EBK NATURE OF MATHEMATICS
13th Edition
ISBN: 9781305855588
Author: SMITH
Publisher: CENGAGE CO
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Chapter 4.2, Problem 8PS
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15. A spring-mass system is governed by the differential equation 2x′′ + 72x = 100 sin(3ωt) .For what value of ω will resonance occur?A. 3 B. 6√2 C. 2 D. 10 E. No value
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).
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(a) Express the rate of change of production 07-2 in time, in terms of the rate of
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(b) Suppose that when L =
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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?
17. 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. All
Chapter 4 Solutions
EBK NATURE OF MATHEMATICS
Ch. 4.1 - IN YOUR OWN WORDS Explain the difference between...Ch. 4.1 - IN YOUR OWN WORDS Discuss the similarities and...Ch. 4.1 - IN YOUR OWN WORDS What do you regard as the...Ch. 4.1 - Prob. 4PSCh. 4.1 - Prob. 5PSCh. 4.1 - Prob. 6PSCh. 4.1 - Prob. 7PSCh. 4.1 - Tell which of the named properties apply to the...Ch. 4.1 - Write each numeral in problems 920 as a decimal...Ch. 4.1 - Prob. 10PS
Ch. 4.1 - Prob. 11PSCh. 4.1 - Prob. 12PSCh. 4.1 - Prob. 13PSCh. 4.1 - Prob. 14PSCh. 4.1 - Prob. 15PSCh. 4.1 - Write each numeral in Problems 920 as a decimal...Ch. 4.1 - Prob. 17PSCh. 4.1 - Prob. 18PSCh. 4.1 - Prob. 19PSCh. 4.1 - Prob. 20PSCh. 4.1 - Prob. 21PSCh. 4.1 - Prob. 22PSCh. 4.1 - Prob. 23PSCh. 4.1 - Prob. 24PSCh. 4.1 - Prob. 25PSCh. 4.1 - Prob. 26PSCh. 4.1 - Prob. 27PSCh. 4.1 - Prob. 28PSCh. 4.1 - Prob. 29PSCh. 4.1 - Prob. 30PSCh. 4.1 - Prob. 31PSCh. 4.1 - Prob. 32PSCh. 4.1 - Prob. 33PSCh. 4.1 - Prob. 34PSCh. 4.1 - Prob. 35PSCh. 4.1 - Prob. 36PSCh. 4.1 - Prob. 37PSCh. 4.1 - Prob. 38PSCh. 4.1 - Prob. 39PSCh. 4.1 - Prob. 40PSCh. 4.1 - Prob. 41PSCh. 4.1 - Prob. 42PSCh. 4.1 - Prob. 43PSCh. 4.1 - Perform the indicated operations in Problems 4348.Ch. 4.1 - Prob. 45PSCh. 4.1 - Prob. 46PSCh. 4.1 - Prob. 47PSCh. 4.1 - Prob. 48PSCh. 4.1 - Prob. 49PSCh. 4.1 - What is the largest number that begins with the...Ch. 4.1 - Prob. 51PSCh. 4.1 - Prob. 52PSCh. 4.1 - Prob. 53PSCh. 4.1 - Prob. 54PSCh. 4.1 - Prob. 55PSCh. 4.1 - a. What is the largest number that uses each of...Ch. 4.1 - Prob. 57PSCh. 4.1 - Prob. 58PSCh. 4.1 - Prob. 59PSCh. 4.1 - Prob. 60PSCh. 4.2 - IN YOUR OWN WORDS Discuss the difference between...Ch. 4.2 - Prob. 2PSCh. 4.2 - Prob. 3PSCh. 4.2 - Prob. 4PSCh. 4.2 - Prob. 5PSCh. 4.2 - Prob. 6PSCh. 4.2 - Prob. 7PSCh. 4.2 - Prob. 8PSCh. 4.2 - Give the meaning of the numeral 5 in each of the...Ch. 4.2 - Prob. 10PSCh. 4.2 - Give the meaning of the numeral 5 in each of the...Ch. 4.2 - Prob. 12PSCh. 4.2 - Prob. 13PSCh. 4.2 - Prob. 14PSCh. 4.2 - Prob. 15PSCh. 4.2 - Prob. 16PSCh. 4.2 - Prob. 17PSCh. 4.2 - Prob. 18PSCh. 4.2 - Prob. 19PSCh. 4.2 - Prob. 20PSCh. 4.2 - Prob. 21PSCh. 4.2 - Prob. 22PSCh. 4.2 - Prob. 23PSCh. 4.2 - Prob. 24PSCh. 4.2 - Prob. 25PSCh. 4.2 - Prob. 26PSCh. 4.2 - Prob. 27PSCh. 4.2 - Prob. 28PSCh. 4.2 - Prob. 29PSCh. 4.2 - Prob. 30PSCh. 4.2 - Prob. 31PSCh. 4.2 - Prob. 32PSCh. 4.2 - Prob. 33PSCh. 4.2 - Prob. 34PSCh. 4.2 - Write each of the numbers in Problems 3142 in...Ch. 4.2 - Prob. 36PSCh. 4.2 - Prob. 37PSCh. 4.2 - Prob. 38PSCh. 4.2 - Prob. 39PSCh. 4.2 - Prob. 40PSCh. 4.2 - Prob. 41PSCh. 4.2 - Prob. 42PSCh. 4.2 - Prob. 43PSCh. 4.2 - Prob. 44PSCh. 4.2 - Prob. 45PSCh. 4.2 - Prob. 46PSCh. 4.2 - Prob. 47PSCh. 4.2 - Prob. 48PSCh. 4.2 - Prob. 49PSCh. 4.2 - Prob. 50PSCh. 4.2 - Prob. 51PSCh. 4.2 - Prob. 52PSCh. 4.2 - Prob. 53PSCh. 4.2 - Prob. 54PSCh. 4.2 - Prob. 55PSCh. 4.2 - Prob. 56PSCh. 4.2 - Prob. 57PSCh. 4.2 - Prob. 58PSCh. 4.2 - Prob. 59PSCh. 4.2 - Prob. 60PSCh. 4.3 - Prob. 1PSCh. 4.3 - Prob. 2PSCh. 4.3 - Prob. 3PSCh. 4.3 - Prob. 4PSCh. 4.3 - Count the number of people in the indicated base....Ch. 4.3 - Count the number of people in the indicated base....Ch. 4.3 - Prob. 7PSCh. 4.3 - Prob. 8PSCh. 4.3 - Prob. 9PSCh. 4.3 - Prob. 10PSCh. 4.3 - Prob. 11PSCh. 4.3 - Prob. 12PSCh. 4.3 - Prob. 13PSCh. 4.3 - Prob. 14PSCh. 4.3 - Prob. 15PSCh. 4.3 - Prob. 16PSCh. 4.3 - Prob. 17PSCh. 4.3 - Prob. 18PSCh. 4.3 - Prob. 19PSCh. 4.3 - Prob. 20PSCh. 4.3 - Prob. 21PSCh. 4.3 - Prob. 22PSCh. 4.3 - Prob. 23PSCh. 4.3 - Prob. 24PSCh. 4.3 - Prob. 25PSCh. 4.3 - Prob. 26PSCh. 4.3 - Prob. 27PSCh. 4.3 - Prob. 28PSCh. 4.3 - Prob. 29PSCh. 4.3 - Prob. 30PSCh. 4.3 - Prob. 31PSCh. 4.3 - Prob. 32PSCh. 4.3 - Prob. 33PSCh. 4.3 - Prob. 34PSCh. 4.3 - Prob. 35PSCh. 4.3 - Prob. 36PSCh. 4.3 - Prob. 37PSCh. 4.3 - Use number bases to answer the questions in...Ch. 4.3 - Prob. 39PSCh. 4.3 - Prob. 40PSCh. 4.3 - Prob. 41PSCh. 4.3 - Prob. 42PSCh. 4.3 - Prob. 43PSCh. 4.3 - Prob. 44PSCh. 4.3 - Prob. 45PSCh. 4.3 - Prob. 46PSCh. 4.3 - Prob. 47PSCh. 4.3 - Prob. 48PSCh. 4.3 - Prob. 49PSCh. 4.3 - Prob. 50PSCh. 4.3 - Prob. 51PSCh. 4.3 - Prob. 52PSCh. 4.3 - Prob. 53PSCh. 4.3 - Prob. 54PSCh. 4.3 - Prob. 55PSCh. 4.3 - Prob. 56PSCh. 4.3 - Prob. 57PSCh. 4.3 - Prob. 58PSCh. 4.3 - Prob. 59PSCh. 4.3 - Prob. 60PSCh. 4.4 - Prob. 1PSCh. 4.4 - Prob. 2PSCh. 4.4 - What decimal number is represented by the light...Ch. 4.4 - Prob. 4PSCh. 4.4 - What decimal number is represented by the light...Ch. 4.4 - Prob. 6PSCh. 4.4 - Prob. 7PSCh. 4.4 - Prob. 8PSCh. 4.4 - Prob. 9PSCh. 4.4 - Prob. 10PSCh. 4.4 - Prob. 11PSCh. 4.4 - Prob. 12PSCh. 4.4 - Prob. 13PSCh. 4.4 - Prob. 14PSCh. 4.4 - Prob. 15PSCh. 4.4 - Prob. 16PSCh. 4.4 - Prob. 17PSCh. 4.4 - Prob. 18PSCh. 4.4 - Prob. 19PSCh. 4.4 - Prob. 20PSCh. 4.4 - Prob. 21PSCh. 4.4 - Prob. 22PSCh. 4.4 - Prob. 23PSCh. 4.4 - Prob. 24PSCh. 4.4 - Prob. 25PSCh. 4.4 - Prob. 26PSCh. 4.4 - Prob. 27PSCh. 4.4 - Prob. 28PSCh. 4.4 - Prob. 29PSCh. 4.4 - Prob. 30PSCh. 4.4 - Prob. 31PSCh. 4.4 - Prob. 32PSCh. 4.4 - Prob. 33PSCh. 4.4 - Prob. 34PSCh. 4.4 - Prob. 35PSCh. 4.4 - Prob. 36PSCh. 4.4 - Prob. 37PSCh. 4.4 - Prob. 38PSCh. 4.4 - Prob. 39PSCh. 4.4 - Prob. 40PSCh. 4.4 - Perform the indicated operations in Problems 3946....Ch. 4.4 - Prob. 42PSCh. 4.4 - Prob. 43PSCh. 4.4 - Prob. 44PSCh. 4.4 - Prob. 45PSCh. 4.4 - Prob. 46PSCh. 4.4 - Prob. 47PSCh. 4.4 - Prob. 48PSCh. 4.4 - Prob. 49PSCh. 4.4 - Prob. 50PSCh. 4.4 - Prob. 51PSCh. 4.4 - Prob. 52PSCh. 4.4 - Prob. 53PSCh. 4.4 - Prob. 54PSCh. 4.4 - Prob. 55PSCh. 4.4 - Prob. 56PSCh. 4.4 - Prob. 57PSCh. 4.4 - Prob. 58PSCh. 4.4 - Prob. 59PSCh. 4.4 - Prob. 60PSCh. 4.5 - IN YOUR OWN WORDS Describe some of the computing...Ch. 4.5 - Prob. 2PSCh. 4.5 - Prob. 3PSCh. 4.5 - Prob. 4PSCh. 4.5 - Prob. 5PSCh. 4.5 - Prob. 6PSCh. 4.5 - Prob. 7PSCh. 4.5 - Prob. 8PSCh. 4.5 - Prob. 9PSCh. 4.5 - Prob. 10PSCh. 4.5 - Prob. 11PSCh. 4.5 - Prob. 12PSCh. 4.5 - Prob. 13PSCh. 4.5 - Prob. 14PSCh. 4.5 - Prob. 15PSCh. 4.5 - Prob. 16PSCh. 4.5 - Prob. 17PSCh. 4.5 - Prob. 18PSCh. 4.5 - Prob. 19PSCh. 4.5 - Prob. 20PSCh. 4.5 - Prob. 21PSCh. 4.5 - Prob. 22PSCh. 4.5 - Prob. 23PSCh. 4.5 - Prob. 24PSCh. 4.5 - Prob. 25PSCh. 4.5 - Prob. 26PSCh. 4.5 - Prob. 27PSCh. 4.5 - Prob. 28PSCh. 4.5 - Prob. 29PSCh. 4.5 - Prob. 30PSCh. 4.5 - Prob. 31PSCh. 4.5 - Prob. 32PSCh. 4.5 - Prob. 33PSCh. 4.5 - Prob. 34PSCh. 4.5 - Prob. 35PSCh. 4.5 - Prob. 36PSCh. 4.5 - Problems 3445 list a specific task. Decide whether...Ch. 4.5 - Prob. 38PSCh. 4.5 - Prob. 39PSCh. 4.5 - Prob. 40PSCh. 4.5 - Prob. 41PSCh. 4.5 - Prob. 42PSCh. 4.5 - Prob. 43PSCh. 4.5 - Prob. 44PSCh. 4.5 - Prob. 45PSCh. 4.5 - Prob. 46PSCh. 4.5 - Prob. 47PSCh. 4.5 - Prob. 48PSCh. 4.5 - Prob. 49PSCh. 4.5 - Prob. 50PSCh. 4.5 - Prob. 51PSCh. 4.5 - Prob. 52PSCh. 4.5 - Prob. 53PSCh. 4.5 - Prob. 54PSCh. 4.5 - Prob. 55PSCh. 4.5 - Prob. 56PSCh. 4.5 - Prob. 57PSCh. 4.5 - Prob. 58PSCh. 4.5 - Prob. 59PSCh. 4.5 - Prob. 60PSCh. 4.CR - Prob. 1CRCh. 4.CR - Prob. 2CRCh. 4.CR - Prob. 3CRCh. 4.CR - Prob. 4CRCh. 4.CR - Prob. 5CRCh. 4.CR - Prob. 6CRCh. 4.CR - Prob. 7CRCh. 4.CR - Prob. 8CRCh. 4.CR - Prob. 9CRCh. 4.CR - Prob. 10CRCh. 4.CR - Prob. 11CRCh. 4.CR - Prob. 12CRCh. 4.CR - Prob. 13CRCh. 4.CR - Prob. 14CRCh. 4.CR - Prob. 15CRCh. 4.CR - Prob. 16CRCh. 4.CR - Prob. 17CRCh. 4.CR - Prob. 18CRCh. 4.CR - Prob. 19CRCh. 4.CR - Prob. 20CR
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- 20. 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_forward9. A 1 kg mass is attached to a spring with constant 13 N/m. The system is immersed in amedium which offers a damping force numerically equal to 6 times the instantaneous velocity.If x is the displacement of the mass from equilibrium, measured in meters,then x′′ + 6x′ + 13x = 0 . Which of the following statements is true?A. x(t) = c1e^−t + c2e^−5t, and the system is underdamped.B. x(t) = c1e^−t + c2e^−5t, and the system is overdamped.C. x(t) = c1e^−3t cos(2t) + c2e^−3t sin(2t), and the system is underdamped.D. x(t) = c1e^−3t cos(2t) + c2e^−3t sin(2t), and the system is overdamped.arrow_forwardQuestion 2 (A partial differential equation). The diffusion equation де Ət = 82 с მx2 where D is a positive constant, describes the diffusion of heat through a solid, or the concentration of a pollutant at time t at a distance x from the source of the pollution, or the invasion of alien species into a new habitat. Verify that the function c(x, t) -x²/(4Dt) = √4πDt is a solution of the diffusion equation.arrow_forward
- 13. Let y(x) be the solution to the initial value problem y′′ − 10y′ + 25y = 0, y(0) = 1, y′(0) = 3.Then y(1) = ? A. −e^5 B. 1 C. e^5 D. 4/5 e^5 + 1/5 e^−5 E. e^−5arrow_forwardQuestion 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_forward
- why the know-show table below is not valid: I know something is wrong in the step p2-p5 but I don't know how to explain it. Can you explain why please.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_forward1. A solution to the differential equation y′′ + 4y′ + 13y = 0 isA. y(t) = e^2t cos 3t B. y(t) = te^2t cos 3t C. y(t) = e^−2t sin 3t D. None of thesearrow_forward
- 2. The appropriate guess for the particular solution to the differential equationy′′ + 3y′ + 2y = 2x + 3e^−x isA. A + Bx + Ce^−x B. A + Bx + Cxe^−x C. Ax + Bx^2 + Ce−^x D. Ax + Bx^2 + Cxe^−xarrow_forwardConsider the following statement: For all integers a and b, if a 0 (mod 6) and b #0 (mod 6), then ab #0 (mod 6). Which of the following statements are true? (select all that apply) Original statement ✓ Contrapositive Converse Negation ☐ None of the statements are truearrow_forwardProposition: If m is an odd integer, then m + 6 is an odd integer. Proof: For m + 6 to be an odd integer, there must exist an integer n such that m+6=2n+1. Subtracting 6 from both sides, we see that m = 2n+1-6 = = 2n― 6+1 = 2(n − 3) + 1. Since the integers are closed under subtraction, then n-3 € Z. Hence, the last equation implies that m = = 2q+1 where q = n = 3. This proves - that if m is an odd integer, then m + 6 is an odd integer. Based upon the Reading assignment and the Elements of Style >>, which of the following is the most significant error in the proof? The proof does not use complete sentences The proof contains a sentence that begins with a mathematical symbol The proof uses cumbersome notation The proof contains a variable used for more than one object The proof is written backwards The proof uses an example to prove the general casearrow_forward
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