Read the following scenario and in the lawsuit of Stella v McDonalds, list up to three arguments in favor of Stella and up to three arguments in Favor of McDonalds.

“I’m Stella Liebeck. I was in the car with my grandson one day, and he drove up to a McDonalds drive-thru. He asked me if I wanted anything. Of course I did! It’s McDonalds! So, I got a cup of coffee. Hey, I was 79. I needed a little caffeine. They handed him his order (Big Mac, supersized, and my coffee). He pulled over to the side of the line so I could add some milk and sugar. I had the cup balanced on my knees and took the lid off, and hot coffee spilled all over me! I spent 8 days in the hospital having skin cut off my body and grafted onto my knees to replace the burned skin! It was awful! My cotton sweatpants absorbed the coffee, scalding my thighs, buttocks, and groin. I suffered third-degree burns on six percent of my skin and lesser burns over sixteen percent. I lost 20 pounds (nearly 20% of her body weight), I lost so much weight I only weighed 83 pounds and had to undergo two more years of medical treatment.”

Given an undirected graph G=(V, E) with weights and a vertex , we ask for a minimum weight spanning tree in G where is not a leaf (a leaf node has degree one). Can you solve this problem in polynomial time? Please write the proof.

A negative charge, -q, has a mass, m, and an initial velocity, v, but is infinitely far away from a fixed large positive charge of +Q and radius R such that if the negative charge continued at constant velocity it would miss the center of the fixec charge by a perpendicular amount b. But because of the Coulomb attraction between the two charges the incoming negative charge is deviated from its straight line course and attracted to the fixed charge and approaches it. Find the closest distance the negative charge gets to the positive one.

Try to use work-energy theorem with U=(kq)/r and KE=(mv^2)/2

Consider atmospheric air at a velocity of V = 20 m/s and a temperature of T= 20C, in cross flow over 10 mm square tube at 45 degrees, maintained at 50C.

1. Sketch
2. Assumptions
3. Calculate the air properties (show the interpolation steps)
4. Re = ?
5. Nu = ? (reference the table number where the equation is obtained)
6. H = ?
7. Calculate the rate of heat transfer per unit length, q.

a)Assume the reaction 2Fe3+ + Sn2+ -> 2Fe2+ + Sn4+ has a rate law v = k[Fe3+][Sn2+]. If Fe2+ is produced at a rate of 0.12 mol L-1 s-1 when the reactant concentrations are 0.30 mol L-1 for Fe3+, and 0.40 mol L-1 for Sn2+, then what is the value of the rate constant, k ? Quote your answer to 2 decimal places.

Answer L.mol-1.s-1

b)

The half-life for the decomposition of a gaseous sample of thioketene, H₂C=C=S at 500 Pa is 42 s. When the thioketene pressure is 250 Pa the half-life is 21 s. Determine the order of the reaction, entering your answer as a number.

c)

At 1100 K, acetic acid decomposes via 2 competing, first order reactions:

CH₃COOH -> CH₄ + CO₂,   k₁ = 3.4 s^-1

CH₃COOH -> CH₂=C=O + H₂O,    k₂ = ? s^-1

The half life of acetic acid at this temperature is 0.10 s. What is the value of the rate constant, k₂?

d)

At 1100 K, acetic acid decomposes via 2 competing, first order reactions:

CH₃COOH -> CH₄ + CO₂,   k₁ = 4.1 s^-1

CH₃COOH -> CH₂=C=O + H₂O,    k₂ = ? s^-1

At 1100K, the yield of ketene (CH₂=C=O) is 71.5%. Estimate the rate constant, k₂, for the second reaction

e)

The following mechanism has been proposed for recombination of iodine atoms:

I + I -> I₂*, k₁ = [k1].0

I₂* -> I + I, k_-1 = [k-1].0

I₂* + M -> I₂, k₂ = [k2]

What is overall rate constant if k₁ = 4, k_-1 = 4 and k₂ = 0.04?

f)

The following mechanism has been proposed for recombination of iodine atoms:

I + I -> I₂*, k₁ = 9.0

I₂* -> I + I, k_-1 = 5.0

I₂* + M -> I₂, k₂ = 0.04

What is overall rate constant?

.

Use Table V in Appendix A to determine the t-percentile that is required to construct each of the following two-sided confidence intervals. Round the answers to 3 decimal places.

(a) Confidence level = 95%, degrees of freedom = 19

(b) Confidence level = 95%, degrees of freedom = 30

(c) Confidence level = 99%, degrees of freedom = 17

(d) Confidence level = 99.9%, degrees of freedom = 14

Let V be the vector space of all functions f : R → R. Consider the subspace W spanned by {sin(x), cos(x), e^x , e^−x}. The function T : W → W given by taking the derivative is a linear transformation

a) B = {sin(x), cos(x), e^x , e^−x} is a basis for W. Find the matrix for T relative to B.

b)Find all the eigenvalues of the matrix you found in the previous part and describe their eigenvectors. (One of the factors of the characteristic polynomial will be λ 2+1. Just ignore this since it has imaginary roots)

d) Use your answer to the previous part to find all the eigenvalues of T and describe their eigenvectors. Check that the functions you found are indeed eigenvectors of T.

v

Question #1: Suppose that you are the economic advisor to a local government that has to deal with a politically embarrassing surplus that was caused by a price floor that the government recently imposed. Your first suggestion is to get rid of the price floor, but the politicians don’t want to do that. Instead, they present you with the following list of options that they hope will get rid of the surplus while keeping the price floor. Identify each one as either could work or can’t work.

1. Restricting supply.
2. Decreasing demand.
3. Purchasing the surplus at the floor price.

A fireworks rocket is moving at a speed of v = 45.7 m/s. The rocket suddenly breaks into two pieces of equal mass, which fly off with velocities v1 at an angle of theta1 = 30.7° and v2 at an angle of theta2 = 59.3° as shown in the drawing below.

A potential difference of 5.00 V will be applied to a 47.00 m length of 18-gauge tungsten wire (diameter = 0.0400 in). Calculate the current.

Calculate the magnitude of the current density.

Calculate the magnitude of the electric field within the wire.

Calculate the rate at which thermal energy will appear in the wire.

Tungsten: 5.28e-8