1. ### The Datasaurus Dozen

Same Stats, Different Graphs: Generating Datasets with Varied Appearance and Identical Statistics through Simulated Annealing
2. ### I Prove that in any simple graph with more than two vertices, two equal paths of maximal length must intersect

In order to try and sovle this problem, my idea here was to use an extremal argument, with two equal length maximum paths on a tree. I said that no matter where the two graphs started, they'd end up having to cross paths since if there were two distinct paths with equal lengths the graph would...
3. ### Which Graph is which

Homework Statement (1) Name the waveform(s) that represent a periodical current flow. (2) Name the waveform(s) that represent a direct current. (3) Name the waveform(s) that represent a non-periodical alternating current. (4) Name the waveform(s) that represent a current with a non-positive...
4. ### Hi, I have a quick question about graph transformations.

One of my homework questions said "Explain how to obtain f(x)=-(3+x)^2+1 from the graph of y=x^2." I know somehow you need to move the graph right 3, reflect about the x-axis, and move up one, but I don't know how to factor and manipulate the equation to show this.
5. ### Potential Difference/Voltage-Graph Help Needed (Long)

Homework Statement Alright, this is a Lab Exercise, so it's light on an actual introduction and data, but I'll do my best to put into words the whole thing. The gist of it is that we have a Vat with water, a millimetre paper at the bottom, and we put two Equipotential surfaces inside. We charge...
6. ### Resonating wineglass problem

I have done an experiment where I vary the levels of water in a wineglass and record the frequencies it produces which differ depending on the height of the water. Below you see 1 equation, apparently I can use this equation to mathematically prove my results from my experiment, (this equation...
7. ### B Explanation of what a parameter is

Please could someone explain, pretty simply, what a parameter and also its relation to graphs? And if possible give a couple of examples. I have trawled through the internet and can't find anything which I understand. Thank you very much.
8. ### Determining Relationship Between Two Variables

Homework Statement An experiment was conducted to determine the relationship between metre-stick projection from a table (L) on the vertical depression of the free end (y). Using the collected data, graphs had to be plotted until a linear relation was found, and the equation of the line had to...
9. ### Log-Plots: Sketching

Homework Statement Homework Equations The Attempt at a Solution I have been trying to rearrange the equation to look something like ln(y) = Aln(x) but to no avail. Something tells me that that's not necessarily the right way to approach the problem, could anyone point out what I should be...
10. ### Graph r = 6 cos() issues with plotting on xy-plane

Homework Statement Hello! Last week I have came here for the help related to this problem. I am creating a new thread to describe the issue more precisely. I will be grateful for your help and explanation. I post the explanation for the book first accompanied by attached pictures, and below I...
11. ### Potential Energy vs. Position Graphs

Homework Statement A particle has the potential energy shown in the figure. (Figure 1) What is the x-component of the force on the particle at x =5, 15, 25, and 35 cm? I'm stuck on finding the Fx at 25 & 35 cm. Homework Equations F = -du/dx 100 N = 1J/cm The Attempt at a Solution Slope...
12. ### A Half-face traversal on general polyhedra

Hi, I'm developing a data structure to represent 3-D meshes for numeric simulation. I want those meshes to be able to handle any type of polyhedron (not only the classic tetra and hexahedron). The best data structure that I could find was one based on half-edges (or darts), such as this one...
13. ### Symmetries of graphs and roots of equations

Is there a good way to relate the symmetries of the graphs of polynomials to the roots of equations? There's lots of material on the web about teaching students how to determine if the graph of a function has a symmetry of some sort, but, aside from the task of drawing the graph, I don't find...
14. ### When accelerating upward off a trampoline...

Homework Statement When accelerating upward off a trampoline, how would you depict this on an acceleration-time graph? I know kinematics is the study of motion without a strict regard to the forces that are capable of changing motion, but according to Newton's 2nd law, an object accelerates in...
15. ### Euler circuit in a directed multigraph

Homework Statement So the question is: Show that a directed multigraph having no isolated vertices has an Euler circuit if and only if the graph is weakly connected and the in degree and out degree of each vertex are equal. Homework Equations Euler circuit: A circuit that has all edges of the...
16. ### B How do I linearize this graph?

Hello! I'm completing my IB Physics IA and after collecting my data and plotting the raw graph my graph seems to be a negative parabola. In order to linearize it I though one had to square the x-axis data; however I simply get the same graph shape. What am I supposed to do? Only when I plot the...
17. ### Help with solving parametric equation

Homework Statement Consider the following parametric curve: x=5cos^7(t) y=5sin^7(t) Write it in cartesian form, giving your answer as an equation of the form F(x,y)=c for some function F and some constant c. The Attempt at a Solution [/B] I know that sin^2(t)+cos^2(t) = 1 but I don't...
18. ### Graphs relating to simple harmonic motion

Homework Statement Homework Equations None. The Attempt at a Solution Hi everyone. Apparently 5 is the right answer, although I chose D. Could anyone please weigh in with their thoughts about why 5 is right and my answer is apparently wrong? Thanks!
19. ### Rearranging x=x0e^-lambda t in the form y=mx+c

Hi, How could I rearrange x=x0e^-lambda t into the form y=mx+c, where y is equal to ln x and x is equal to t? Thank you in advance I tried to solve the problem myself, by taking the natural log of both sides, this left me with: ln x = -lambda t * lnx0 However, I am not sure if this answer is...
20. ### Displacement-distance vs Displacement-time graphs for waves

Hi guys, I'm finding it hard to conceptualise the difference between a displacement-distance and displacement-time graphs for transverse waves. Could somebody explain the difference please?
21. ### Position vs. Time Graphs

Homework Statement Three objects can only move along a straight, level path. The graphs below show the po- sition d of each of the objects plotted as a function of time t. The magnitude of the velocity ∥⃗v∥ of the object increases in which of the cases? (view image/attached file) Homework...
22. ### Re-scaling Functions under the Same Axes

Consider two functions ##f\left(x, y\right)## and ##g\left(px, qy\right)##, where ##p## and ##q## are known. How can I plot the two functions on the same graph (i.e. the same axes)? The function ##f\left(x, y\right)## will have axes with values ##x## and ##y##, while the other will have axes...
23. ### Transforming functions

Homework Statement If f(x)=|x-1/2|-5 determine g(x)=2f(-x+(3/2)) Homework Equations The Attempt at a Solution Well, I tried to factor out the k-value in the g(x) formula. So I was left with: g(x)=2f(-1)(x-3/2) Then I multiply f(x) by 2 and am left with: g(x)=2|x-(1/2)|-10 Then I subtract...
24. ### How do I go from an Electric Field graph to Charge Density?

Homework Statement Homework Equations E= kq/(r^2), E*dA = Q/e0 The Attempt at a Solution Typically I understand how to interpret basic graphs such as going for V (potential) vs x graph to Electric field vs x graph by finding the slope of V since E= -grad V...and from their it's basic...
25. ### Independence from a variable - Graphical confusion

http://postimg.org/image/pb0eu3ap3/ So I've got this graph, and magnitude, M, depends on the number of points, N,.... but it shouldn't. http://postimg.org/image/pb0eu3ap3/ The line of best fit is..... M = a*N ^b It's been a while since I studied, but knowing their relationship would it be...
26. ### Plotting surfaces in 3-space

Homework Statement Given the eqn x=2, y=sin(t), z=cos(t), draw this function in 3-space. Homework Equations ABOVE^ The Attempt at a Solution I did this: x^2+y^2+z^2=2^2+(sin(t))^2+(cos(t))^2=5 Therefore we get x^2+y^2+z^2=5 Which is the eqn of a sphere with radius root5. My friend said it's...
27. ### Motion Down a Ramp help?

The question is For the same time interval , how did the area beneath the velocity-time graph compare with the displacement of the cart? How should it compare? I don't understand what they`re asking me to do, please help.
28. ### How to find the vertex of G(t)=1/2(t^2-4t)

Homework Statement G(t)=1/2(t^2-4t) The Attempt at a Solution Since this is a polynomial it's all real numbers for domain y-int: G(0)=1/2(0^2-4(0) y-int=(0,0) x-int: 0=1/2(t^2-4t) 0=(1/2)t(t-4) Not sure... And not sure about the vertex. I know the formula -b/2a but how do i find those two...
29. ### How to determine a hole in a graph?

I'm aware that in order to find the hole in a graph, you need to factor both the numerator and denominator, and look for terms that cancel out. However, is it merely just looking for a term that cancels out, or is it more specifically a term that cancels out and makes the numerator equal to...
30. ### Why Graphing Tools doesn't represent hole in a graph

Why Graphing Tools doesn't represent hole in a graph of a function. A Hole at a point in a graph is point where function is not defined.Suppose there is a function ##\frac{x}{\root{x-1}-1}## Its should be like this But online tools and even my android graphing tool app shows graph like this...