Mathematics For Machine Technology
8th Edition
ISBN: 9781337798310
Author: Peterson, John.
Publisher: Cengage Learning,
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Chapter 20, Problem 47A
To determine
Evaluation of the lengths of A, B, C, and D.
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1. A Blue Whale's resting heart rate has period that happens to be approximately equal to 2π. A typical ECG of a whale's heartbeat
over one period may be approximated by the function,
f(x)
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0.005x³-0.364x² + 1.27x
on the interval [0, 27]. Find an nth-order Fourier approximation to the Blue Whale's heartbeat, where n ≥ 3 is different from
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7. The demand for a product, in dollars, is
p = D(x) = 1000 -0.5 -0.0002x²
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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:
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+10y=15, y(0) = 0;
(b) 2 + 4y = 6, y(0) =
Chapter 20 Solutions
Mathematics For Machine Technology
Ch. 20 - Use a decimal equivalents table to find the...Ch. 20 - Compute (27.52.5+4.36)21.75 . Express the result...Ch. 20 - A cylinder has a volume, V, of 32.85 mm3. Use the...Ch. 20 - The volume V of a cube is V=s3 , where s is the...Ch. 20 - Multiply 15.328.75 .Ch. 20 - Express the decimal fraction 0.4275 as a common...Ch. 20 - Prob. 7ACh. 20 - Express the following ratios in lowest fractional...Ch. 20 - Prob. 9ACh. 20 - Express the following ratios in lowest fractional...
Ch. 20 - Prob. 11ACh. 20 - Prob. 12ACh. 20 - Prob. 13ACh. 20 - Express the following ratios in lowest fractional...Ch. 20 - Prob. 15ACh. 20 - Express the following ratios in lowest fractional...Ch. 20 - Length A in Figure 205 is 3 inches and length B is...Ch. 20 - Prob. 18ACh. 20 - Prob. 19ACh. 20 - In Figure 208, gear A is turning at 120...Ch. 20 - Solve for the unknown value in each of the...Ch. 20 - Solve for the unknown value in each of the...Ch. 20 - Prob. 23ACh. 20 - Prob. 24ACh. 20 - Prob. 25ACh. 20 - Prob. 26ACh. 20 - Prob. 27ACh. 20 - Solve for the unknown value in each of the...Ch. 20 - Solve for the unknown value in each of the...Ch. 20 - Prob. 30ACh. 20 - Prob. 31ACh. 20 - Prob. 32ACh. 20 - Prob. 33ACh. 20 - Prob. 34ACh. 20 - Prob. 35ACh. 20 - Prob. 36ACh. 20 - Prob. 37ACh. 20 - Prob. 38ACh. 20 - Prob. 39ACh. 20 - Prob. 40ACh. 20 - Prob. 41ACh. 20 - Prob. 42ACh. 20 - The proportion AB=CDcompares the sides of two...Ch. 20 - Prob. 44ACh. 20 - It is sometimes impractical to make engineering...Ch. 20 - Prob. 46ACh. 20 - Prob. 47ACh. 20 - A drawing has a scale of 14=3 . Determine the...
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- 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) = 0arrow_forward1. 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_forward
- 9. 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_forward6. 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_forward
- 7. 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_forward3. 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_forward
- 2. 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_forward7. 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_forward
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