Numerade

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Time (s) Velocity (mph) The velocity change respect to time of a free fall is given left. Accordingly, calculate the velocity value at 5.5 s 0 0 1 22 a) using the $2^{nd}$ order Lagrangian interpolation polynomial (determine the appropriate points to be selected yourself). 2 42 3 60 4 75 b) Obtain the $2^{nd}$ order polynomial equation suitable for these data by using the least squares method and calculate the velocity value at 5.5 s using this equation. c) Determine the quality (determination coefficient) of the polynomial obtained in part b using the $R^2$ method. 5 87 6 96 7 103 8 108 9 111 10 114

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Danny Inc. is considering two projects that have the following cash flows: Project 1 Project 2 able[[Year, Cash Flow],[0, -$2,000],[-$1,900, 1],[500, 1,100],[700, 900],[800, 800],[1,000, 600],[1,100, 400]] At what cost of capital would the two projects have the same net present value? a. 4.73% b. 5.85% c. 6.70% d. 7.50% e. 8.20% KMG is considering two mutually exclusive projects that have the following cash flows: Project A Project B able[[Year, Cash Flow],[0, -$10,000],[-$8,000, 1],[1,000, 7,000],[2,000, 1,000],[6,000, 1,000],[6,000, 1,000]] At what cost of capital do the two projects have the same net present value? (That is, what is the crossover rate?) a. 11.20% b. 12.26% c. 12.54% d. 13.03% e. 14.15%

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2.33 A small river is found to be polluted due to the chemical waste from two major industries, A and B. Due to the strict standards enforced by the EPA, the probability of controlling the pollutions from A and B are 0.7 and 0.85, respectively, in the next two years. It is estimated that, if only one of the industries complies with the strict standards of EPA, there is a 75 percent probability of controlling the pollution in the river to an acceptable level. (a) Find the probability of controlling the pollution in the river in the next two years. (b) If the pol- lution in the river is not controlled in the next two years, what is the probability that it is caused entirely by the industry A?

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A segment of the cylindrical capacitor is defined by ρ₁ < ρ < ρ₂, 0 < φ < α. If V(φ = 0) = 0 and V(φ = α) = y, show that the capacitance of the segment is C = (2πεL) / ln(ρ₂ / ρ₁), where L is the length and ε is the permittivity of the dielectric.

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9. [8 points] A flat circular plate has the shape of the region $x^2 + y^2 \le 1$. The plate, including the boundary where $x^2 + y^2 = 1$, is heated so that the temperature at the point $(x, y)$ is given by $T(x, y) = x^2 + 2y^2 - x$ Find the points on the plate that are the hottest and the coldest. For the boundary of the plate, use Lagrange Multipliers. To aid in your calculation, note that $T\left(\frac{1}{2}, \pm \frac{\sqrt{3}}{2}\right) = \frac{9}{4}$

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6. $u(x, y) = 40\sqrt{x} + y$ $p_x = 2, p_y = 1, m = 100$ 7. $u(x, y, z) = xyz^2$ $p_x = 3, p_y = 5, p_z = 1, m = 60$

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(C) The diagram shows an ordinary vapor compression cycle for refrigeration. When the evaporator pressure increases but saturated vapor still leaves the evaporator, the coefficient of performance _____. (5 points) pressure (MPa) 5 1 4 condenser 3 0.5 liquid vapor evaporator 1 2 0.1 150 200 250 2- phase 300 350 400 450 500 A. Increases B. Decreases C. Does not change enthalpy (kJ/kg)

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am 1 Spring 2021 Led: Feb 17 at 10:01am uiz Instructions Question 3 3 pts In the framework for analyzing good decision-making discussed in the text and the lectures, when is a decision a good decision? (What's a good decision, in this very general framework?)

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9. Which of the following is the best indicator of the standard of living? a. nominal GDP b. real GDP c. real GDP per capita d. productivity e. productivity per unit of labor

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Please show all your work including all the formulas you used to derive your answers. For each of the following, identify where demand is elastic, inelastic, perfectly elastic, perfectly inelastic, or unit elastic: (a) Price rises by 10 percent, and the quantity demanded falls by 2 percent (b) Price falls by 5 percent, and the quantity demanded rises by 4 percent. (c) Price falls by 6 percent, and the quantity demanded does not change. (d) Price rises by 2 percent and the quantity demanded falls by 1 percent.

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colin p.