Precalculus 10th Edition Annotated Instructor's Edition
10th Edition
ISBN: 9781337279765
Author: Ron Larson
Publisher: Cengage Learning
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Chapter 7.6, Problem 3E
To determine
To fill:
The blank(s) with appropriate word(s) in the statement, “The ____ function of a linear programming problem gives the quantity to be maximized (or minimized).”
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Find the first and second derivatives of the function.
f(u) = √7 3u
−
3
f'(u)
2
(7-34) (½)
f"(u) =
9
4(7-3u)
32
X
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11. Consider the 2nd-order non-homogeneous differential equation y′′ − 4y′ + 3y = et + t2What is the complementary (or homogeneous) solution?A. yc = c1e^t + c2t^2 B. yc = c1e^−t + c2e^−3t C. yc = c1e^t + c2e^3t D. yc = c1e^t + c2e^−3t
5. A trial solution for the non-homogeneous equation y′′ + y′ − 2y = e^x isA. Ae^x B. Ae^x+ Be^−2x C. Ae^x + Be^−x D. Axe^x E. None of these.
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- Question 3. A manufacturer has modeled its yearly production function P (the value of its entire production, in millions of dollars) as a Cobb-Douglas function P(L, K) = 1.47L0.65 0.35 where L is the number of labor hours (in thousands) and K is the invested capital (in millions of dollars). ӘР Ət (a) Express the rate of change of production 07-2 in time, in terms of the rate of change of the labor force and the rate of change of the capital in time. (b) Suppose that when L = 30 and K = 8, the labor force is decreasing at a rate of 2000 labor hours per year and capital is increasing at a rate of 500,000 per year. What is the rate of change of production per year?arrow_forward17. Consider a mass-spring system that satisfies 2y′′(t) + by′(t) + 50y(t) = 0.Which of the following is/are true?(i) If b = 0, the motion is critically damped with period π/5 .(ii) If b = 12, the motion is underdamped.(iii) If b = 40, the motion is overdamped.A. (ii) and (iii) only B. (ii) only C. (i) and (ii) only D. (i) and (iii) only E. Allarrow_forward20. Find the general solution to the differential equation y(4) − 8y′′ + 16y = 0A. y = c1e^2x + c2e^−2xB. y = c1xe^2x + c2xe^−2xC. y = c1e^2x + c2e^−2x + c3xe^2x + c4xe^−2xD. y = c1xe^2x + c2xe^−2x + c3x^2e^2x + c4x^2e^−2xE. y = c1 cos 2x + c2 sin 2x + c3x cos 2x + c4x sin 2xarrow_forward
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- Question 1 (Implicit differentiation). Use implicit differentiation to find Əz/Əx and Əz/ǝy. (a) x²+2y²+3z² 1 (b) ez = xyz (c) x2. y²+ z² − 2z = 4 (d) yz+xln(y) = z²arrow_forward4. The general solution of the differential equation y′′ + 2y′ + 5y = 0 isA. c1 + c2x B. c1 cos 2x + c2 sin 2x C. c1e^x cos 2x + c2e^x sin 2xD. c1e^−x cos 2x + c2e^−x sin 2x E. None of these.arrow_forward3. The general solution of the differential equation y′′ + 2y′ + y = 0 isA. c1e^−x + c2e^−x B. c1e^−x + c2e^x C. c1e^−x + c2xe^−xD. c1 cos x + c2 sin x E. c1e^−xarrow_forward
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