Finite Mathematics and Calculus with Applications
1st Edition
ISBN: 9781323188361
Author: Margaret Lial
Publisher: Pearson Education
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Chapter 16.2, Problem 31E
To determine
To find: The average value of the function
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(6) (8 points) Change the order of integration and evaluate
(z +4ry)drdy .
So S√ ²
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(10) (16 points) Let R>0. Consider the truncated sphere S given as
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where F(x, y, z) = −yi + xj .
(a) (8 points) Consider the vector field
V (x, y, z) = (▼ × F)(x, y, z)
Think of S as a hot-air balloon where the vector field V is the velocity vector
field measuring the hot gasses escaping through the porous surface S. The flux
of V across S gives the volume flow rate of the gasses through S. Calculate
this flux.
Hint: Parametrize the boundary OS. Then use Stokes' Theorem.
(b) (8 points) Calculate the surface area of the balloon. To calculate the surface
area, do the following:
Translate the balloon surface S by the vector (-15)k. The translated
surface, call it S+ is part of the sphere x² + y²+z² = R².
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Chapter 16 Solutions
Finite Mathematics and Calculus with Applications
Ch. 16.1 - Find xe2xdx.Ch. 16.1 - Find ln2xdx.Ch. 16.1 - Prob. 3YTCh. 16.1 - Find 1ex2lnxdx.Ch. 16.1 - Prob. 5YTCh. 16.1 - Prob. 1WECh. 16.1 - Find the following. W2.(3x52x3)dxCh. 16.1 - Find the following. W3.(x23+1x)dxCh. 16.1 - Prob. 4WECh. 16.1 - Use integration by parts to find the integrals in...
Ch. 16.1 - Prob. 6WECh. 16.1 - Use integration by parts to find the integrals in...Ch. 16.1 - Use integration by parts to find the integrals in...Ch. 16.1 - Prob. 3ECh. 16.1 - Prob. 4ECh. 16.1 - Prob. 5ECh. 16.1 - Use integration by parts to find the integrals in...Ch. 16.1 - Prob. 7ECh. 16.1 - Prob. 8ECh. 16.1 - Prob. 9ECh. 16.1 - Prob. 10ECh. 16.1 - Prob. 11ECh. 16.1 - Prob. 12ECh. 16.1 - Prob. 13ECh. 16.1 - Prob. 14ECh. 16.1 - Prob. 15ECh. 16.1 - Prob. 16ECh. 16.1 - Prob. 17ECh. 16.1 - Prob. 18ECh. 16.1 - Prob. 19ECh. 16.1 - Exercises 1322 are mixedsome require integration...Ch. 16.1 - Prob. 21ECh. 16.1 - Prob. 22ECh. 16.1 - Prob. 23ECh. 16.1 - Prob. 24ECh. 16.1 - Prob. 25ECh. 16.1 - Prob. 26ECh. 16.1 - Prob. 27ECh. 16.1 - Prob. 28ECh. 16.1 - What rule of differentiation is related to...Ch. 16.1 - Prob. 30ECh. 16.1 - Suppose that u and v are differentiable functions...Ch. 16.1 - Prob. 32ECh. 16.1 - Prob. 33ECh. 16.1 - Prob. 34ECh. 16.1 - Prob. 35ECh. 16.1 - Prob. 36ECh. 16.1 - Prob. 37ECh. 16.1 - Prob. 38ECh. 16.1 - Prob. 39ECh. 16.1 - Prob. 40ECh. 16.1 - Prob. 41ECh. 16.1 - Prob. 42ECh. 16.1 - Prob. 43ECh. 16.1 - Prob. 44ECh. 16.2 - Prob. 1YTCh. 16.2 - Prob. 2YTCh. 16.2 - Prob. 1WECh. 16.2 - Prob. 2WECh. 16.2 - Prob. 3WECh. 16.2 - Prob. 4WECh. 16.2 - Prob. 5WECh. 16.2 - Prob. 6WECh. 16.2 - Prob. 1ECh. 16.2 - Prob. 2ECh. 16.2 - Prob. 3ECh. 16.2 - Prob. 4ECh. 16.2 - Prob. 5ECh. 16.2 - Prob. 6ECh. 16.2 - Prob. 7ECh. 16.2 - Prob. 8ECh. 16.2 - Prob. 9ECh. 16.2 - Prob. 10ECh. 16.2 - Prob. 11ECh. 16.2 - Prob. 12ECh. 16.2 - Prob. 13ECh. 16.2 - Prob. 14ECh. 16.2 - Prob. 15ECh. 16.2 - Prob. 16ECh. 16.2 - Prob. 17ECh. 16.2 - Prob. 18ECh. 16.2 - Prob. 19ECh. 16.2 - Prob. 20ECh. 16.2 - Prob. 21ECh. 16.2 - Prob. 22ECh. 16.2 - Prob. 23ECh. 16.2 - Prob. 24ECh. 16.2 - Prob. 25ECh. 16.2 - Prob. 26ECh. 16.2 - Prob. 27ECh. 16.2 - Prob. 28ECh. 16.2 - Prob. 29ECh. 16.2 - Prob. 30ECh. 16.2 - Prob. 31ECh. 16.2 - Prob. 32ECh. 16.2 - Prob. 33ECh. 16.2 - Prob. 34ECh. 16.2 - Prob. 35ECh. 16.2 - Prob. 36ECh. 16.2 - Prob. 37ECh. 16.2 - Prob. 38ECh. 16.2 - Prob. 39ECh. 16.2 - Prob. 40ECh. 16.2 - Prob. 41ECh. 16.2 - Prob. 42ECh. 16.2 - Prob. 43ECh. 16.2 - Typing Speed The function W(t)=3.75t2+30t+40...Ch. 16.2 - Prob. 45ECh. 16.3 - Prob. 1YTCh. 16.3 - Prob. 2YTCh. 16.3 - Prob. 3YTCh. 16.3 - Prob. 4YTCh. 16.3 - Prob. 1WECh. 16.3 - Prob. 2WECh. 16.3 - Prob. 3WECh. 16.3 - Prob. 4WECh. 16.3 - Each of the functions in Exercises 114 represents...Ch. 16.3 - Prob. 2ECh. 16.3 - Prob. 3ECh. 16.3 - Prob. 4ECh. 16.3 - Prob. 5ECh. 16.3 - Each of the functions in Exercises 114 represents...Ch. 16.3 - Prob. 7ECh. 16.3 - Prob. 8ECh. 16.3 - Each of the functions in Exercises 114 represents...Ch. 16.3 - Prob. 10ECh. 16.3 - Prob. 11ECh. 16.3 - Prob. 12ECh. 16.3 - Prob. 13ECh. 16.3 - Prob. 14ECh. 16.3 - Prob. 15ECh. 16.3 - Prob. 16ECh. 16.3 - Prob. 17ECh. 16.3 - Prob. 18ECh. 16.3 - Present Value A money market fund has a continuous...Ch. 16.3 - Accumulated Amount of Money Flow Find the amount...Ch. 16.4 - Prob. 1YTCh. 16.4 - Prob. 2YTCh. 16.4 - Prob. 1WECh. 16.4 - Prob. 2WECh. 16.4 - Prob. 3WECh. 16.4 - Prob. 4WECh. 16.4 - Prob. 1ECh. 16.4 - Prob. 2ECh. 16.4 - Prob. 3ECh. 16.4 - Prob. 4ECh. 16.4 - Prob. 5ECh. 16.4 - Prob. 6ECh. 16.4 - Prob. 7ECh. 16.4 - Prob. 8ECh. 16.4 - Prob. 9ECh. 16.4 - Prob. 10ECh. 16.4 - Prob. 11ECh. 16.4 - Prob. 12ECh. 16.4 - Prob. 13ECh. 16.4 - Prob. 14ECh. 16.4 - Prob. 15ECh. 16.4 - Prob. 16ECh. 16.4 - Prob. 17ECh. 16.4 - Prob. 18ECh. 16.4 - Prob. 19ECh. 16.4 - Prob. 20ECh. 16.4 - Prob. 21ECh. 16.4 - Prob. 22ECh. 16.4 - Prob. 23ECh. 16.4 - Prob. 24ECh. 16.4 - Determine whether each improper integral converges...Ch. 16.4 - Prob. 26ECh. 16.4 - Prob. 27ECh. 16.4 - Prob. 28ECh. 16.4 - Determine whether each improper integral converges...Ch. 16.4 - Prob. 30ECh. 16.4 - Prob. 31ECh. 16.4 - Prob. 32ECh. 16.4 - Prob. 33ECh. 16.4 - Prob. 34ECh. 16.4 - Prob. 35ECh. 16.4 - Prob. 36ECh. 16.4 - Prob. 37ECh. 16.4 - Prob. 38ECh. 16.4 - Prob. 39ECh. 16.4 - Prob. 40ECh. 16.4 - Prob. 41ECh. 16.4 - Prob. 42ECh. 16.4 - Prob. 43ECh. 16.4 - Prob. 44ECh. 16.4 - Prob. 45ECh. 16.4 - Prob. 46ECh. 16.4 - Prob. 47ECh. 16.4 - Prob. 48ECh. 16.4 - Prob. 49ECh. 16.4 - Prob. 50ECh. 16.4 - Prob. 51ECh. 16.4 - Prob. 52ECh. 16.4 - Radioactive Waste The rate at which radioactive...Ch. 16.4 - Prob. 54ECh. 16.5 - Find all solutions of the differential equation...Ch. 16.5 - Prob. 2YTCh. 16.5 - Prob. 3YTCh. 16.5 - In Example 6, find the goat population in 5 years...Ch. 16.5 - Prob. 1WECh. 16.5 - Prob. 2WECh. 16.5 - Prob. 3WECh. 16.5 - Prob. 4WECh. 16.5 - Prob. 5WECh. 16.5 - Prob. 1ECh. 16.5 - Prob. 2ECh. 16.5 - Prob. 3ECh. 16.5 - Prob. 4ECh. 16.5 - Prob. 5ECh. 16.5 - Prob. 6ECh. 16.5 - Prob. 7ECh. 16.5 - Prob. 8ECh. 16.5 - Prob. 9ECh. 16.5 - Prob. 10ECh. 16.5 - Prob. 11ECh. 16.5 - Prob. 12ECh. 16.5 - Prob. 13ECh. 16.5 - Prob. 14ECh. 16.5 - Prob. 15ECh. 16.5 - Prob. 16ECh. 16.5 - Prob. 17ECh. 16.5 - Prob. 18ECh. 16.5 - Prob. 19ECh. 16.5 - Find the particular solution for each initial...Ch. 16.5 - Prob. 21ECh. 16.5 - Prob. 22ECh. 16.5 - Prob. 23ECh. 16.5 - Prob. 24ECh. 16.5 - Prob. 25ECh. 16.5 - Prob. 26ECh. 16.5 - Prob. 27ECh. 16.5 - Prob. 28ECh. 16.5 - Find the particular solution for each initial...Ch. 16.5 - Prob. 30ECh. 16.5 - Prob. 31ECh. 16.5 - Prob. 32ECh. 16.5 - Prob. 33ECh. 16.5 - Prob. 34ECh. 16.5 - Prob. 35ECh. 16.5 - Prob. 36ECh. 16.5 - Suppose that 0 y0 N. Let b = (N y0)/y0, and let...Ch. 16.5 - Prob. 38ECh. 16.5 - Prob. 39ECh. 16.5 - Prob. 40ECh. 16.5 - Prob. 41ECh. 16.5 - Prob. 42ECh. 16.5 - Prob. 43ECh. 16.5 - Prob. 45ECh. 16.5 - Prob. 46ECh. 16.5 - Soil Moisture The evapotranspiration index I is a...Ch. 16.5 - Fish Population An isolated fish population is...Ch. 16.5 - Prob. 49ECh. 16.5 - Prob. 50ECh. 16.5 - Prob. 53ECh. 16.5 - Prob. 54ECh. 16.5 - Prob. 55ECh. 16.5 - Worker Productivity A company has found that the...Ch. 16.5 - Spread of a Rumor Suppose the rate at which a...Ch. 16.5 - Prob. 59ECh. 16.5 - Prob. 60ECh. 16.5 - Prob. 61ECh. 16.5 - Prob. 62ECh. 16.5 - Prob. 63ECh. 16.5 - Prob. 64ECh. 16 - Determine whether each of the following statements...Ch. 16 - Determine whether each of the following statements...Ch. 16 - Determine whether each of the following statements...Ch. 16 - Prob. 4RECh. 16 - Determine whether each of the following statements...Ch. 16 - Determine whether each of the following statements...Ch. 16 - Determine whether each of the following statements...Ch. 16 - Prob. 8RECh. 16 - Prob. 9RECh. 16 - Prob. 10RECh. 16 - Prob. 11RECh. 16 - Prob. 12RECh. 16 - Prob. 13RECh. 16 - Prob. 14RECh. 16 - Prob. 15RECh. 16 - Compare finding the average value of a function...Ch. 16 - Prob. 17RECh. 16 - Prob. 18RECh. 16 - Prob. 19RECh. 16 - Prob. 20RECh. 16 - Prob. 21RECh. 16 - Prob. 22RECh. 16 - Prob. 23RECh. 16 - Prob. 24RECh. 16 - Prob. 25RECh. 16 - Prob. 26RECh. 16 - Find each integral, using techniques from this or...Ch. 16 - Prob. 28RECh. 16 - Prob. 29RECh. 16 - Prob. 30RECh. 16 - Prob. 31RECh. 16 - Prob. 32RECh. 16 - Prob. 33RECh. 16 - Prob. 34RECh. 16 - Prob. 35RECh. 16 - Prob. 36RECh. 16 - Prob. 37RECh. 16 - Prob. 38RECh. 16 - Prob. 39RECh. 16 - Prob. 40RECh. 16 - Prob. 41RECh. 16 - Prob. 42RECh. 16 - Prob. 43RECh. 16 - Prob. 44RECh. 16 - Prob. 45RECh. 16 - Prob. 46RECh. 16 - Prob. 47RECh. 16 - Prob. 48RECh. 16 - Prob. 49RECh. 16 - Prob. 50RECh. 16 - Prob. 51RECh. 16 - Prob. 52RECh. 16 - Prob. 53RECh. 16 - Prob. 54RECh. 16 - Prob. 55RECh. 16 - Prob. 56RECh. 16 - Prob. 57RECh. 16 - Prob. 58RECh. 16 - Prob. 59RECh. 16 - Prob. 60RECh. 16 - Prob. 61RECh. 16 - Prob. 62RECh. 16 - Prob. 63RECh. 16 - Prob. 64RECh. 16 - Prob. 65RECh. 16 - Prob. 66RECh. 16 - Prob. 67RECh. 16 - Prob. 68RECh. 16 - Prob. 69RECh. 16 - Prob. 70RECh. 16 - Prob. 71RECh. 16 - Prob. 72RECh. 16 - Prob. 73RECh. 16 - Prob. 74RECh. 16 - Prob. 75RECh. 16 - Prob. 76RECh. 16 - Prob. 77RECh. 16 - Prob. 78RECh. 16 - Prob. 79RECh. 16 - Prob. 80RECh. 16 - Prob. 81RECh. 16 - Prob. 82RECh. 16 - Prob. 83RECh. 16 - Prob. 84RECh. 16 - Prob. 85RECh. 16 - Growth of a Mite Population A population of mites...Ch. 16 - Prob. 87RECh. 16 - Prob. 88RECh. 16 - Prob. 89RECh. 16 - Prob. 91RECh. 16 - Prob. 92RECh. 16 - Average Temperatures Suppose the temperature...Ch. 16 - Prob. 94RECh. 16 - Prob. 95RE
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