Introductory Mathematics for Engineering Applications
1st Edition
ISBN: 9781118141809
Author: Nathan Klingbeil
Publisher: WILEY
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Chapter 4, Problem 41P
Repeat problem P4-40 if
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7. The demand for a product, in dollars, is
p = D(x) = 1000 -0.5 -0.0002x²
1
Find the consumer surplus when the sales level is 200.
[Hints: Let pm be the market price when xm units of product are sold. Then the consumer
surplus can be calculated by foam (D(x) — pm) dx]
4. Find the general solution and the definite solution for the following differential equations:
(a)
+10y=15, y(0) = 0;
(b) 2 + 4y = 6, y(0) =
5. Find the solution to each of the following by using an appropriate formula developed in the
lecture slides:
(a) + 3y = 2, y(0) = 4;
(b) dy - 7y = 7, y(0) = 7;
(c) 3d+6y= 5, y(0) = 0
Chapter 4 Solutions
Introductory Mathematics for Engineering Applications
Ch. 4 - Prob. 1PCh. 4 - Prob. 2PCh. 4 - Prob. 3PCh. 4 - Prob. 4PCh. 4 - The tip of a one-link robot is represented as a...Ch. 4 - Repeat problem P4-5 if P=14.42 cm and =123.7.Ch. 4 - Repeat problem P4-5 if P=15 cm and =120.Ch. 4 - Repeat problem P4-5 if P=6 in, and =60.Ch. 4 - The x- and y-components of a vector P shown in...Ch. 4 - The x- and y-components of a vector P shown in...
Ch. 4 - The x- and y-components of a vector P shown in...Ch. 4 - The x- and y-components of a vector P shown in...Ch. 4 - A state trooper investigating an accident pushes a...Ch. 4 - Repeat problem P4-13 if the trooper is applying a...Ch. 4 - In a RL circuit, the voltage across the inductor...Ch. 4 - Repeat problem P4-15 if VR=10 V and VL=15 V.Ch. 4 - In an RC circuit, the voltage across the capacitor...Ch. 4 - Repeat problem P4-17 if VR=10 V and VL=20 V.Ch. 4 - In an electrical circuit, voltage V2 lags voltage...Ch. 4 - In an electrical circuit, voltage V2 leads voltage...Ch. 4 - Prob. 21PCh. 4 - Prob. 22PCh. 4 - Prob. 23PCh. 4 - A ship is crossing a river at a heading of -150...Ch. 4 - Prob. 25PCh. 4 - A two-link planar robot is shown in Fig. P4.26....Ch. 4 - A two-link planar robot is shown in Fig. P4.27....Ch. 4 - A two-link planar robot is shown in Fig. P4.28....Ch. 4 - A two link planar robot is shown in Fig. P4.29....Ch. 4 - Prob. 30PCh. 4 - A weight of 100 kg is suspended from the ceiling...Ch. 4 - Prob. 32PCh. 4 - A vehicle weighing 2000 lb is parked on an...Ch. 4 - A crate of weight W=100 lb sits on a ramp oriented...Ch. 4 - A 500 N television sits on an inclined ramp, shown...Ch. 4 - Prob. 36PCh. 4 - Prob. 37PCh. 4 - A force F=100N is applied to a two-bar truss as...Ch. 4 - Prob. 39PCh. 4 - A waiter extends his arm to hand a plate of food...Ch. 4 - Repeat problem P4-40 if Fm=50 lb, Wa=50 lb, Wp=50...Ch. 4 - Using motion capture, the positions P1 and P2 of...Ch. 4 - Repeat problem P4-42 if P1=1 ft, P2=1.5 ft, 1=45,...
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- 1. Evaluate the following improper integrals: (a) fe-rt dt; (b) fert dt; (c) fi da dxarrow_forward8. Given the rate of net investment I(t) = 9t¹/2, find the level of capital formation in (i) 16 years and (ii) between the 4th and the 8th years.arrow_forward9. If the marginal revenue function of a firm in the production of output is MR = 40 - 10q² where q is the level of output, and total revenue is 120 at 3 units of output, find the total revenue function. [Hints: TR = √ MRdq]arrow_forward
- 6. Solve the following first-order linear differential equations; if an initial condition is given, definitize the arbitrary constant: (a) 2 + 12y + 2et = 0, y(0) = /; (b) dy+y=tarrow_forward4. Let A = {a, b, c, d, e, f}, B = {e, f, g, h} and C = {a, e, h,i}. Let U = {a, b, c, d, e, f, g, h, i, j, k}. • Draw a Venn Diagram to describe the relationships between these sets Find (AB) NC • Find (AC) UB Find AUBUC • Find (BC) N (A - C)arrow_forward7. A consumer lives on an island where she produces two goods x and y according to the production possibility frontier x² + y² < 200 and she consumes all the goods. Her utility function is U(x, y) = x y³. She faces an environmental constraint on her total output of both goods. The environmental constraint is given by x + y ≤20. • (a) Write down the consumer's optimization problem. (b) Write out the Kuhn-Tucker first order conditions. (c) Find the consumer's optimal consumption bundle (x*, y*).arrow_forward
- 3. Answer the following questions: (a) Given the marginal propensity to import M'(Y) = 0.1 and the information that M = 20 when Y = 0, find the import function M(Y). (b) Given a continuous income stream at the constant rate of $1,000 per year, what will be the present value II if the income stream terminates after exactly 3 years and the discount rate is 0.04? (c) What is the present value of a perpetual cash flow of $2,460 per year, discounted at r = 8%?arrow_forward5. Let A and B be arbitrary sets. Prove AnB = AUB.arrow_forward2. Answer the following questions: (a) Given the marginal-revenue function R'(Q) = 28Q - €0.3Q, find the total-revenue function R(Q). What initial condition can you introduce to definitize the constant of integration? = (b) Given the marginal propensity to consume C'(Y) 0.80.1Y-1/2 and the information that C = Y when Y = 100, find the consumption function C(Y).arrow_forward
- 7. Let X, A, and B be arbitrary sets such that ACX and BC X. Prove AUB CX.arrow_forward1. Write out the following sets as a list of elements. If necessary you may use ... in your description. {x EZ: |x|< 10 A x < 0} {x ЄN: x ≤ 20 A x = 2y for some y = N} {n EN: 3 | n^ 1 < n < 20} {y Є Z: y² <0}arrow_forward3. For each statement below, write an equivalent statement using the justification given. = y Є A or yЄ B by the definition of union = y Є A or y Є B by the definition of set complement = x = C and x & D by DeMorgan's Law =Vx (x EnFxЄEUF) by definition of subset. = (X CYUZ)A (YUZ CX) by definition of set equalityarrow_forward
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