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angela lambert

angela l.

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2. In class we described how to formulate a shortest path problem as a linear program. Consider the following graph, which has 12 edges: The graph that we saw in class was a directed graph, that is, we could cross the edges only in one direction. Here the edges are undirected and we could cross them in both directions. This can be handled by "splitting" the undirected edges into pairs of directed edges, pointing in opposite directions. There are then separate variable for crossing each edge from the pair, for example $x_{a0,a1}$ and $x_{a1,a0}$. MATH 208W D100 MATH 208W D100 ASSIGNMENT #2 a. For the purposes of finding the shortest path from a2 to b0, you may not need to split all the edges to formulate the problem. Explain which edges need to be split and why. b. Assign "distances" to the edges by placing your 12 numbers from part 0. on the edges starting from the outside cycle, and ending with the inside cycle. Formulate the problem of finding the shortest path from a2 to b0 as a linear program. Solve the problem in Excel.

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Position vs t graph: Object started to east (a) Slope represents (b) Straight lines indicate ----velocity (c) Positive position indicates object to ----side of origin (d) Negative position indicates object to ----side of origin (e) Velocity from t= 0 to t = 3s = ----positive slope ----moving east (f) Velocity from t= 3 to t = 4s = (g) Velocity from t= 4 to t = 7 s= (h) Moving in------- direction (i) Velocity from t= 7 to t=9s= (j) How does velocity from 7 s to 9 s compare to velocity from 4 s to 7 s----increased / decreased (k) what is the length of the path the object followed? Add the total distance (b) what is the displacement of the object? Total length joining the two points (a) what is the average speed of the object? ---Total distance/total time (b) what is the average velocity of the object? --- slope between two points

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Exercise 4: Perturbation theory and convergence Consider the integral \[ Z(g)=\int \frac{d x}{\sqrt{2 \pi}} e^{-\frac{1}{2} x^{2}-\frac{g}{4} x^{4}}, \] corresponding to the classical partition function for a particle in a quadratic plus quartic potential, \( Z=\int d x e^{-V(x)} \) with \[ V(x)=\frac{1}{2} x^{2}+\frac{g}{4} x^{4} . \] a. Lookup the exact solution to this integral. (Hint: Bessel function) b. What happens in physical terms if \( g \) changes sign? c. Now we will treat the quartic term in perturbation theory. To this end, perform a Taylor expansion of the exponential of the quartic term and determine the coefficients \( Z_{n} \) in the expansion \( Z=\sum_{n=0}^{\infty} g^{n} Z_{n} \). d. Plot the residual error \( R_{m} \) if the series is truncated to order \( m \) as function of \( m \) for different values of \( g>0 \). When is the series a good approximation to the correct answer?

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What is the effect on the accounting equation when services are performed on account?

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Problem 5 Two positively charged spheres with charges $Q_1 = q$ and $Q_2 = 4q$ are located 1 mm apart. An additional charge $Q_3$ of which magnitude needs to be placed where for $Q_1$ and $Q_2$ to remain in their positions? Give your answer in terms of the distances $l_1$ from $Q_1$ and $l_2$ from $Q_2$.

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What has been explained that "Good developers do constantly, almost sub-consciously" and "must understand both the cost and revenue sides of the market?" Market Analysis Market Study Back of the Envelope Pro Forma Market Segmentation Analysis

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Patrick Henry ultimately opposed ratification of the Constitution because he believed it assigned too much power to the national government at the expense of state authority. Patrick Henry is, therefore, best considered a/an _______.

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Why is CA-MRSA considered an emerging disease, given that MRSA has been around for years?

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Once the cells from the first time point are fixed, you will start to measure flagellar length on the C. reinhardtii. Which of the following statements is true? Always measure one flagella from each of the first ten cells you see without selecting for long or short flagella. Always choose to measure the shortest flagella you can find. Always choose to measure the longest flagella you see. It is important to measure flagella as quickly as possible because they will continue to grow flagella even when mixed with Lugol's iodine.

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In a max heap, if the value 25 is at index 3, what are the indices of its parent, left child, and right child (indexes start from zero)? Parent: 1, Left Child: 6, Right Child: 7 Parent: 1, Left Child: 5, Right Child: 6 Parent: 2, Left Child: 6, Right Child: 7 Parent: 6, Left Child: 9, Right Child: 10 Parent: 1, Left Child: 7, Right Child: 8

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