Graph Definition and 999 Threads

$$\d{r}{\theta}=\frac{r^2}{\theta},\quad r(1)=2$$ from i would deduct that $dr=r^2$ and $d\theta = \theta then$ $$\d{r}{\theta}=\frac{\theta}{r^2} \text{ or } \frac{1}{r^2}dr=\frac{1}{\theta}d\theta$$ intregrate

2000 (a) Find the solution of the given initial value problem in explicit form. $$xdx+ye^{-x}dy=0, \quad y(0)=1$$ \begin{align*}\displaystyle xdx&=-ye^{-x}dy \\ \frac{x}{e^{-x}}\, dx&=-y\, dy\\ xe^x\, dx&=-y\, dy \end{align*} (b) Plot the graph of the solution $\quad...

I posted this link a couple years ago, but just in case you need to draw a Christmas Tree: https://tex.stackexchange.com/questions/39149/how-can-we-draw-a-christmas-tree-with-decorations-using-tikz There are a lot of interesting variations posted, maybe PF could have our own contest! Here's...

Dear all, given a dataset of (x,y) coordinates, how can someone determine the equation of a plot created with Origin or Excel that passes through all these points? Depending on the dataset, it is safe to use a trendline ( i.e logarithmic, polynomial) in Excel. The problem is that the graph...

Homework Statement [see attached photo] I seek specific help with (a) only. The answers to this question are provided in the back of the textbook, so I know the answers (I hope). Homework Equations ##x(t)=Acos(\omega t+\phi _{0}),## ##v_{x}(t)=-A\omega sin(\omega t+\phi...

Homework Statement Let us have ##n \geq 3## points in a square whose side length is ##1##. Prove that there exists a graph with these points such that ##G## is connected, and $$\sum_{\{v_i,v_j\} \in E(G)}{|v_i - v_j|} \leq 10\sqrt{n}$$ Prove also the ##10## in the inequality can't be replaced...

Homework Statement Serway Physics Section 2.4 Acceleration (a) Use the data in Problem 5 to construct a smooth graph of position versus time. (b) By constructing tangents to the x(t) curve, find the instantaneous velocity of the car at several instants. (c) Plot the instantaneous velocity...

Homework Statement Serway Physics Section 2.4 Acceleration 17. Figure P2.17 shows a graph of ##v_x## versus t for the motion of a motorcyclist as he starts from rest and moves along the road in a straight line. (a) Find the average acceleration for the time interval t = 0 to t = 6.00 s. (b)...

Is there something that visualizes the connection between different areas of all(/almost all) phyics? It could be easily done with wikipedia articles: every article is a point in a graph and two points are connected if there's a link (one or both ways) between them. Given this, it could help to...

Homework Statement Serway Physics Section 2.4 Acceleration 15. A velocity-time graph for an object moving along the x-axis is shown in Figure P2.15. (a) Plot a graph of the acceleration versus time. Determine the average acceleration of the object (b) in the time interval t=5.00 s to t=15.0 s...

Homework Statement If X represents the intensity of monochromatic blue light and Y represents the energy of each photon of the light, which one is the correct graph below? Homework Equations KE=hƒ-∅, where ∅ is the work function Energy of a photon= hƒ The Attempt at a Solution Increasing the...

Homework Statement Given the graph of f(x) shown below, find the value of the integral. Photo attached. Homework Equations [/B] ∫23 5x·f(x2)dx The Attempt at a Solution [/B] I tried integration by parts to simplify the problem, but finding the integral of the composite function (f(x2))...

I'm asking how they managed to get those formulas to describe the graph. a few of my homework questions rely on me being able to get the correct formulas from a graph like this. So i can then find the voltage and amperes in the questions. I'm just trying to understand how 50t represents 0 < t <...

If I select two columns of data what are the steps to make a simple x vs y graph of that data? I know its sort of a dumb question but i can't see how to do this. It automatically suggests any graph other than a basic x vs y. Thanks for any help

Homework Statement These are the experimental results we got from the ticker tape lab we did in projectile motion. How exactly do I find Vy? My graph looks weird. I'm assuming Vy initial must be exactly the first velocity on the table. Homework EquationsThe Attempt at a Solution

Homework Statement The figure below shows the speed of a person's body as he does a chin-up. Assume the motion is vertical and the mass of the person's body is 72.7 kg. Determine the force exerted by the chin-up bar on his body at the following times. My answers: Homework Equations F = ma...

Homework Statement Use the graph (attached below) to determine the time intervals when the velocity is positive, negative, or zero. Homework EquationsThe Attempt at a Solution The graph is of a position function. Velocity is the derivative of position. Velocity will be zero when the derivative...

What is the resistance of Device Q when a current of 200mA flows through it? Wouldn't the resistance of the device be approaching 0 Ω as its characteristic resembles one of a diode (gradient = 1/R)? Apparently, the answer is just using V = I R, and solving for the resistance. Is there...

Homework Statement Graph the set of points whose polar coordinates satisfy the given equation or inequality. 0 ≤ θ ≤ , 0 ≤ r ≤ 4 Homework Equations - The Attempt at a Solution Is it correct ?

Homework Statement Parametric equations and a parameter interval for the motion of a particle in the xy-plane are given. Identify the particle's path by finding a Cartesian equation for it. Graph the Cartesian equation. Indicate the portion of the graph traced by the particle and the direction...

Homework Statement Parametric equations and a parameter interval for the motion of a particle in the xy-plane are given. Identify the particle's path by finding a Cartesian equation for it. Graph the Cartesian equation. Indicate the portion of the graph traced by the particle and the direction...

Homework Statement Identify the particle's path by finding a Cartesian equation for it . Graph the Cartesian equation . indicate the portion of the graph traced by the particle . ##x=2sinh t## , ##y=2cosh t## , ##-\infty < t < \infty## Homework Equations ##cosh^2 t - sinh^2 t = 1## The...

Homework Statement Find the equation of the tangent line to the graph of the given equation at the indicated point. ##xy^2+sin(πy)-2x^2=10## at point ##(2,-3)## Homework EquationsThe Attempt at a Solution Please see attached image so you can see my thought process. I think it would make more...

1. Homework Statement How to determine the change of R of a non-ohmic conductor from different parts of I-V graph? Please see the sketch attached. Homework Equations R=V/I The Attempt at a Solution For the part that passes through the origin, it is obvious that the...

Homework Statement Sketch the graph of the following function and use the definition of the derivative to show that the function is not differentiable at x=1. $$f(x) = \begin{cases} {-x^2+2} & \text{if } x \leq 1 \\ x & \text{if } x > 1 \end{cases}$$ Homework Equations Derivative: $$f'(x) =...

Homework Statement Graph the ellipse 4x² + 2y² = 1 Homework Equations 4x² + 2y² = 1 The Attempt at a Solution 2x² + y²/2 = 1/2 I searched for exercises on Google, and i didn't find an equation like that. I watched videoleassons too but it didn't teach this type of equation.

Homework Statement By relative velocity, we mean velocity with respect to a specified coordinate system. (The term velocity, alone, is understood to be relative to the observer’s coordinate system.) (a) A point is observed to have velocity Va relative to coordinate system A.What is its...

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...

Mathematicians, I summon thee to help me identify which field deals with this stuff. I come here not as a physicist but as a sunday programmer trying to solve some numerical problems. I set out to model a lattice version of a smooth space. A discretization procedure not uncommon in physics, but...

If you count the frequency of letters in a message, then have one axis with letters and another with numbers, is that a histogram or a bar graph or something different still?

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.

Just curious: Can I "recover" the analytic description ( say, like a Mathematical expression) from a graph? I just did well on a Sudoku recently . Please see below:

Homework Statement We're supposed to convert a position-time graph to a velocity-time graph to an acceleration time graph. These are the values for the position-time graph: Homework Equations m = y2-y1/x2-x1 The Attempt at a Solution I found the slopes for each time which were 5, 8.5, 17...

Homework Statement A particle starts from x_0 = 14m at t_0 = 0 and moves with the velocity graph shown What is the object's position at t = 2 s? Homework Equations Area under velocity time graph is the displacement of the particle. The Attempt at a Solution The part that confuses me is where...

Hey! :o Let $G$ be a graph of which the vertices are the permutations of $\{1,2,3,4,5,6,7,8,9,9,9\}$ with the property that two vertices $(\epsilon_1, \epsilon_2, \ldots, \epsilon_{11})$, $(\epsilon_1', \epsilon_2', \ldots, \epsilon_{11}')$ are connected with an edge if and only if the one is...

Hey! :o We have the matrix $$A=\begin{pmatrix}0&1&0&0&0&0&0&1\\1&0&1&0&0&0&0&0\\0&1&0&1&0&0&0&0\\0&0&1&0&1&0&0&0\\0&0&0&1&0&1&0&0\\0&0&0&0&1&0&1&0\\0&0&0&0&0&1&0&1\\1&0&0&0&0&0&1&0\end{pmatrix}$$ and we want to determine the diameter of the graph. For that do we have to calculate the...

Homework Statement f Homework Equations Hooke's Law: F = -kx Series spring combinations: ##\frac{1}{k_{eq}} = \frac{1}{k_1}+\frac{1}{k_2}## Parallel spring combinations: ##k_{eq} = k_1+k_2## The Attempt at a Solution The slope of 1 is ##\frac{4}{5}## and the slope of 2 is ##\frac{3}{2}## I...

Problem goes: A rubber ball, traveling in a horizontal direction, strikes a vertical wall. It rebounds at right angles to the wall. The graph below illustrates the variation of the ball’s momentum p with time t when the ball is in contact with the wall. Which of the following statements is...

Homework Statement Draw a probable graph of ln (A/R) vs 1/T. Homework Equations Arrhenius equation: k= Ae-E/RT The Attempt at a Solution Taking natural log on both sides of arrhenius equation : ln k = ln A - E/RT ln k - ln R = ln A - E/RT - ln R (subtracting ln R from both sides) ln...

Homework Statement Use a (simplified) graph to compare the maximum probability (electron density) of the Radial Distribution Function for the 1s and 2s orbitals. Homework Equations xxx The Attempt at a Solution The rest I don't how to solve.[/B]

Homework Statement Using the data presented in the accompanying pressure-versus-volume graph, estimate the work done (including the algerbraic sign) when the system changes from A to B to C along the path shown. Homework Equations The work done is the area from change in position and time...

Homework Statement A researcher studies the heat transference between an iron block and an unknown substance, inside an adiabatic calorimeter. In successive experiences he puts inside the calorimeter the unknown substance, always in its solid state and with temperature θs = 20ºC, and the iron...

Homework Statement Suppose this the velocity time graph given and we want to plot position time grah from this. What are the things to be considered while plotting the position time graph from this graph? 2. Homework Equations The uniform acceleration motion equations. The Attempt at a...

How do I solve these? https://imgur.com/a/NvzxFcS

Hi. I have a graph that looks like this: https://www.desmos.com/calculator/9skgbhqmpl I want to draw the same thing on a different website so that I know that I am moving in the right direction in my understanding. The different website is: https://www.geogebra.org/graphing/e2ZtMfDv desmos: {...

Hello, I've recently discovered the sine integral and have been playing around with it a bit on some graphing software. I looked at the graph of ##Si(x^2) - \frac π 2## and saw that both the amplitude and period was decreasing as x increased. Curiosity got the best of me so I decided to...

Homework Statement I would like to ask about parts c) and d) , the graph sketching bits. 2. Homework Equations ##V(r) = ( \frac{J^2}{r^2}+\epsilon)(r-\frac{1}{r}) ## where the value of ## \epsilon ## is set according to whether time-like or null etc. The Attempt at a Solution Q1)for...

Could someone explain to me how from this graph you can deduce that ##\tan(\theta) = \frac {df} {dx}##. Thanks

I have to construct suitable circuits to show the operational principles of some sensors: pH meter, sound, light and temperature. Would these count as circuits? or diagrams? (I'd say diagrams). https://www.electronics-tutorials.ws/io/io45.gif I am finding it hard to find circuits showing how...

What does the slope/gradient of an acceleration-time graph indicate?