Graph Definition and 998 Threads

Classical problems for hookes law generally give either mass or spring constant. What if I have a graph of a wavelike structure that is oscillating which I can use to measure for example: T (period), t (time), Δx (displacement), v (velocity), a (acceleration) and other variables is this...

Why velocity in graph 1 is positive and in graph 2 is negative?

Hello all, I have designed an intake manifold for boxer-6 naturally aspirated petrol engine with 1:1 bore to stroke ratio and has a bore dia of 117.89mm and a volume of 7.8l as part of my master's project. The engine was to produce 450 bhp @ 6500 rpm and I did set a rev limit @7500 rpm. The...

2.62 An object's velocity is measured to be $v(t)=\alpha-\beta t^2$ where $\alpha=4.00\, m/s$ and $\beta=2.00 \, m/s^3$ At $t=0$ the object is an $x=0$. (a) Calculate the objects position and acceleration as functions of time (b) What is the object's maximum positive displacement from the...

Given a minimal non-planar graph G, we need to find out if G', which is G-e, where e is a removed edge, we need to prove that there exists an edge e such that its removal would make G' a maximal planar graph. My idea in trying to figure this out would be by taking a minimal non-planar graph and...

Our problem involves a graph G that is simple and connected, where every biconnected component is a cycle that has at least four vertices in it. The maximum number of components we can get from removing a cut vertex is 4, and we are asked to find tight bounds on the chromatic number of G. My...

The problem is for us to consider a biconnected decomposition, and that proof for a graph, the degrees of all the vertices in a graph is even iff the degrees of all the vertices in all of its maximal biconnected components is even For solving that if the degrees of all the vertices in the...

What can we infer about the connectivity and edge connectivity of a graph given the number of edge disjoint paths? So the number of edge disjoint u,v paths in a graph is x. Doing this problem, I thought back to Menger's theorem, and thought that the graph is x-edge-connceted and so the number...

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...

Let ##P = (u_1, u_2, \dots, u_7)## and ##P' = (v_1, v_2, \dots, v_7)##. If there were a vertex ##w## such that ##w## is adjacent to ##u_1## and for all ##i##, ##u_i \neq w##, then we'd have a path of length 8 ##(w, u_1, u_2, \dots, u_7)##. So no such ##w## exists in ##G##. By definition of...

For my base case I just used a graph with three vertices and 2 edges. Decomposing this would just give us the same graph, which has a path length of 2. The inductive step is where I'm having some trouble: One idea I have is that we take a graph G then inductively remove an edge to create two...

We learned in class how to do this problem the more traditional way, but we are required to reprove this using induction, which I'm not too sure how to do. My Attempt: For the base case I had three vertices connected by three edges, with the last one looping back to the first to create a cycle...

My Problem: Given a Graph G = (V,E), where the number of vertices is less than or equal to the number of edges, use induction to prove that the graph contains at least one cycle (the graph is not required to be completely connected). My attempt: For my base case, I used only one vertex with one...

I assumed to find it I would need to find the area under the graph. I also assumed that the part under x would cancel out so I would be left with 2b*10=1 if it was, in fact, true that it had to equal to one. So my final answer was (1/10)/2 nm^-1 but the actual answer was 0.0845 nm^-1/2 and I'm...

Hi. I have physics homework that I don't understand. Hopefully, someone here can give me some advice. So, the homework goes like this: Draw an electric circuit potential graph and find out the potential difference between points B and C. The two resistors have equal values. Believe me or...

Hi all, I have experimental nuclear magnetic resonance data that describe T2-relaxation of the nuclei in the sample of interest. The experimental points obey bi-exponential dependence: I = I1*exp(-t/T2_1) + I2*exp(-t/T2_2), where I is current intensity, I1 and I2 are intensities which represent...

If i were to take one point as my origin and draw the two momentum, one for the initial collestion and one going from the wall after, from the origin point, then drawing horizontally i would get the answer as B as the resultant? Should i assume that for any resultant vector the direction can...

I did the cases ##n=2, 4, 6, 8## by hand and got this far: Answer: If ##n = 2k## for some integer ##k##, the equal degrees is ##k##. Proof: Let ##n \ge 2## be an integer and consider two cases: case1: ##n = 2k## for some integer ##k##. Let ##P(2l)## be the assertion that for ##2l \ge 2## there...

I do not know how to declare time t and unit steps. The image of problems to get a better understanding as well.

If the derivative of a function f is given by $$f'(x)=\frac{1}{5}(x^2-4)^5-x^2$$ how many points of inflection will the graph of the function have?solution find $f"(x)$ $$f''(x)=2x((x^2-4)^4-1)$$ at $f''(x)=0$ we have factored $$2 x (x^2 - 5) (x^2 - 3) (x^4 - 8 x^2 + 17) = 0$$ then...

For part (b), I counted the number of squares underneath the 2 day sample to be roughly 33 'whole' squares (the 5by5 tiny squares is 1 whole sqaure). I then equated 33 whole square = 0.35 MJ to calculate 1 whole square to be 0.0106 MJ. I then counted the number of whole squares underneath the...

Hi all, Given that the question: From what i know , I am not sure how this equation can help me estimate the von-klitzing constant? Or is there another way? Thanks!

there must be an even number of vertices of odd degree, and from the handshake theorem, 2m = 2(12) = 24 the only way we can get this from 6 vertices using 2 and 5 is: 4 vertices of degree 5, 2 vertices of degree 2 does this seem correct??

1.To shift the graph of a function : Vertical Shifts : ## y=f(x) +h## where the graph shifts ##k## units up if ##k## is positive and downwards when ##k## is negative. Horizontal Shifts : ##y=f(x+h)## where the graph shifts to the left by ##h## units when positive and to the right when ##h## is...

They all seem to mean the same thing. I personally have been using locus.

Using integrals, consider the 7 requirements: Any my attempted solution that I have no idea where I am going: And the other one provides the graph:

When viewing an HR diagram, the main sequence curve is apparent, and the general shape of it is obvious. However, in this truncated version, it's unclear to me exactly which stars should be considered main sequence. I've added a shaded grey area as what I think I should count as main sequence...

Homework Statement The graph shows the variation with time t of the acceleration a of an object (graph attached). What is the change in velocity of the object in the time interval 0 to 4s? Homework Equations a = v/t The Attempt at a Solution My initial answer was -8 m/s, by simply finding the...

Homework Statement Hi Everyone, So I'm doing writing up my weekly physics lab report and I had an idea to better present my findings. I have a chart displaying the frequencies of numerous tuning forks as well as their experimentally determined wavelengths and I have to find the speed of sound...

I don't even know what a conjecture is y=-1/2[cos(x+pi)+cos(x-pi)]

Can a graph of voltage or current on the y-axis over distance represent the inverse square law?

I'd like to know how to solve this. I'm pretty lost as to how to solve this. I want to say that the graph would look periodic because of the graph of the time would go down and then go back up again, but I really don't have anything concrete. The question states: The circular clock has a...

Hello. I am reading DeAngelis - Introduction to particle and astroparticle physics and I have come across a plot showing proton proton cross section vs energy. I am trying to reconcile the statement in the book that says cross section total = cross section elastic whenever there is no available...

Homework Statement A point moves rectilinearly in one direction. The figure shows the distance s traveled by the point as a function of time. Using the graph, find: The average speed of the point during the movement time. Maximum speed The moment t0 in which the instantaneous speed is equal to...

I have two questions (1) If we have two areas, for example one in America and the other on Asia, both with the same latitude φ, which one of the areas will receive more Solar Radiation? Or will it be the same? (2) If Earth's eccentricity graph for the past 750k years is this...

Homework Statement https://imgur.com/a/bvcxjNy Homework Equations Since the elevator is accelerating upwards, N - mg = ma or N = m(g+a) ------------ (1) The Attempt at a Solution In order to get the accelerations at that instant, I drew a tangent at that point and used v2 - v1/t2 - t1 = a...

Dear community, For my electric vehicle project I want to select a gear ratio (single) of my gear box and send this information to the supplier. In order to calculate this ratio I thought of the following steps but am not sure and want some expert to recheck and answer my queries: 1. Calculate...

Homework Statement the question asks for the concentration of ethanoic acid, therefore I need to find out the volume of ethanoic acid used during the titrations. I thought it would be 30mL because that's when the temperature reaches maximum. But the answer says that the volume should be in the...

Homework Statement The diagram shows a circuit used for the investigation of photoelectric emission. The two electrodes E and F are made of different metals. The work function of electrode E is higher than that of electrode F. Which of the following graphs show the variation the current...

Homework Statement [/B] picture 1: picture 2: Homework EquationsThe Attempt at a Solution For the first picture I was thinking answer B because at the start velocity increases, but as terminal velocity is hit the velocity doesn't increase as much.. why is it graph A? For the second...

$$\d{r}{\theta}=\frac{r^2}{\theta},\quad r(1)=2$$ 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...