Numerade

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Question 7 Why do credit card companies charge higher interest rates for some customers than others?

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Consider function $f$ given by \begin{equation*} f(x) = \begin{cases} 0, & 0 < x < \frac{\pi}{5}, \\ \pi - x, & \frac{\pi}{5} \le x < \pi. \end{cases} \end{equation*} We periodically extend the function $f(x)$ in an even manner for $-\pi < x < 0$. (a) The Fourier cosine series is given by \begin{equation*} f(x) = a_0 + \sum_{n=1}^{\infty} a_n \cos(nx). \end{equation*} Find the Fourier coefficients $a_0$ and $a_n$ by evaluating the relevant integrals. $a_0 = $ $a_n = $ Incorrect Your Answer: $(3\text{Pi})/8$ Correct Answer: $8/25\text{Pi}$ (b) Syntax advice: Use Pi for $\pi$. Note that $(-m)^n$ is different to $-m^n$. Which of the following plot is the even periodic extension of $f(x)$ over $-3\pi < x < 3\pi$?

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You are the Key Account Manager of a large manufacturing company. The old situation is as follows: Price in $ 400 Variable unit costs in $ 250 Units sold 1 000 000 Sales in $ 400 000 000 Total variable costs in $ 250 000 000 Total fixed costs in $ 30 000 000 Profit in $ 120 000 000 Your client promises you more quantity if you give her a price reduction. You consider changing the price by -15%. By what percentage does your quantity have to increase if you want the profit (in $) to stay constant? Your pricing department tells you that variable unit costs and total fixed costs will not be affected by the increase of quantity.

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Return on Common Stockholders’ Equity, Dividend Yield, and Dividend Payout The following information relates to Menlo, Inc.: Previous Year Current Year Net income $125,000 $200,000 Preferred stock dividends $15,000 $18,000 Average common stockholders’ equity $5,000,000 $4,200,000 Dividend per common share $2.80 $3.00 Earnings per share $5.80 $6.00 Market price per common share, year-end $60.00 $59.50 a. Calculate the company’s return on common stockholders’ equity for each year. b. Calculate the company’s dividend yield for each year. c. Calculate the company’s dividend payout for each year. Round answers to one decimal point. Previous Year Current Year a. Return on Common Stockholder Equity Answer 0 Answer 0 b. Dividend Yield Answer 0 Answer 0 c. Dividend Payout Answer 0 Answer 0

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Identify the level curve of the function $f(x, y) = xy - 3x$ for $c = -8$. Write your answer in terms of $y$ as a function of $x$. y =

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Calculate the total inductance for three coupled coils given in figure below. 2 H 4 H 5 H 6 H 8 H 10 H

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A hydraulic jack has piston diameters of $D_1 = 1.5$ in and $D_2 = 5$ in as shown below. Hydraulic oil has a specific gravity of 0.92. If a force of $F_1 = 35$ lb is applied to the 30 in lever, determine: (a) Force acting on the small piston (b) Pressure $P_1$ and $P_2$ acting on in the pistons $P_1 = ?$ $P_2 = ?$ (c) Force $F_2$ produced by the larger piston $F_2 = ?$ Neglect the effect of piston weights. $D_1 = 1.5$ in $D_2 = 5$ in $sg = 0.92$ $F_1 = 35$ lb $r = .75$ $r = 2.5$ b) $sg = \frac{P}{P_w}$ $0.92 = \frac{P_1}{9.81}$ $P_1 = 9.025$ $P_1 = \frac{F}{A} = \frac{35 lb}{\pi (.75)^2}$ $P_1 = 19.81 lb/in^2$ $P = P_1 - P_2$ $9.025 = 19.81 - P_2$ $P_2 = 10.785 lb/in^2$

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Apply the grid method to calculate the density of an ideal gas using the formula. Express your answer in lbm/ft^3. Use the following data: absolute pressure is, the gas constant is, and the temperature is.

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3) The composite function denoted by $f \circ g$ is defined as a. $(f \circ g)(x) = f(g(x))$ b. $(f \circ g)(x) = g(f(x))$ c. $(f \circ g)(x) = f(x) \bullet g(x)$ d. $(f \circ g)(x) = g(x) \bullet f(x)$

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Use the properties of limits to help decide whether the limit exists. If the limit exists, find its value.\\ $\lim_{x \to \infty} \frac{8x}{9x - 6}$ \\ Select the correct choice below and, if necessary, fill in the answer box within your choice.\\ A. $\lim_{x \to \infty} \frac{8x}{9x - 6} = \boxed{}$ \\ (Simplify your answer. Type an integer or a fraction.)\\B. The limit does not exist and is neither $\infty$ nor $-\infty$

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magdalena p.