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colton murphy

colton m.

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(c) Define the complex exponential function \( \exp (z) \). For any \( z, w \in C \), prove that (i) \( \exp (z+w)=\exp (z) \exp (w) \), (ii) \( \quad \exp (z y=\exp (\operatorname{Re} z) \).

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Question 1: (30 Marks) The mine manager has expressed his concerns regarding the increase of toes (high spots) in the pit. Put a proposal forward to investigate the cause/s and discuss what blast assessment equipment / tools are recommended to measure / monitor the potential cause/s. Briefly describe how you would use the recommended equipment.

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2 1 point A projectile is launched from a point on level ground with initial speed 5.42 miles/hour and initial angle of 4.52 degrees above the horizontal. Air resistance may be ignored and normal earth gravity is present. Calculate the final value of the horizontal component of velocity in m/s just prior to the projectile striking the ground. 'Note: Don't forget to convert units as needed.

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Charles, a security analyst, needs to check his network for vulnerabilities. He wants a scan that interacts with network nodes and repairs security issues found. Which kind of scanning BEST describes Charles' requirements? answer Internal assessment Host-based assessment Active scanning Passive scanning

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4. Catch-A-Match Dating Corporation has a target capital structure that calls for 40% debt, 10% preferred stock and 50% common equity. The firm's current bonds have a before tax cost of debt of 5.5% and the firm is in the 40% tax bracket. The firm can sell as much debt as it wishes at this rate. The firm's preferred stock currently sells for $985 a share and pays a dividend of $120 per share; however, the firm will pay flotation costs of 15% per share. Catch-A-Match's common stock sells for $40 per share with flotation costs of $8 per share from the sale of new common stock. The firm recently paid a dividend of $.85 per share on its common stock, and investors expect the dividend to grow indefinitely at a constant rate of 8% per year. Assume the firm has sufficient retained earnings to fund the equity portion of its capital budget. A. What is the firm's cost of retained earnings? B. What is the firm's cost of newly issued common stock? C. What is the firm's cost of newly issued preferred stock? D. What is the firm's weighted average cost of capital?

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4. The Buffet You have decided to eat sushi for lunch and have a grand total of $20 to spend. Whatever money you have left over from buying sushi rolls will be spent on cans of soda to get you through the rest of the day. Your problem is to choose the best combination of sushi rolls and cans of soda. (a) You decide to head over to Oshio Cafe due to its convenient proximity to the economics department. A sushi roll is $6 and cans of soda are $1. Sketch your Problem Set 1 3 budget constraint, being certain to label any relevant intercepts. (Throughout this problem, assume that you can purchase fractions of sushi rolls and fractions of cans of soda.) (b) Let's say that your utility for a bundle of sushi rolls (R) and cans of soda (C) is given by the following function: $U(R, C) = 30R^{\frac{1}{3}}C^{\frac{2}{3}}$. Derive the marginal utility of R and the marginal utility of C. (2)

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Given: $x = t^3 - 3t$, $y = t^2 - 3$ a) Find the values of $t$ that corresponds to horizontal and vertical tangent lines to the graph of $C$ b) Find $\frac{d^2y}{dx^2}$ in terms of $t$.

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A 1 mm thick sample of material is sandwiched between a heat source and a cold sink. If the area of the sample is 60 mm x 60 mm and the heat flux is measured to be 45 W, and the temperature differential between the hot and cold sides is 4°C, what is the thermal conductivity of the sample in W/mK.

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Consider the market for wheat where demand is given by: $Q^d = 100 - 1p$ and supply is given by: $Q^s = 10 + 2p$. Now suppose that, due to a market failure (an artificial shipping constraint), a maximum of 65.00 units of wheat can be supplied by firms in the market. The amount of the deadweight loss caused by the market failure is $ \boxed{} (Enter your answer rounded to the nearest penny and as a positive number.)

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Question 1.8 6 pts Suppose the horses in a large stable have a mean weight of 1467 lbs, and a standard deviation of 93 lbs. What is the probability that the mean weight of the sample of horses would differ from the population mean by less than 9 lbs if 49 horses are sampled at random from the stable? 0.915 0.497 0.503 None of these 0.612

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