Answered: Given ⃗x =(−1) (2) (3)…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A rectangular dock that measures 12 feet by 16 feet is treated with auniform strip of nonslip coating along both sides and both ends. How wide isthe strip if one-half of the dock is treated? If we let x represent the width of thestrip, then we can use the equation (16 -2x)(12 - 2x) = 1/2(12)(16) to determinethat the width of the strip is 2 feet. I've been doing well with polynomials I just do not understand visually what "treated along both ends and sides" mean. What is the end of a rectangle? Also, I do not understand the 2 in '2x' (2 times the width of the strip) why is that added? I guess I am more concerned about how the equation actually maps to the real world scenario.
Given the function q(x) =x³, which of the following is equivalent to q(2x+a)+q(x)? A) 8x+a? B) 9x +a? C) D) 9x +12x?a+ 6xa² +a³ 8x +12x²a+6xa² +a?
Given a function f(x) with the function values ƒ(−6) = −24, ƒ(−2) = −20, ƒ(−1) = 0, and ƒ(4) = 64, which value of x is a factor of the function? A. x = -6 4. 5. The function y = 4(−x + 9)¹(2x − 3)²(x + 6) changes signs at A. x = -9 B. x = 9 C. x = A. B. x = -2 C. x = 3 6. Which list best represents the values of x that make the following equation true: 3x³ + 6x² + 11x + 6 = 0 ? A. +1, +2, +3, +6 B. ±1,±2, ±3,±6,±½‚±z C. +1, +2, +², +², +³ D. 0, 11, 12, 13, +++ 3x-1 7. 6x4 - 2x³ - 21x² + 7x +8 is divided by 3x – 1 to give a quotient of 2x³ 7x and a remainder of 8. Which statement is true? 6x4-2x³-21x² +7x+8 = 2x³ - 7x + C. x = -1 8 3x-1 8. What is the solution to − (x − 3)(x + 8) < 0 ? - A. x € (-∞, -3) U (8,00) 3 2 B. x € (-∞, -8) U (3,00) D. x = 4 2 D. x = -6 C. x € (-∞, -8] U [3,00⁰) B. 6x4 - 2x³ - 21x² + 7x+8 = (3x − 1)(2x³ – 7x) - 8 D. All of these statements are true D. x € (-8,3)
Use the information provided below to answer the questions. The management of ThermoMaster Company, whose Mexican subsidiary manufactures an indoor-outdoor thermometer, has estimated that the total weekly revenue (in dollars) for producing x thermometers is R(x) = -0.04x² + 800x Similarly, they determined their total weekly cost (in dollars) for producing x thermometers is C(x) = 130x – 40,000. a) Find the profit function P(x). b) Find the marginal profit function P'(x), which is the derivative of P(x). c) What is the largest possible profit that the restaurant could make in one month?
When h(t) 7t2 + 3t – 2, evaluate h( – 3) h( – 3) =
4. Given f(x) = 2x2 + x- 7, evaluate the following: a) f(3) b) f(a) c) f(a +3) d) 4f(3) – 2f (2) flx+h)-f(x) 5. Use the figure shown to make the following lists. y

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Given ⃗x =(−1) (2) (3) y =(3) (4) (2) and z =(2) (6) (6) Is z in the span of x and y? Justify your answer.