Basic Technical Mathematics with Calculus (11th Edition)
11th Edition
ISBN: 9780134437736
Author: Allyn J. Washington, Richard Evans
Publisher: PEARSON
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Chapter 2.2, Problem 2E
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9. 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.
Question 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.
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^−5
Chapter 2 Solutions
Basic Technical Mathematics with Calculus (11th Edition)
Ch. 2.1 - What is the measure of the complement of in Fig....Ch. 2.1 - Prob. 2PECh. 2.1 - In Exercises 1–4, answer the given questions about...Ch. 2.1 - Prob. 2ECh. 2.1 - Prob. 3ECh. 2.1 - Prob. 4ECh. 2.1 - In Exercises 5–12, identify the indicated angles...Ch. 2.1 - In Exercises 5–12, identify the indicated angles...Ch. 2.1 - In Exercises 5–12, identify the indicated angles...Ch. 2.1 - In Exercises 5–12, identify the indicated angles...
Ch. 2.1 - In Exercises 5–12, identify the indicated angles...Ch. 2.1 - In Exercises 5–12, identify the indicated angles...Ch. 2.1 - In Exercises 5–12, identify the indicated angles...Ch. 2.1 - In Exercises 5–12, identify the indicated angles...Ch. 2.1 - In Exercises 13–15, use Fig. 2.11. In Exercises...Ch. 2.1 - In Exercises 13–15, use Fig. 2.11. In Exercises...Ch. 2.1 - In Exercises 13–15, use Fig. 2.11. In Exercises...Ch. 2.1 - In Exercises 13–15, use Fig. 2.11. In Exercises...Ch. 2.1 - In Exercises 13–15, use Fig. 2.11. In Exercises...Ch. 2.1 - In Exercises 13–15, use Fig. 2.11. In Exercises...Ch. 2.1 - In Exercises 19–24, find the measures of the...Ch. 2.1 - In Exercises 19–24, find the measures of the...Ch. 2.1 - In Exercises 19–24, find the measures of the...Ch. 2.1 - In Exercises 19–24, find the measures of the...Ch. 2.1 - In Exercises 19–24, find the measures of the...Ch. 2.1 - In Exercises 19–24, find the measures of the...Ch. 2.1 - In Exercises 25–30, find the measures of the...Ch. 2.1 - In Exercises 25-30, find the measures of the...Ch. 2.1 - In Exercises 25-30, find the measures of the...Ch. 2.1 - In Exercises 25-30, find the measures of the...Ch. 2.1 - In Exercises 25-30, find the measures of the...Ch. 2.1 - In Exercises 25-30, find the measures of the...Ch. 2.1 - In Exercises 31–34, find the indicated distances...Ch. 2.1 - In Exercises 31–34, find the indicated distances...Ch. 2.1 - In Exercises 31–34, find the indicated distances...Ch. 2.1 - In Exercises 31–34, find the indicated distances...Ch. 2.1 - In Exercises 35–40, find all angles of the given...Ch. 2.1 - In Exercises 35–40, find all angles of the given...Ch. 2.1 - In Exercises 35–40, find all angles of the given...Ch. 2.1 - In Exercises 35–40, find all angles of the given...Ch. 2.1 - In Exercises 35–40, find all angles of the given...Ch. 2.1 - In Exercises 35–40, find all angles of the given...Ch. 2.1 - In Exercises 41-46, solve the given problems
41. A...Ch. 2.1 - In Exercises 41–16, solve the given...Ch. 2.1 - In Exercises 41-46, solve the given problems
43. A...Ch. 2.1 - Prob. 44ECh. 2.1 - Prob. 45ECh. 2.1 - Prob. 46ECh. 2.1 - Prob. 47ECh. 2.1 - Prob. 48ECh. 2.1 - Prob. 49ECh. 2.1 - Prob. 50ECh. 2.2 - Prob. 1PECh. 2.2 - Prob. 2PECh. 2.2 - Prob. 3PECh. 2.2 - Prob. 1ECh. 2.2 - Prob. 2ECh. 2.2 - Prob. 3ECh. 2.2 - Prob. 4ECh. 2.2 - In Exercises 5–8, determine ∠A in the indicated...Ch. 2.2 - In Exercises 5–8, determine ∠A in the indicated...Ch. 2.2 - In Exercises 5–8, determine ∠A in the indicated...Ch. 2.2 - In Exercises 5–8, determine ∠A in the indicated...Ch. 2.2 - In Exercises 9–16, find the area of each...Ch. 2.2 - In Exercises 9–16, find the area of each...Ch. 2.2 - In Exercises 9–16, find the area of each...Ch. 2.2 - In Exercises 9–16, find the area of each...Ch. 2.2 - In Exercises 9–16, find the area of each...Ch. 2.2 - In Exercises 9–16, find the area of each...Ch. 2.2 - In Exercises 9–16, find the area of each...Ch. 2.2 - In Exercises 9–16, find the area of each...Ch. 2.2 - In Exercises 17–20, find the perimeter of each...Ch. 2.2 - In Exercises 17–20, find the perimeter of each...Ch. 2.2 - In Exercises 17–20, find the perimeter of each...Ch. 2.2 - In Exercises 17–20, find the perimeter of each...Ch. 2.2 - In Exercises 21–26, find the third side of the...Ch. 2.2 - In Exercises 21–26, find the third side of the...Ch. 2.2 - In Exercises 21–26, find the third side of the...Ch. 2.2 - In Exercises 21–26, find the third side of the...Ch. 2.2 - In Exercises 21–26, find the third side of the...Ch. 2.2 - In Exercises 21–26, find the third side of the...Ch. 2.2 - In Exercises 27–30, use the right triangle in Fig....Ch. 2.2 - In Exercises 27–30, use the right triangle in Fig....Ch. 2.2 - In Exercises 27–30, use the right triangle in Fig....Ch. 2.2 - Prob. 30ECh. 2.2 - In Exercises 31–58, solve the given problems.
31....Ch. 2.2 - In Exercises 31–58, solve the given problems.
32....Ch. 2.2 - In Exercises 31–58, solve the given problems.
33....Ch. 2.2 - In Exercises 31–58, solve the given...Ch. 2.2 - In Exercises 31–58, solve the given problems.
35....Ch. 2.2 - In Exercises 31–58, solve the given problems.
36....Ch. 2.2 - In Exercises 31–58, solve the given...Ch. 2.2 - Prob. 38ECh. 2.2 - Prob. 39ECh. 2.2 - Prob. 40ECh. 2.2 - Prob. 41ECh. 2.2 - In Exercises 31–58, solve the given...Ch. 2.2 - In Exercises 31–58, solve the given...Ch. 2.2 - In Exercises 31–58, solve the given...Ch. 2.2 - Prob. 45ECh. 2.2 - Prob. 46ECh. 2.2 - Prob. 47ECh. 2.2 - Prob. 48ECh. 2.2 - In Exercises 31–58, solve the given...Ch. 2.2 - Prob. 50ECh. 2.2 - In Exercises 31–58, solve the given problems.
51....Ch. 2.2 - Prob. 52ECh. 2.2 - Prob. 53ECh. 2.2 - Prob. 54ECh. 2.2 - Prob. 55ECh. 2.2 - Prob. 56ECh. 2.2 - Prob. 57ECh. 2.2 - Prob. 58ECh. 2.3 - Prob. 1PECh. 2.3 - Prob. 2PECh. 2.3 - Prob. 3PECh. 2.3 - Prob. 1ECh. 2.3 - Prob. 2ECh. 2.3 - Prob. 3ECh. 2.3 - Prob. 4ECh. 2.3 - Prob. 5ECh. 2.3 - In Exercises 5–12, find the perimeter of each...Ch. 2.3 - In Exercises 5–12, find the perimeter of each...Ch. 2.3 - In Exercises 5–12, find the perimeter of each...Ch. 2.3 - In Exercises 5–12, find the perimeter of each...Ch. 2.3 - In Exercises 5–12, find the perimeter of each...Ch. 2.3 - In Exercises 5–12, find the perimeter of each...Ch. 2.3 - In Exercises 5–12, find the perimeter of each...Ch. 2.3 - In Exercises 13–20, find the area of each...Ch. 2.3 - In Exercises 13–20, find the area of each...Ch. 2.3 - In Exercises 13–20, find the area of each...Ch. 2.3 - In Exercises 13–20, find the area of each...Ch. 2.3 - In Exercises 13–20, find the area of each...Ch. 2.3 - In Exercises 13–20, find the area of each...Ch. 2.3 - In Exercises 13–20, find the area of each...Ch. 2.3 - In Exercises 13–20, find the area of each...Ch. 2.3 - Prob. 21ECh. 2.3 - Prob. 22ECh. 2.3 - Prob. 23ECh. 2.3 - In Exercises 21–24, set up a formula for the...Ch. 2.3 - In Exercises 25–46, solve the given...Ch. 2.3 - What conclusion can you make about the two...Ch. 2.3 - Find the area of a square whose diagonal is 24.0...Ch. 2.3 - Noting the quadrilateral in Fig. 2.67, determine...Ch. 2.3 - The sum S of the measures of the interior angles...Ch. 2.3 - Express the area A of the large rectangle in Fig....Ch. 2.3 - Express the area of the square in Fig. 2.69 in...Ch. 2.3 - Part of an electric circuit is wired in the...Ch. 2.3 - A walkway 3.0 m wide is constructed along the...Ch. 2.3 - An architect designs a rectangular window such...Ch. 2.3 - Find the area of the cross section of concrete...Ch. 2.3 - A beam support in a building is in the shape of a...Ch. 2.3 - Each of two walls (with rectangular windows) of an...Ch. 2.3 - Prob. 40ECh. 2.3 - Prob. 41ECh. 2.3 - Prob. 42ECh. 2.3 - Prob. 43ECh. 2.3 - Prob. 44ECh. 2.3 - Prob. 45ECh. 2.3 - Prob. 46ECh. 2.4 - Prob. 1PECh. 2.4 - Prob. 2PECh. 2.4 - Prob. 3PECh. 2.4 - In Exercises 1-4, answer the given questions about...Ch. 2.4 - Prob. 2ECh. 2.4 - Prob. 3ECh. 2.4 - Prob. 4ECh. 2.4 - Prob. 5ECh. 2.4 - In Exercises 5-8, refer to the circle with center...Ch. 2.4 - In Exercises 5-8, refer to the circle with center...Ch. 2.4 - In Exercises 5-8, refer to the circle with center...Ch. 2.4 - In Exercises 9–12, find the circumference of the...Ch. 2.4 - In Exercises 9–12, find the circumference of the...Ch. 2.4 - In Exercises 9–12, find the circumference of the...Ch. 2.4 - In Exercises 9–12, find the circumference of the...Ch. 2.4 - In Exercises 13–16, find the area of the circle...Ch. 2.4 - In Exercises 13–16, find the area of the circle...Ch. 2.4 - In Exercises 13–16, find the area of the circle...Ch. 2.4 - In Exercises 13–16, find the area of the circle...Ch. 2.4 - In Exercises 17 and 18, find the area of the...Ch. 2.4 - In Exercises 17 and 18, find the area of the...Ch. 2.4 - In Exercises 19–22, refer to Fig. 2.86, where AB...Ch. 2.4 - In Exercises 19–22, refer to Fig. 2.86, where AB...Ch. 2.4 - In Exercises 19–22, refer to Fig. 2.86, where AB...Ch. 2.4 - In Exercises 19–22, refer to Fig. 2.86, where AB...Ch. 2.4 - In Exercises 23–26, refer to Fig. 2.87. Determine...Ch. 2.4 - In Exercises 23–26, refer to Fig. 2.87. Determine...Ch. 2.4 - In Exercises 23–26, refer to Fig. 2.87. Determine...Ch. 2.4 - In Exercises 23–26, refer to Fig. 2.87. Determine...Ch. 2.4 - In Exercises 27–30, change the given angles to...Ch. 2.4 - In Exercises 27–30, change the given angles to...Ch. 2.4 - In Exercises 27–30, change the given angles to...Ch. 2.4 - In Exercises 27–30, change the given angles to...Ch. 2.4 - In Exercises 31–34, find a formula for the...Ch. 2.4 - In Exercises 31–34, find a formula for the...Ch. 2.4 - Prob. 33ECh. 2.4 - Prob. 34ECh. 2.4 - Prob. 35ECh. 2.4 - Prob. 36ECh. 2.4 - Prob. 37ECh. 2.4 - Prob. 38ECh. 2.4 - Prob. 39ECh. 2.4 - Prob. 40ECh. 2.4 - Prob. 41ECh. 2.4 - Prob. 42ECh. 2.4 - Prob. 43ECh. 2.4 - Prob. 44ECh. 2.4 - Prob. 45ECh. 2.4 - Prob. 46ECh. 2.4 - Prob. 47ECh. 2.4 - Prob. 48ECh. 2.4 - Prob. 49ECh. 2.4 - Prob. 50ECh. 2.4 - Prob. 51ECh. 2.4 - Prob. 52ECh. 2.4 - In Exercises 35–58, solve the given...Ch. 2.4 - Prob. 54ECh. 2.4 - Prob. 55ECh. 2.4 - Prob. 56ECh. 2.4 - Prob. 57ECh. 2.4 - Prob. 58ECh. 2.5 - Prob. 1PECh. 2.5 - Prob. 1ECh. 2.5 - Prob. 2ECh. 2.5 - Prob. 3ECh. 2.5 - Prob. 4ECh. 2.5 - Prob. 5ECh. 2.5 - Prob. 6ECh. 2.5 - In Exercises 7–18, calculate the indicated areas....Ch. 2.5 - In Exercises 7–18, calculate the indicated areas....Ch. 2.5 - In Exercises 7–18, calculate the indicated areas....Ch. 2.5 - In Exercises 7–18, calculate the indicated areas....Ch. 2.5 - Prob. 11ECh. 2.5 - Prob. 12ECh. 2.5 - Prob. 13ECh. 2.5 - Prob. 14ECh. 2.5 - Prob. 15ECh. 2.5 - Prob. 16ECh. 2.5 - Prob. 17ECh. 2.5 - Prob. 18ECh. 2.5 - Prob. 19ECh. 2.5 - Prob. 20ECh. 2.5 - Prob. 21ECh. 2.5 - In Exercises 19–22, calculate the area of the...Ch. 2.6 - Prob. 1PECh. 2.6 - Prob. 2PECh. 2.6 - Prob. 1ECh. 2.6 - Prob. 2ECh. 2.6 - Prob. 3ECh. 2.6 - Prob. 4ECh. 2.6 - Prob. 5ECh. 2.6 - Prob. 6ECh. 2.6 - Prob. 7ECh. 2.6 - Prob. 8ECh. 2.6 - In Exercises 5–22, find the volume or area of each...Ch. 2.6 - Prob. 10ECh. 2.6 - Prob. 11ECh. 2.6 - In Exercises 5–22, find the volume or area of each...Ch. 2.6 - Prob. 13ECh. 2.6 - Prob. 14ECh. 2.6 - Prob. 15ECh. 2.6 - Prob. 16ECh. 2.6 - Prob. 17ECh. 2.6 - Prob. 18ECh. 2.6 - Prob. 19ECh. 2.6 - Prob. 20ECh. 2.6 - Prob. 21ECh. 2.6 - Prob. 22ECh. 2.6 - Prob. 23ECh. 2.6 - Prob. 24ECh. 2.6 - Prob. 25ECh. 2.6 - Prob. 26ECh. 2.6 - Prob. 27ECh. 2.6 - Prob. 28ECh. 2.6 - Prob. 29ECh. 2.6 - Prob. 30ECh. 2.6 - Prob. 31ECh. 2.6 - Prob. 32ECh. 2.6 - Prob. 33ECh. 2.6 - Prob. 34ECh. 2.6 - Prob. 35ECh. 2.6 - In Exercises 23–46, solve the given problems.
36....Ch. 2.6 - Prob. 37ECh. 2.6 - Prob. 38ECh. 2.6 - Prob. 39ECh. 2.6 - Prob. 40ECh. 2.6 - Prob. 41ECh. 2.6 - Prob. 42ECh. 2.6 - Prob. 43ECh. 2.6 - In Exercises 23–46, solve the given problems.
44....Ch. 2.6 - In Exercises 23–46, solve the given problems.
45....Ch. 2.6 - Prob. 46ECh. 2 - Prob. 1RECh. 2 - Prob. 2RECh. 2 - Prob. 3RECh. 2 - Prob. 4RECh. 2 - Prob. 5RECh. 2 - Prob. 6RECh. 2 - Prob. 7RECh. 2 - Prob. 8RECh. 2 - Prob. 9RECh. 2 - Prob. 10RECh. 2 - Prob. 11RECh. 2 - Prob. 12RECh. 2 - Prob. 13RECh. 2 - Prob. 14RECh. 2 - Prob. 15RECh. 2 - Prob. 16RECh. 2 - Prob. 17RECh. 2 - Prob. 18RECh. 2 - Prob. 19RECh. 2 - Prob. 20RECh. 2 - Prob. 21RECh. 2 - Prob. 22RECh. 2 - In Exercises 19–26, find the perimeter or area of...Ch. 2 - Prob. 24RECh. 2 - Prob. 25RECh. 2 - Prob. 26RECh. 2 - Prob. 27RECh. 2 - Prob. 28RECh. 2 - Prob. 29RECh. 2 - In Exercises 27–32, find the volume of the...Ch. 2 - Prob. 31RECh. 2 - Prob. 32RECh. 2 - Prob. 33RECh. 2 - Prob. 34RECh. 2 - Prob. 35RECh. 2 - Prob. 36RECh. 2 - Prob. 37RECh. 2 - Prob. 38RECh. 2 - Prob. 39RECh. 2 - Prob. 40RECh. 2 - Prob. 41RECh. 2 - Prob. 42RECh. 2 - Prob. 43RECh. 2 - Prob. 44RECh. 2 - Prob. 45RECh. 2 - Prob. 46RECh. 2 - Prob. 47RECh. 2 - Prob. 48RECh. 2 - Prob. 49RECh. 2 - Prob. 50RECh. 2 - If the dimensions of a plane geometric figure are...Ch. 2 - Prob. 52RECh. 2 - Prob. 53RECh. 2 - Prob. 54RECh. 2 - Prob. 55RECh. 2 - Prob. 56RECh. 2 - Prob. 57RECh. 2 - Prob. 58RECh. 2 - Prob. 59RECh. 2 - Prob. 60RECh. 2 - Prob. 61RECh. 2 - Prob. 62RECh. 2 - Prob. 63RECh. 2 - Prob. 64RECh. 2 - Prob. 65RECh. 2 - Prob. 66RECh. 2 - Prob. 67RECh. 2 - Prob. 68RECh. 2 - In Exercises 55–84, solve the given problems.
69....Ch. 2 - Prob. 70RECh. 2 - Prob. 71RECh. 2 - Prob. 72RECh. 2 - Prob. 73RECh. 2 - Prob. 74RECh. 2 - Prob. 75RECh. 2 - Prob. 76RECh. 2 - Prob. 77RECh. 2 - Prob. 78RECh. 2 - Prob. 79RECh. 2 - Prob. 80RECh. 2 - Prob. 81RECh. 2 - Prob. 82RECh. 2 - Prob. 83RECh. 2 - Prob. 84RECh. 2 - Prob. 85RECh. 2 - Prob. 1PTCh. 2 - Prob. 2PTCh. 2 - Prob. 3PTCh. 2 - Prob. 4PTCh. 2 - Prob. 5PTCh. 2 - Prob. 6PTCh. 2 - Prob. 7PTCh. 2 - Find the surface area of a tennis ball whose...Ch. 2 - Prob. 9PTCh. 2 - Prob. 10PTCh. 2 - Prob. 11PTCh. 2 - Prob. 12PTCh. 2 - Prob. 13PTCh. 2 - Prob. 14PT
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