos(t), sin(t), 2\}}$? Calculus Parametric Functions Introduction to ... and sin(t), with positive coefficients, to parametrize the intersection of... See all questions in Introduction … A parametrization for a plane can be written as. 4. Be able to –nd the points at which a line intersect with the coordinate planes. 1.5.2 Planes Find parametric equations for the line segment joining the first point to the second point. So one parameter is going to be the angle between our radius and the x-z plane. Plugged in$z=2$into the plane$\frac {x^2} {3}+y^2+\frac 25=1$. Otherwise, when the denominator is nonzero and rI is a real number, then the ray R intersects the plane P only when . For the plane ???2x+y-z=3?? For example, for g(x,y,z) = z−x2−y2 = 0, we have the graph z = x2 + y2 of the function f(x,y) = x2 + y2 which is a paraboloid. It only takes a minute to sign up. To get it, we’ll use the equations of the given planes as a system of linear equations. Have Texas voters ever selected a Democrat for President? (Recall that the standard form is$\frac{(x - h)^2}{a^2} + \frac{(y - k)^2}{b^2} = 1$. Do Magic Tattoos exist in past editions of D&D? They intersect along the line (0,t,0). Any point x on the plane is given by s a + t b + c for some value of ( s, t). into the vector equation. ?r=a\bold i+b\bold j+c\bold k???. If we set ???z=0??? Assume we have a ray R (or segment S) from P0 to P1, and a plane P through V0 with normal n. The intersection of the parametric line L: and the plane P occurs at the point P(rI) with parameter value: When the denominator , the line L is parallel to the plane P , and thus either does not intersect it or else lies completely in the plane (whenever either P0 or P1 is in P ). Note however that most surfaces of the form g(x,y,z) = c can not be written as graphs. Sign in Register; Hide. Then describe the projections ofjjthis curve onto the three coordinate planes. However, none of those equations had three variables in them and were really extensions of graphs that we could look at in two dimensions. And what we're going to do is have two parameters. Use sine and cosine to parametrize the intersection of the cylinders x2 + y2 = 1 and x2 + z2 = 1 (use two vector-valued functions). ?r=2\bold i-\bold j+0\bold k+0\bold it-3\bold jt-3\bold kt??? Two non-parallel planes intersect not at a single point but at a collection of points which is a line. semi ellipsoid and cylinder parametrize the curve, Vector Valued Functions: Parametrize the intersection of 2 surfaces w/ trigonometric functions, Line integral, curve of intersection between elliptic sylinder and plane, Find the line of intersection between 2 planes. x = s a + t b + c. where a and b are vectors parallel to the plane and c is a point on the plane. is a point on the line and ???v??? Notes. The normal vectors ~n 1 and ~n Parametrization of the intersection of a cone and plane. The vector equation for the line of intersection is given by. Find the parametric equations for the line of intersection of the planes. Then describe the projections ofjjthis curve onto the three coordinate planes. The intersection of two planes is an infinitely long line! That's a different plane. Therefore, it shall be normal to each of the normals of the planes. ?r=2\bold i-\bold j-3\bold jt-3\bold kt??? ?, we get, Putting these values together, the point on the line of intersection is. Step-by-step math courses covering Pre-Algebra through Calculus 3. math, learn online, online course, online math, orthogonal trajectories, family of curves, differential equations, math, learn online, online course, online math, u-sub, u-substitution, substitution, integrals, integration. Try a simpler example. A direction vector for the line of intersection of the planes x−y+2z=−4 and 2x+3y−4z=6 is a. d=i−j+5k Practical example, Algorithm for simplifying a set of linear inequalities, How Close Is Linear Programming Class to What Solvers Actually Implement for Pivot Algorithms. To reach this result, consider the curves that these equations define on certain planes. line and when two lines intersect then we get a plane containing these two lines. The intersection of two surfaces will be a curve, and we can find the vector equation of that curve. ?r=(2)\bold i+(-1-3t)\bold j+(-3t)\bold k?? \frac{x^2}{\frac{9}{5}} + \frac{y^2}{\frac{3}{5}} &= 1 projection is (iii), rather than the two other graphs. The sphere is an example, where we need two graphs to cover it. Thus, find the cross product. Find the symmetric equation for the line of intersection between the two planes x + y + z = 1 and x−2y +3z = 1. One is the angle that this radius makes with the x-z plane, so you can imagine the x-axis coming out. ... there is a geometric theorem that says “if two lines in a plane are perpendicular to the same line, they are parallel to each other.” Explain why this is true by writing and comparing equations for two different lines that are perpendicular to y=-1/3x . Technology-enabling science of the computational universe. Why is "issued" the answer to "Fire corners if one-a-side matches haven't begun"? The projection of curve (B) onto the xy-plane is a periodic wave as illustrated in (i). Note that the equation (P) implies y = 2−x, and substituting this into equation (S) gives: x2 +(2−x)2 +z2 = 9 x2 +4−4x+x2 +z2 = 9 2x2 −4x+z2 = 5 This calculator will find out what is the intersection point of 2 functions or relations are. The intersection of two planes is always a line. By recognizing how lucky you are! How do you find the vector parametrization of the line of intersection of two planes #2x - y - z = 5# and #x - y + 3z = 2#? Wolfram Natural Language Understanding System. Homework Statement Parameterize the curve of intersection of the cylinder x^2 + y^2 = 16 and the plane x + z = 5 Homework Equations The Attempt at a Solution i think i must first parameterize the plane x = 5t, y = 0, z = -5t then i think i plug those into the eq. and ???c??? Be able to –nd the points at which a line intersect with the coordinate planes. ?? The normal vector to each plane will be orthogonal to the line of intersection (since the line lies in both planes). parametrization of lines and planes as explained in class, line in the plane is presented in parametrized form if the coordinates of points on the line are. Therefore, we can get the direction vector of the line by taking the cross product of the two planes’ normal vectors. What is the name for the spiky shape often used to enclose the word "NEW!" You can imagine the x-axis coming out here. need answer ASAP. Note that the cylinder can be parametrized as x = 3 cos(t), y = sin(t), where 0 t<2ˇ, with z2R. Step 1: Find an equation satisfied by the points of intersection in terms of two of the coordinates. I am not sure how to do this problem at all any help would be great. parametrize the line that lies at the intersection of two planes. The intersection of two planes is an infinitely long line! MAINTENANCE WARNING: Possible downtime early morning Dec 2, 4, and 9 UTC…, Intersection curve between a circle and a plane - Stokes theorem. we’ll talk about Friday) with a plane. Find a vector function that represents the curve of intersection of the cylinder x2+y2 = 9 and the plane x+ 2y+ z= 3. Plugging these in the equation of the plane gives z= 3 x 2y= 3 3cos(t) 6sin(t): The curve of intersection is therefore given by The parameters s and t are real numbers. Some geometry helps. The cross product of the normal vectors is, We also need a point on the line of intersection. site design / logo © 2020 Stack Exchange Inc; user contributions licensed under cc by-sa. Find the total length of this intersection curve. This case appears when the axes of the cylinders are not parallel and the two cylinders have two common tangent planes. ... Intersection of Planes Solving Equations. For this reason, a not uncommon problem is one where we need to parametrize the line that lies at the intersection of two planes. Here is what I did. How many computers has James Kirk defeated? use sine and cosine to parametrize the intersection of the surfaces x^2+y^2=1 and z=4x^2 (use two vector valued functions). ?? Read more. N 1 ´ N 2 = 0.: When two planes intersect, the vector product of their normal vectors equals the direction vector s of their line of intersection,. Try setting z = 0 into both: x+y = 1 x−2y = 1 =⇒ 3y = 0 =⇒ y = 0 =⇒ x = 1 So a point on the line is (1,0,0) Now we need the direction vector for the line. Knowledge-based, broadly deployed natural language. Parametrize the intersection of the plane y = 1/2 with the sphere x^2 + y^2 + z^2 = 1. In order to get it, we’ll need to first find ???v?? z = f(x,y) of a function of two variables. 1.5.2 Planes Find parametric equations for the line segment joining the first point to the second point. ?, the normal vector is ???a\langle2,1,-1\rangle??? Thanks and ???r_0??? Let me do that in the same color. We need to find the vector equation of the line of intersection. Section 3-1 : Parametric Equations and Curves. First, the line of intersection lies on both planes. Matching up ?? Here is what I did. Two planes cannot meet in more than one line. Parametrize the intersection of the surfaces using t = y as the parameter. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. They're two-dimensional vectors, but we can extend it to an arbitrary number of dimensions. The line of intersection will have a direction vector equal to the cross product of their norms. Added Dec 18, 2018 by Nirvana in Mathematics. We start be attemping to solve this system of two equations. p 1:x+2y+3z=0,p 2:3x−4y−z=0. back into ???x-y=3?? ?r=(2)\bold i+(-1-3t)\bold j+(-3t)\bold k??? You can imagine the x-axis coming out here. Parameterizing the Intersection of a Sphere and a Plane Problem: Parameterize the curve of intersection of the sphere S and the plane P given by (S) x2 +y2 +z2 = 9 (P) x+y = 2 Solution: There is no foolproof method, but here is one method that works in this case and But this is consistent with our above conclusion that the intersection is a line, not a point. where ???a?? 1 = 4 To find a parametrization of the curve of intersection… L: x = -t. y = -2. z = 3 + 2t _____ Then find the intersection point between the line above and the plane which passes thru the original point and. a curve of the 4th order with one double points, which occurs when the cylinders have a common tangent plane. So just to kind of hit the point home, let's do one more example in R2, where, it's kind of the classic algebra problem where you need to find the equation for the line. ?, the normal vector is ???b\langle1,-1,1\rangle??? Use MathJax to format equations. Why are manufacturers assumed to be responsible in case of a crash? Did something happen in 1987 that caused a lot of travel complaints? in adverts? Uploaded By 1717171935_ch. 3. rev 2020.12.8.38142, The best answers are voted up and rise to the top, Mathematics Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us. 9. Find parametric equations for the line L. 2 (a) A circle centered at the origin. 23. I'm krista. Pages 15. Dublin City University. School University of Illinois, Urbana Champaign; Course Title MATH 210; Type. I am not sure how to do this problem at all any help would be great. The vector normal to the plane is: n = Ai + Bj + Ck this vector is in the direction of the line connecting sphere center and the center of the circle formed by the intersection of the sphere with the plane. Since$y = 4z + 2$, then$\frac{t}{3} - \frac{2}{3} = 4z + 2$, and so$z = \frac{t}{12} - \frac{2}{3}$. So this is the x-z plane. 23 Use sine and cosine to parametrize the intersection of the surfaces x 2 y 2. 26. With the vector equation for the line of intersection in hand, we can find the parametric equations for the same line. are the coefficients from the vector equation ?? Parametrize the intersection of 2 planes. Adding and subtracting the plane equations isn't getting you any closer to finding the intersection. I'm afraid you have make something wrong.Plugged in$z=2$into the plane$\frac {x^2} {3}+y^2+\frac 25=1$. For example, in my textbook there is a question escribe the intersection of the sphere x^2+y^2+z^2=1 and the elliptic cylinder x^2+2z^2=1. There are, of course, many ways to parametrize a line. How can I install a bootable Windows 10 to an external drive? In the first section of this chapter we saw a couple of equations of planes. 23 use sine and cosine to parametrize the. I got$y^2=9-5x^2$Then I substituted$y^2$into the plane$\frac {x^2} {3}+9-5x^2+\frac25=1$to solve for$x^2$. I got x 2 = 1.8 and then got y = 0. One is the angle that this radius makes with the x-z plane, so you can imagine the x-axis coming out. This preview shows page 9 - 11 out of 15 pages. Dear @user95087, you have the right idea, however your answer would be incorrect due to a mistake I made in my original post - please see my edited post. r = r 0 + t … Thanks Example 1. 2. Can I build a wheel with two different spoke types? When two three-dimensional surfaces intersect each other, the intersection is a curve. This type of intersection is called partial intersection. (x13.5, Exercise 65 of the textbook) Let Ldenote the intersection of the planes x y z= 1 and 2x+ 3y+ z= 2. 9) Find a set of scalar parametric equations for the line formed by the two intersecting planes. p1 = (2,0,1) and p2 = (0,4,0). 4. Why is my half-wave rectifier output in mV when the input is AC 10Hz 100V? where ???r_0??? University. An intersection point of … 3. Parametrize the intersection of$\frac {x^2} {3}+y^2+\frac {z^2} {10} = 1$with$z=2$(level curve) plane. What is an escrow and how does it work? Be able to –nd the angle between two lines which intersect. Be able to tell if two lines are parallel, intersect or are skewed. In general, we need to restrict the function to a do-main D in the plane like for f(x,y) = 1/y, where (x,y) is defined everywhere except on the x-axes y = 0. I got$x^2=1.8$and then got$y=0$. In short, there are multiple ways to express the solution, but there is still only one solution. The intersection of a sphere and a plane is a circle. For example, in my textbook there is a question escribe the intersection of the sphere x^2+y^2+z^2=1 and the elliptic cylinder x^2+2z^2=1. N 1 ´ N 2 = s.: To write the equation of a line of intersection of two planes we still need any point of that line. The intersection user contributions licensed under cc by-sa the points of intersection of two of the given.... Its direction user contributions licensed under cc by-sa cylinders of revolution can not meet in more than two tangent. Of travel complaints output in mV when the input is AC 10Hz 100V Magic Tattoos exist past! When two lines '' the answer to Fire corners if one-a-side matches have n't begun '',... Example: parametrize the line that goes through the other in my textbook there is still only one.. Of … a parametrization for a game to activate on Steam on opinion ; back up. Fire corners if one-a-side matches have n't begun '' direction vector the. Key for a game to activate on Steam and?????? a\langle2,1, -1\rangle??. They 're two-dimensional vectors, but there is a question escribe the intersection of the normal and cross of..., what does not compromise sovereignty '' mean in both planes there are, of Course many... Our radius and the two planes is always a line in the first section of this chapter we saw couple... Containing these two lines which intersect not be written as writing great answers of dimensions making statements based on ;! Match the space curves … they 're two-dimensional vectors, but there is still only one solution?. ) _3 z = r ( t )$ and $y t... Vectors Quickest way to find a point of our FREE online STEM camps!, 2018 by Nirvana in Mathematics two-dimensional vectors, but there is a circle centered the... The substitution -4 ) have two common tangent planes planes as a system of linear equations other the... It shall be normal to each plane will be orthogonal to the line intersection! = 1 planes x=0 and z=0 we get the direction vector of the line of intersection vectors of the are. Ac 10Hz 100V you can find the vector equation of the cylinders are not parallel and x-z... The plane x+ 2y+ z= 3 your answer ”, you can imagine the x-axis coming out caused a of. Issued '' the answer to Mathematics Stack Exchange Inc ; user contributions licensed under cc by-sa in =... By taking the cross product method of the sphere x^2+y^2+z^2=1 and the x-z plane points 2. Or are skewed or responding to other answers chapter we saw a couple of equations of the x^2+y^2=1. X+ 2y+ z= 3 same line math 210 ; Type z= 3 at all help! Can say that, therefore, it shall be normal to each of the cross product the. The cross product of the plane x 2 3 + y z = r ( t ) we saw couple... Are multiple ways to parametrize a line to tell if two planes normal... Projections of this curve on the three coordinate planes rock your math class +y^2+\frac 25=1$ are, Course! Orthogonal to the line of intersection is a line a cone and.! P only when intersection is a periodic wave as illustrated in ( i ) v?... Under cc by-sa? b\langle1, -1,1\rangle?? z=0???? v?? a\langle2,1,?. Scalar parametric equations for the line segment joining the first point to the line which is question. To parametrize the line of intersection of a crash a more general equation for line... { 3 } +y^2+\frac 25=1 $finding the intersection of two cylinders is two conics 10 to an external?...? b\langle1, -1,1\rangle??? v???? a\langle2,1, -1\rangle????... 4, -2,1 ) and p2 = ( 0,4,0 ) define on certain planes out of 15.... Line by taking the cross product of the cylinders have a common tangent plane goes through the points 2. Projection is ( iii ), sin ( t ) _3 z = r ( )., but there is a circle Friday ) with a plane containing these two are... To parametrize a line =9 \text { and } z=x+y Enroll in one our. Would be great one double points, which occurs when the cylinders x^2+y^2=1 and (! +Y^ { 2 } +y^ { 2 } +y^ { 2 parametrize the intersection of two planes +y^ { 2 } \text. Any help would be great the name for the line of intersection is periodic... Line L. 2 ( a ) a circle, what does not compromise sovereignty ''?! \Frac { x^2 } { 3 } +y^2+\frac 25=1$ intersect along the line ( 0, )... Intersection between two planes ’ normal vectors of the planes x=0 and z=0 we get direction., Urbana Champaign ; Course Title math 210 ; Type ( iii ) 2\. Double points, which occurs when the cylinders x^2+y^2=1 and z=4x^2 ( use two vector-valued functions.... I buy an activation key for a plane planes ’ normal vectors zero... ) =sin ( t ) define on certain planes 2y+ z= 3 vs i am not sure how do! We 're going to do this problem at all any help would great! Circle centered at the basics of representing a surface with parametric equations for the line segment the. Single point but at a collection of points which is our y-axis surfaces x^2+y^2=1 and x^2+z^2=1 ( two... One solution, 2018 by Nirvana in Mathematics section of this curve on the three coordinate planes scalar. My half-wave rectifier output in mV when the input is AC 10Hz 100V the input is AC 10Hz?. And x^2+z^2=1 ( use two vector-valued functions ) two graphs to cover it this of! Finding the intersection of a cone and plane = 2 into the plane ${. Our terms of two planes ’ normal vectors of the two planes is always a line the angle between lines! It work 2020 Stack Exchange Urbana Champaign ; Course Title math 210 ; Type parametrize a line? a\langle2,1 -1\rangle... Plane can be written as graphs ray r intersects the plane P only when a vertical line, the. Ways to parametrize a line 1/2 with the coordinate planes first, the parametric equations for line! 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Policy and cookie policy +t ( 0\bold i-3\bold j-3\bold k ) +t ( 0\bold i-3\bold j-3\bold )... Lines intersect then we get a plane containing these two lines intersect then we,. J-3\Bold k )????? v?? v???. Line of intersection p1 = ( 0,4,0 ) parametrize the intersection of two planes way to find a function! People studying math at any level and professionals in related fields a wheel with two spoke! To help you rock your math class 1/2 with the x-z plane } +y^ { 2 =9. Equations of the coordinates a surface with parametric equations for the line of intersection of curve ( a onto! I got x 2 3 + y z = r ( t ) =sin t... $x ( t ), rather than the two normals are ( 4, -2,1 ) (! I-3\Bold j-3\bold k )?? a\langle2,1, -1\rangle????... At which a line the denominator is nonzero and rI is a curve x^2=1.8$ and $(! Vector product of the line of intersection ( since the line lies in both planes ) RSS..: Hi they intersect along the line lies in both planes ) 2 ( a ) a...., 9 ) find a set of scalar parametric equations for the line formed by the two planes certain.. A point on the line segment joining the first point to the second point,. P2 = ( 2,0,1 ) and ( 7, 9 ) find a point on the L.... 3X+2Y+Z=1 and check the parametrization lies intersects the plane$ \frac { x^2 } { 3 } +y^2+\frac 25=1.... Travel complaints periodic wave as illustrated in ( i ) of Course, many ways to the... i am not really into it '' this result, consider the curves these. Plane x+ 2y+ z= 3, we get the direction vector of given. To parametrize a line NEW! only one solution 3 + y z =.! Or responding to other answers subtracting the plane x+ 2y+ z= 3 a single point but at collection! At a collection of points which is a question escribe the intersection of the planes and! Right to make a Contact the Police '' poster matches have n't begun?! -3T ) \bold j+ ( -3t ) \bold i+ ( -1-3t ) \bold (. Attemping to solve this system of linear equations the cylinder x2+y2 = 9 and the x-z plane, you. Escribe the intersection will always be a line at a collection of points which is our y-axis ''! | 8,445 | 32,063 | {"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": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.1875 | 4 | CC-MAIN-2024-33 | latest | en | 0.913326 |
https://gpuzzles.com/mind-teasers/rebus-word-brain-teaser/ | 1,500,728,068,000,000,000 | text/html | crawl-data/CC-MAIN-2017-30/segments/1500549424060.49/warc/CC-MAIN-20170722122816-20170722142816-00542.warc.gz | 649,661,002 | 11,019 | • Views : 70k+
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# Mind Teasers : Rebus Word Brain Teaser
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what word does this rebus means ?
Discussion
Suggestions
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# Mind Teasers : Tough River Crossing Riddle
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This one is a bit of tricky river crossing puzzle than you might have solved till now. We have a whole family out on a picnic on one side of the river. The family includes Mother and Father, two sons, two daughters, a maid and a dog. The bridge broke down and all they have is a boat that can take them towards the other side of the river. But there is a condition with the boat. It can hold just two persons at one time (count the dog as one person).
No it does not limit to that and there are other complications. The dog can’t be left without the maid or it will bite the family members. The father can’t be left with daughters without the mother and in the same manner, the mother can’t be left alone with the sons without the father. Also an adult is needed to drive the boat and it can’t drive by itself.
How will all of them reach the other side of the river?
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# Mind Teasers : Terrorist Attack Security Puzzle
Difficulty Popularity
UNO plans a gathering.
However there is threat of terrorist attack. So security guard who is a mathematical plans somethings to secure the place.
A terrorist stands nearby the door where
1st ambassador comes , the security guard said 'twelve' and ambassador replied with 'six'.
2nd ambassador comes , the security guard said 'six' and ambassador replied with 'three'.
The terrorist thinks its enough and walks to the door.
The security person said 'eight' , terrorist replied 'four' and get immediately arrested.
why ?
• Views : 70k+
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# Mind Teasers : How Many Seconds In A Year Riddle
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Without the use of calculation, can you find how many seconds are there in a year ?
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# Mind Teasers : Matchsticks Picture Brain Teaser
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In the figure given below, you can see that there are five squares. Supposedly if this figure is formed using different matchsticks (refer the slight gap between matchsticks), can you remove just two matchsticks so that only two squares remain ?
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# Mind Teasers : Break Chocolate Bar Logic Puzzle
Difficulty Popularity
You have a rock solid dark chocolate bar of size 2 x 8. You need to break it and get 1 x 1 pieces of that chocolate.
If you can break that bar only along its length or breadth, how many times will you have to break to get the 1 x 1 pieces?
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# Mind Teasers : Suicide Mystery Riddle
Difficulty Popularity
A man 5'11" high is found dead in an closed room.
This room is found empty with some puddle of water.
The man was died by hanging himself to a 12 feet high fan.
How did the man die ?
• Views : 40k+
• Sol Viewed : 10k+
# Mind Teasers : Draw Direction Problem
Difficulty Popularity
B is to the North-East of D; A is to the North-East of C; C is to the West of D; E is to the South-West of D and to the South of C; and A is to the north of D and in line with B.
Can you find out in which direction of E is B located?
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• Sol Viewed : 10k+
# Mind Teasers : Riddle 1 - 1 !=3
Difficulty Popularity
Can you move four matchsticks to make the equation true?
• Views : 80k+
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# Mind Teasers : Tricky Maths Riddle
Difficulty Popularity
Hockey Stick and ball cost \$50. If the Stick cost \$49 more than the ball.
what is the cost of each ?
• Views : 80k+
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# Mind Teasers : Tough Number Problem Riddle
Difficulty Popularity
Find smallest number that you can write using all the vowels(A,E,O,I,U) exactly once?
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In his mathematics activity class, Andy ... | 1,126 | 4,455 | {"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} | 2.90625 | 3 | CC-MAIN-2017-30 | latest | en | 0.923221 |
https://apcocoa.uni-passau.de/wiki/index.php?title=ApCoCoA-1:BB.BBasisForMP&diff=prev&oldid=10062 | 1,653,237,914,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662545875.39/warc/CC-MAIN-20220522160113-20220522190113-00720.warc.gz | 161,048,882 | 7,006 | # Difference between revisions of "ApCoCoA-1:BB.BBasisForMP"
## BB.BBasisForMP
Computes the border basis of a zero-dimensional ideal generated by marked polynomials.
### Syntax
```BB.BBasisForMP(F:LIST of LIST):LIST of LIST
```
### Description
The input is a list of tuples [P, T] where P is a polynomial and T must be a term of the support of P such that deg(P) = deg(T). This function computes the border basis of the zero-dimensional ideal I generated by the polynomials P with respect to the given term marking. The output is a list of tuples [P, T] denoting a border basis of I where P is a polynomial and T is the term of the support of P such that deg(P) = deg(T) and T is a border term. An error will be raised if the given term marking does not lead to a successful computation.
• @param F List of tuples [P, T] where P is a polynomial and T must be a term of the support of P such that deg(P) = deg(T). The polynomials P must generate a zero-dimensional ideal.
• @return A list of tuples [P, T] denoting a border basis of I where P is a polynomial and T is the term of the support of P such that deg(P) = deg(T) and T is a border term.
#### Example
```Use Q[x,y], DegLex;
F := [
[ x^2 + xy - 1/2y^2 - x - 1/2y, xy ],
[ y^3 - y, y^3 ],
[ xy^2 - xy, xy^2 ]
];
BB.BBasisForMP(F);
[[x^2 + xy - 1/2y^2 - x - 1/2y, xy],
[y^3 - y, y^3],
[xy^2 + x^2 - 1/2y^2 - x - 1/2y, xy^2],
[x^3 - x, x^3],
[x^2y - 1/2y^2 - 1/2y, x^2y]]
-------------------------------
```
#### Example
```Use Q[x,y,z], DegLex;
F := [
[ x^2 + xy + y^2 - x - 1, x^2 ],
[ xy + y^2 + z, xy ],
[ -x^2 + yz + z + 1, x^2 ]
];
BB.BBasisForMP(F);
[[x^2 - x - z - 1, x^2],
[xy + z^2 + x + z + 1, xy],
[yz - x, yz],
[y^2 - z^2 - x - 1, y^2],
[x^2z - xz - z^2 - z, x^2z],
[xz^2 + xz - z^2 + 2x + y, xz^2],
[xyz - x - z - 1, xyz],
[z^3 + xz + z^2 + x + 2z + 1, z^3],
[yz^2 - xz, yz^2]]
-------------------------------
``` | 699 | 1,899 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.875 | 3 | CC-MAIN-2022-21 | latest | en | 0.779693 |
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# Boolean Algebra
Boolean Algebra is a sub-discipline of algebra which deals with the truth values of specific variables. These truth variables can either be true or false, which are usually denoted in Boolean Algebra as 1 and 0 respectively. Instead of the traditional arithmetic operations seen in Elementary Algebra, Boolean Algebra is mainly concerned with three types of operations: conjunction (and), disjunction (or) and negation (not).
Conjunction is denoted as ∧
Disjunction is denoted as ∨
Negation is denoted as ¬
These operations do not behave like normal arithmetic operations. In Boolean Algebra 1+1 does not equal 2. Instead 1+1 may equal 0, with the + sign being the symbol for another Boolean Operation XOR. Thus, it can be seen that Boolean Algebra stands apart from the realm of Elementary Algebra – as it has its own set of rules and principles.
Boolean Algebra is prevalent in the study of electrical circuits, as a two valued Boolean algebra can be used to describe the operations of a two-valued electrical switching circuit. Thus, it can be seen that understanding Boolean Algebra is crucial for the modern study of Computer Science, Programming, Statistics and Digital Circuits.
### K-Map mimimization
Draw a Karnaugh map (K-map) for the function below and then solve using the Karnaugh map (K-map) you have designed. For each K-map provide ALL SOLUTIONS AVAILABLE by finding all of the EPI and PI groupings and applying the rules for them: This means the K-Map steps for solutions and NOT the Boolean Algebra steps as some tried on
### The solution gives detailed explanations on writting an ABEL program for a combinational logic function with five input bits N4-N0) representing an integer between 0 and 31 and two outputs M3 and M5 to indicate if the number is a multiple of 3 or 5. And my complete is included in the answer also.
Write an ABEL program for a combinational logic function with five input bits N4-N0) representing an integer between 0 and 31 and two outputs M3 and M5 to indicate if the number is a multiple of 3 or 5.
### Boolean Algebra with Conjunction and Disjunction
Please explain Boolean algebra with conjunction and disjunction as case studies.
### Reflexive, Symmetric, Transitive and Boolean products
1. Determine if the relation R on the set of all real numbers is reflexive, symmetric, antisymmetric, and/or transitive where (x,y) R if and only if x = 1. a. reflexive b. symmetric c. antisymmetric d. transitive 2. Find the Boolean product of the two matrices: [ 0 1 0 ] [ 0 1 0 ]
### Boolean Matrix: Airline Flights
Assume the Boolean matrix below is MR, and that MR represents the relation R where R represents the connecting flights that an airline have between four cities: a,b,c,d. The 1 in row a column b means there is a flight from city a to city b. In general, there is a 1 in row x, column y if and only if there is a connecting flight b
### Solving Boolean Algebra Equations
Let B = {0, 1} be a Boolean algebra and let f: B3 →B be the Boolean function such that f(0, 0, 0) = f(1, 0, 0) = f(0, 0, 1) = 1 and f(x, y, z) = 0 for all other (x, y, z) in B3. a) Write f in disjunctive normal form and in conjunctive normal form. b) Give the truth table of f? (the complement of f). c) Give f
### Calculations with Isomorphic Groups
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### Abstract Algebra - Boolean ring
A ring R is called a Boolean ring if a^2=a for all a?R. Let R=P(X)be the power set of X. Define addition and multiplication in R as follows: a+b=(a?b^')?(a^'?b) a×b=a?b Show that (R,+,*) is a Boolean ring.
### Control Systems Problem
A process involves moving speed, load weight, and rate of loading in a conveyor system. The variables are provided as high (1) and low (0) levels for digital control. An alarm should be initiated whenever any of the following occur: a. speed is low; both weight and load rater are high b. speed is high; load rate is low Fi
### Boolean Matrix Questions
Assume the Boolean matrix below is MR and that MR represents the relation R where R represents the connecting flights that an airline has between 4 cities: a, b, c, and d. so there is a 1 in row x column y iff there is a connecting flight between (from) city x and (to)city y That is, the rows of the matrix represent the cities o
### Boolean Algebra and Digital Logic for simple digital circuits
For this module you will design some simple digital circuits based on Boolean expressions. Draw circuits that implement the following Boolean expressions using some combination of AND, OR, NOT, NAND, and NOR gates. (I recommend you draw your circuits on white paper with black pen, scan the images, and paste them into your Word
### Boolean Algebra and Digital Logic
See attached file. Read the required material on Boolean Algebra and circuit design in the Background Information, and complete the problems below. You can locate additional material on the Web (Google "Boolean algebra" , "logic circuits" and "logic gates." if you need further explanations. 1. Convert the following bi
### Boolean Algebra and Karnaugh Mapping
** Please see the attached file for the complete problem description ** Hello, I am struggling with the questions in the attached PDF on Boolean and Karnaugh Mapping. Not sure of the correct sequences to get the answers on questions d i ii iii iv v and e. Could you please show full step by step working and final answer
### Make the given Java class thread safe.
The following class public class HardwareData { private boolean value = false; public HardwareData(boolean value) { this.value = value; } public boolean get() { return value; } public void set(boolean newValue) { value = newValue; } public boolean getAndSet(boolean newValue) {
### Boolean Function/Logic Diagrams/Truth Table !
Consider the Boolean function: F = b'c' + a'bc' A. Represent F using a truth table B. Represent F using a logic diagram that closely matches the algebraic expression (Use only AND gates, OR gates, and inverters). C. Represent F using a logic diagram that contains NAND gates only. Explain how you arrived at your answer.
### Boolean Algebra and circuit design
2. Convert the following decimal numbers to their binary, octal, and hexadecimal equivalents a. 16 b. 32 c. 48 d. 80 3. Do the following work and answer the following questions: a. Explain the relationship between an AND gate and a NAND gate in terms of Boolean Algebra and draw truth tables
### Boolean Function Multiplexer and External Gates.
Implement the following boolean function with a 4x1 multiplexer and external gates. Connect inputs A and B to the selection lines. The input requirements for the four data lines will be a function of variables C and D. These values are obtained by expressing F as a function of C and D for each of the four cases AB = 00, 01, 10 a
### Logic Circuits for Boolean Expressions
1. Using Boolean algebra, reduce the following Boolean expression to its simplest form and implement it using your method of choice. F = A'B'D + ABC' + AB'CD + BC + A'CD + BCD 2. Using a Karnaugh map (K-map), reduce the following Boolean to its simplest form and implement it using SOP (Sum of Products) F = B'C'D + B'D +
### History of Mathematical Happenings
Choose a time in history (pre-20th century) that is of interest to you. It can be any time from ancient Egypt to the American Civil War. Next, visit the following site and choose the link that covers the time period you chose: http://www-groups.dcs.st-and.ac.uk/history/Chronology/index.html Select two of the events listed
### truth table for Boolean Algebra
Construct the truth table of (x y)^ (x¬Y). Is this a contradiction?
### Rules of Products
How many rows are there for any logical expression? containing: (i) Two (logical) variables? Why is the solution 2^2 ? What would be an example of this? Determine the number of different (that is nonequivalent) Boolean functions (logical expressions) containing: (ii) Two Variables? Why is the Solution 2^2^² ? What would b
### Descrete Math multiple choice
Note: Please see attachment for full details. 3. A grammar that has no restrictions on production is called a: A) phrase-structure grammar. B) context-sensitive grammar. C) context-free grammar. D) regular grammar. 5. A Karnaugh map for 6 variables will have __________ squares. A) 16 B) 32 C) 64 D)
### Draw a Combinational Circuit for a Boolean Expression
Digital information can be represented through the use of Boolean algebra, which is an important concept to study if one wishes to understand how computers work. First: I am given an assignment on drawing a combinational circuit that directly implements Boolean expression for F(x, y, z)= xz + (xy + z'). Second: In my
### Using de Morgan's law to complement boolean expression
Using de Morgan's Law, write an expression for the complement of F if F(x, y, z) = xy + x'z + yz' .
### BNF Grammar for Boolean Expressions
A) Create a BNF grammar that describes simple Boolean expressions of the form var AND var var OR var where var is one of the symbols w, x, y, and z. B) Modify your grammar from part (a) so that the Boolean expressions can be of the form expr AND expr expr OR expr where expr is either a simple variable (w, x, y,
### Boolean Algebra
Boolean Algebra Homework Help Required Translating formal propositions ¬ = not ∃ =there exists ∨ = or ≡ equivalent ∀= for all ⇒ =implies ∧ = and ⇔ if and only if (a)An argument to show that two propositions are equivale
### Turing machines for Bitwise and Boolean NOT operations
Give Turing machines for bitwise and boolean NOT operations under following restrictions. - only single tape deterministic turing machines can be used. - The input and output alpahbets should consist of {0,1}* only (and the empty cell symbol #}.
### Simplifying Boolean Equations
Simplify the following to their simplest form showing each step you take: D3 =Q3 Q2 Q1 + Q3 Q2 Q1 D2 = Q3 Q2 Q1 + Q3 Q2 Q1 D1 = Q3 Q1 + Q2 Q1 | 2,609 | 10,925 | {"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-2020-05 | latest | en | 0.919175 |
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