Single Variable Calculus Format: Unbound (saleable)
3rd Edition
ISBN: 9780134765761
Author: Briggs, William L.^cochran, Lyle^gillett, Bernard^
Publisher: Prentice Hall
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Chapter 12.4, Problem 14E
To determine
Whether the equation
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Suppose an oil spill covers a circular area and the radius, r, increases according to the graph shown below where t
represents the number of minutes since the spill was first observed.
Radius (feet)
80
70
60
50
40
30
20
10
0
r
0 10 20 30 40 50 60 70 80 90
Time (minutes)
(a) How large is the circular area of the spill 30 minutes after it was first observed? Give your answer in terms of π.
square feet
(b) If the cost to clean the oil spill is proportional to the square of the diameter of the spill, express the cost, C, as a
function of the radius of the spill, r. Use a lower case k as the proportionality constant.
C(r) =
(c) Which of the following expressions could be used to represent the amount of time it took for the radius of the spill to
increase from 20 feet to 60 feet?
r(60) - r(20)
Or¹(80-30)
r(80) - r(30)
r-1(80) - r−1(30)
r-1(60) - r¹(20)
6. Graph the function f(x)=log3x. Label three points on the graph (one should be the intercept) with
corresponding ordered pairs and label the asymptote with its equation. Write the domain and range of the function
in interval notation. Make your graph big enough to see all important features.
Find the average value gave of the function g on the given interval.
gave =
g(x) = 8√√x, [8,64]
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Chapter 12 Solutions
Single Variable Calculus Format: Unbound (saleable)
Ch. 12.1 - Identify the graph generated by the parametric...Ch. 12.1 - Prob. 2QCCh. 12.1 - Prob. 3QCCh. 12.1 - Prob. 4QCCh. 12.1 - Prob. 5QCCh. 12.1 - Prob. 6QCCh. 12.1 - Explain how a pair of parametric equations...Ch. 12.1 - Prob. 2ECh. 12.1 - Prob. 3ECh. 12.1 - Prob. 4E
Ch. 12.1 - Prob. 5ECh. 12.1 - Prob. 6ECh. 12.1 - Prob. 7ECh. 12.1 - Prob. 8ECh. 12.1 - Prob. 9ECh. 12.1 - Prob. 10ECh. 12.1 - Prob. 11ECh. 12.1 - Prob. 12ECh. 12.1 - Prob. 13ECh. 12.1 - Prob. 14ECh. 12.1 - Prob. 15ECh. 12.1 - Prob. 16ECh. 12.1 - Prob. 17ECh. 12.1 - Prob. 18ECh. 12.1 - Prob. 19ECh. 12.1 - Prob. 20ECh. 12.1 - Prob. 21ECh. 12.1 - Prob. 22ECh. 12.1 - Prob. 23ECh. 12.1 - Prob. 24ECh. 12.1 - Prob. 25ECh. 12.1 - Prob. 26ECh. 12.1 - Prob. 27ECh. 12.1 - Prob. 28ECh. 12.1 - Prob. 29ECh. 12.1 - Prob. 30ECh. 12.1 - Eliminating the parameter Eliminate the parameter...Ch. 12.1 - Prob. 32ECh. 12.1 - Prob. 33ECh. 12.1 - Prob. 34ECh. 12.1 - Prob. 35ECh. 12.1 - Prob. 36ECh. 12.1 - Parametric equations of circles Find parametric...Ch. 12.1 - Parametric equations of circles Find parametric...Ch. 12.1 - Parametric equations of circles Find parametric...Ch. 12.1 - Parametric equations of circles Find parametric...Ch. 12.1 - Prob. 41ECh. 12.1 - Prob. 42ECh. 12.1 - Curves to parametric equations Give a set of...Ch. 12.1 - Prob. 44ECh. 12.1 - Prob. 45ECh. 12.1 - Curves to parametric equations Find parametric...Ch. 12.1 - Prob. 47ECh. 12.1 - Prob. 48ECh. 12.1 - Prob. 49ECh. 12.1 - Prob. 50ECh. 12.1 - Prob. 51ECh. 12.1 - Prob. 52ECh. 12.1 - Circular motion Find parametric equations that...Ch. 12.1 - Circular motion Find parametric equations that...Ch. 12.1 - Circular motion Find parametric equations that...Ch. 12.1 - Prob. 56ECh. 12.1 - Prob. 57ECh. 12.1 - More parametric curves Use a graphing utility to...Ch. 12.1 - More parametric curves Use a graphing utility to...Ch. 12.1 - Prob. 60ECh. 12.1 - Prob. 61ECh. 12.1 - Prob. 62ECh. 12.1 - Implicit function graph Explain and carry out a...Ch. 12.1 - Prob. 64ECh. 12.1 - Prob. 65ECh. 12.1 - Prob. 66ECh. 12.1 - Prob. 67ECh. 12.1 - Prob. 68ECh. 12.1 - Derivatives Consider the following parametric...Ch. 12.1 - Prob. 70ECh. 12.1 - Prob. 71ECh. 12.1 - Prob. 72ECh. 12.1 - Tangent lines Find an equation of the line tangent...Ch. 12.1 - Prob. 74ECh. 12.1 - Tangent lines Find an equation of the line tangent...Ch. 12.1 - Tangent lines Find an equation of the line tangent...Ch. 12.1 - Slopes of tangent lines Find all the points at...Ch. 12.1 - Slopes of tangent lines Find all the points at...Ch. 12.1 - Prob. 79ECh. 12.1 - Prob. 80ECh. 12.1 - Arc length Find the arc length of the following...Ch. 12.1 - Arc length Find the arc length of the following...Ch. 12.1 - Arc length Find the arc length of the following...Ch. 12.1 - Arc length Find the arc length of the following...Ch. 12.1 - Arc length Find the arc length of the following...Ch. 12.1 - Arc length Find the arc length of the following...Ch. 12.1 - Prob. 87ECh. 12.1 - Prob. 88ECh. 12.1 - Prob. 89ECh. 12.1 - Prob. 90ECh. 12.1 - Prob. 91ECh. 12.1 - Prob. 92ECh. 12.1 - Prob. 93ECh. 12.1 - Parametric equations of ellipses Find parametric...Ch. 12.1 - Prob. 95ECh. 12.1 - Prob. 96ECh. 12.1 - Prob. 97ECh. 12.1 - Prob. 98ECh. 12.1 - Prob. 99ECh. 12.1 - Beautiful curves Consider the family of curves...Ch. 12.1 - Prob. 101ECh. 12.1 - Prob. 102ECh. 12.1 - Area under a curve Suppose the function y = h(x)...Ch. 12.1 - Area under a curve Suppose the function y = h(x)...Ch. 12.1 - Prob. 105ECh. 12.1 - Prob. 106ECh. 12.1 - Prob. 107ECh. 12.1 - Prob. 108ECh. 12.1 - Prob. 109ECh. 12.1 - Prob. 110ECh. 12.1 - Prob. 111ECh. 12.1 - Prob. 112ECh. 12.1 - Prob. 113ECh. 12.1 - Prob. 114ECh. 12.2 - Which of the following coordinates represent the...Ch. 12.2 - Prob. 2QCCh. 12.2 - Prob. 3QCCh. 12.2 - Prob. 4QCCh. 12.2 - Prob. 5QCCh. 12.2 - Prob. 6QCCh. 12.2 - Prob. 1ECh. 12.2 - Prob. 2ECh. 12.2 - Prob. 3ECh. 12.2 - Prob. 4ECh. 12.2 - Prob. 5ECh. 12.2 - Prob. 6ECh. 12.2 - Prob. 7ECh. 12.2 - Prob. 8ECh. 12.2 - Prob. 9ECh. 12.2 - Prob. 10ECh. 12.2 - Prob. 11ECh. 12.2 - Prob. 12ECh. 12.2 - Prob. 13ECh. 12.2 - Prob. 14ECh. 12.2 - Prob. 15ECh. 12.2 - Prob. 16ECh. 12.2 - Prob. 17ECh. 12.2 - Prob. 18ECh. 12.2 - Prob. 19ECh. 12.2 - Prob. 20ECh. 12.2 - Prob. 21ECh. 12.2 - Prob. 22ECh. 12.2 - Rader Airplanes are equipped with transponders...Ch. 12.2 - Prob. 24ECh. 12.2 - Converting coordinates Express the following polar...Ch. 12.2 - Prob. 26ECh. 12.2 - Converting coordinates Express the following polar...Ch. 12.2 - Converting coordinates Express the following polar...Ch. 12.2 - Converting coordinates Express the following polar...Ch. 12.2 - Prob. 30ECh. 12.2 - Converting coordinates Express the following...Ch. 12.2 - Prob. 32ECh. 12.2 - Prob. 33ECh. 12.2 - Prob. 34ECh. 12.2 - Converting coordinates Express the following...Ch. 12.2 - Prob. 36ECh. 12.2 - Prob. 37ECh. 12.2 - Prob. 38ECh. 12.2 - Prob. 39ECh. 12.2 - Prob. 40ECh. 12.2 - Prob. 41ECh. 12.2 - Prob. 42ECh. 12.2 - Prob. 43ECh. 12.2 - Prob. 44ECh. 12.2 - Prob. 45ECh. 12.2 - Prob. 46ECh. 12.2 - Prob. 47ECh. 12.2 - Prob. 48ECh. 12.2 - Cartesian-to-polar coordinates Convert the...Ch. 12.2 - Prob. 50ECh. 12.2 - Prob. 51ECh. 12.2 - Cartesian-to-polar coordinates Convert the...Ch. 12.2 - Prob. 53ECh. 12.2 - Prob. 54ECh. 12.2 - Prob. 55ECh. 12.2 - Prob. 56ECh. 12.2 - Graphing polar curves Graph the following...Ch. 12.2 - Prob. 58ECh. 12.2 - Prob. 59ECh. 12.2 - Prob. 60ECh. 12.2 - Prob. 61ECh. 12.2 - Graphing polar curves Graph the following...Ch. 12.2 - Graphing polar curves Graph the following...Ch. 12.2 - Prob. 64ECh. 12.2 - Prob. 65ECh. 12.2 - Prob. 66ECh. 12.2 - Prob. 67ECh. 12.2 - Prob. 68ECh. 12.2 - Prob. 69ECh. 12.2 - Using a graphing utility Use a graphing utility to...Ch. 12.2 - Prob. 71ECh. 12.2 - Prob. 72ECh. 12.2 - Prob. 73ECh. 12.2 - Prob. 74ECh. 12.2 - Prob. 75ECh. 12.2 - Using a graphing utility Use a graphing utility to...Ch. 12.2 - Prob. 77ECh. 12.2 - Prob. 78ECh. 12.2 - Prob. 79ECh. 12.2 - Prob. 80ECh. 12.2 - Prob. 81ECh. 12.2 - Prob. 82ECh. 12.2 - Prob. 83ECh. 12.2 - Prob. 84ECh. 12.2 - Navigating A plane is 150 miles north of a radar...Ch. 12.2 - Prob. 86ECh. 12.2 - Prob. 87ECh. 12.2 - Prob. 88ECh. 12.2 - Prob. 89ECh. 12.2 - Prob. 90ECh. 12.2 - Prob. 91ECh. 12.2 - Prob. 92ECh. 12.2 - Prob. 93ECh. 12.2 - Prob. 94ECh. 12.2 - Prob. 95ECh. 12.2 - Prob. 96ECh. 12.2 - Prob. 97ECh. 12.2 - Prob. 98ECh. 12.2 - Prob. 99ECh. 12.2 - Prob. 100ECh. 12.2 - Prob. 101ECh. 12.2 - Spirals Graph the following spirals. Indicate the...Ch. 12.2 - Prob. 103ECh. 12.2 - Spirals Graph the following spirals. Indicate the...Ch. 12.2 - Prob. 105ECh. 12.2 - Prob. 106ECh. 12.2 - Prob. 107ECh. 12.2 - Prob. 108ECh. 12.2 - Prob. 109ECh. 12.2 - Prob. 110ECh. 12.2 - Prob. 111ECh. 12.3 - Verify that if y = f() sin , then y'() =f'() sin ...Ch. 12.3 - Prob. 2QCCh. 12.3 - Prob. 3QCCh. 12.3 - Prob. 4QCCh. 12.3 - Prob. 1ECh. 12.3 - Prob. 2ECh. 12.3 - Prob. 3ECh. 12.3 - Prob. 4ECh. 12.3 - Prob. 5ECh. 12.3 - Find a polar equation of the line with slope 1...Ch. 12.3 - Prob. 7ECh. 12.3 - Prob. 8ECh. 12.3 - Prob. 9ECh. 12.3 - Prob. 10ECh. 12.3 - Prob. 11ECh. 12.3 - Prob. 12ECh. 12.3 - Slopes of tangent lines Find the slope of the line...Ch. 12.3 - Prob. 14ECh. 12.3 - Prob. 15ECh. 12.3 - Prob. 16ECh. 12.3 - Slopes of tangent lines Find the slope of the line...Ch. 12.3 - Prob. 18ECh. 12.3 - Prob. 19ECh. 12.3 - Prob. 20ECh. 12.3 - Tangent line at the origin Find the polar equation...Ch. 12.3 - Tangent line at the origin Find the polar equation...Ch. 12.3 - Prob. 23ECh. 12.3 - Prob. 24ECh. 12.3 - Horizontal and vertical tangents Find the points...Ch. 12.3 - Prob. 26ECh. 12.3 - Horizontal and vertical tangents Find the points...Ch. 12.3 - Prob. 28ECh. 12.3 - Prob. 29ECh. 12.3 - Prob. 30ECh. 12.3 - Prob. 31ECh. 12.3 - Prob. 32ECh. 12.3 - Areas of regions Make a sketch of the region and...Ch. 12.3 - Areas of regions Make a sketch of the region and...Ch. 12.3 - Areas of regions Make a sketch of the region and...Ch. 12.3 - Areas of regions Make a sketch of the region and...Ch. 12.3 - Areas of regions Make a sketch of the region and...Ch. 12.3 - Areas of regions Make a sketch of the region and...Ch. 12.3 - Areas of regions Make a sketch of the region and...Ch. 12.3 - Prob. 40ECh. 12.3 - Intersection points and area a. Find all the...Ch. 12.3 - Intersection points and area a. Find all the...Ch. 12.3 - Prob. 43ECh. 12.3 - Intersection points and area a. Find all the...Ch. 12.3 - Prob. 45ECh. 12.3 - Prob. 46ECh. 12.3 - Prob. 47ECh. 12.3 - Prob. 48ECh. 12.3 - Areas of regions Make a sketch of the region and...Ch. 12.3 - Areas of regions Make a sketch of the region and...Ch. 12.3 - Areas of regions Make a sketch of the region and...Ch. 12.3 - Prob. 52ECh. 12.3 - Area of plane regions Find the areas of the...Ch. 12.3 - Area of plane regions Find the areas of the...Ch. 12.3 - Area of plane regions Find the areas of the...Ch. 12.3 - Area of plane regions Find the areas of the...Ch. 12.3 - Area of polar regions Find the area of the regions...Ch. 12.3 - Prob. 58ECh. 12.3 - Area of polar regions Find the area of the regions...Ch. 12.3 - Area of polar regions Find the area of the regions...Ch. 12.3 - Two curves, three regions Determine the...Ch. 12.3 - Prob. 62ECh. 12.3 - Arc length of polar curves Find the length of the...Ch. 12.3 - Prob. 64ECh. 12.3 - Prob. 65ECh. 12.3 - Prob. 66ECh. 12.3 - Prob. 67ECh. 12.3 - Prob. 68ECh. 12.3 - Arc length of polar curves Find the length of the...Ch. 12.3 - Prob. 70ECh. 12.3 - Prob. 71ECh. 12.3 - Prob. 72ECh. 12.3 - Prob. 73ECh. 12.3 - Prob. 74ECh. 12.3 - Prob. 75ECh. 12.3 - Prob. 76ECh. 12.3 - Prob. 77ECh. 12.3 - Prob. 78ECh. 12.3 - Prob. 79ECh. 12.3 - Area of roses Assume m is a positive integer. a....Ch. 12.3 - Prob. 81ECh. 12.3 - Prob. 82ECh. 12.3 - Prob. 83ECh. 12.3 - Prob. 84ECh. 12.3 - Grazing goat problems Consider the following...Ch. 12.3 - Prob. 86ECh. 12.3 - Prob. 87ECh. 12.4 - Prob. 1QCCh. 12.4 - Prob. 2QCCh. 12.4 - Prob. 3QCCh. 12.4 - Prob. 4QCCh. 12.4 - Prob. 5QCCh. 12.4 - Prob. 6QCCh. 12.4 - Prob. 1ECh. 12.4 - Prob. 2ECh. 12.4 - Prob. 3ECh. 12.4 - Prob. 4ECh. 12.4 - Prob. 5ECh. 12.4 - Prob. 6ECh. 12.4 - Prob. 7ECh. 12.4 - Prob. 8ECh. 12.4 - Prob. 9ECh. 12.4 - Prob. 10ECh. 12.4 - Prob. 11ECh. 12.4 - Prob. 12ECh. 12.4 - Prob. 13ECh. 12.4 - Prob. 14ECh. 12.4 - Prob. 15ECh. 12.4 - Prob. 16ECh. 12.4 - Prob. 17ECh. 12.4 - Prob. 18ECh. 12.4 - Prob. 19ECh. 12.4 - Prob. 20ECh. 12.4 - Prob. 21ECh. 12.4 - Prob. 22ECh. 12.4 - Prob. 23ECh. 12.4 - Prob. 24ECh. 12.4 - Prob. 25ECh. 12.4 - Prob. 26ECh. 12.4 - Prob. 27ECh. 12.4 - Prob. 28ECh. 12.4 - Prob. 29ECh. 12.4 - Prob. 30ECh. 12.4 - Prob. 31ECh. 12.4 - Prob. 32ECh. 12.4 - Prob. 33ECh. 12.4 - Prob. 34ECh. 12.4 - Prob. 35ECh. 12.4 - Prob. 36ECh. 12.4 - Prob. 37ECh. 12.4 - Prob. 38ECh. 12.4 - Prob. 39ECh. 12.4 - Prob. 40ECh. 12.4 - Prob. 41ECh. 12.4 - Prob. 42ECh. 12.4 - Prob. 43ECh. 12.4 - Prob. 44ECh. 12.4 - Prob. 45ECh. 12.4 - Prob. 46ECh. 12.4 - Prob. 47ECh. 12.4 - Prob. 48ECh. 12.4 - Prob. 49ECh. 12.4 - Prob. 50ECh. 12.4 - Prob. 51ECh. 12.4 - Prob. 52ECh. 12.4 - Prob. 53ECh. 12.4 - Prob. 54ECh. 12.4 - Prob. 55ECh. 12.4 - Prob. 56ECh. 12.4 - Prob. 57ECh. 12.4 - Prob. 58ECh. 12.4 - Prob. 59ECh. 12.4 - Prob. 60ECh. 12.4 - Prob. 61ECh. 12.4 - Prob. 62ECh. 12.4 - Tracing hyperbolas and parabolas Graph the...Ch. 12.4 - Tracing hyperbolas and parabolas Graph the...Ch. 12.4 - Tracing hyperbolas and parabolas Graph the...Ch. 12.4 - Prob. 66ECh. 12.4 - Prob. 67ECh. 12.4 - Prob. 68ECh. 12.4 - Prob. 69ECh. 12.4 - Prob. 70ECh. 12.4 - Prob. 71ECh. 12.4 - Prob. 72ECh. 12.4 - Prob. 73ECh. 12.4 - Prob. 74ECh. 12.4 - Prob. 75ECh. 12.4 - Prob. 76ECh. 12.4 - Prob. 77ECh. 12.4 - The ellipse and the parabola Let R be the region...Ch. 12.4 - Prob. 79ECh. 12.4 - Prob. 80ECh. 12.4 - Prob. 81ECh. 12.4 - Prob. 82ECh. 12.4 - Prob. 83ECh. 12.4 - Prob. 84ECh. 12.4 - Prob. 85ECh. 12.4 - Prob. 86ECh. 12.4 - Prob. 87ECh. 12.4 - Prob. 88ECh. 12.4 - Prob. 89ECh. 12.4 - Focal chords A focal chord of a conic section is a...Ch. 12.4 - Focal chords A focal chord of a conic section is a...Ch. 12.4 - Focal chords A focal chord of a conic section is a...Ch. 12.4 - Prob. 93ECh. 12.4 - Prob. 94ECh. 12.4 - Prob. 95ECh. 12.4 - Prob. 96ECh. 12.4 - Prob. 97ECh. 12.4 - Prob. 98ECh. 12 - Explain why or why not Determine whether the...Ch. 12 - Prob. 2RECh. 12 - Prob. 3RECh. 12 - Eliminating the parameter Eliminate the parameter...Ch. 12 - Prob. 5RECh. 12 - Prob. 6RECh. 12 - Prob. 7RECh. 12 - Prob. 8RECh. 12 - Prob. 9RECh. 12 - Prob. 10RECh. 12 - Prob. 11RECh. 12 - Prob. 12RECh. 12 - Prob. 13RECh. 12 - Prob. 14RECh. 12 - Prob. 15RECh. 12 - Prob. 16RECh. 12 - Prob. 17RECh. 12 - Prob. 18RECh. 12 - Prob. 19RECh. 12 - Prob. 20RECh. 12 - Prob. 21RECh. 12 - Prob. 22RECh. 12 - Prob. 23RECh. 12 - Prob. 24RECh. 12 - Prob. 25RECh. 12 - Prob. 26RECh. 12 - Prob. 27RECh. 12 - Prob. 28RECh. 12 - Prob. 29RECh. 12 - Prob. 30RECh. 12 - Prob. 31RECh. 12 - Prob. 32RECh. 12 - Prob. 33RECh. 12 - Prob. 34RECh. 12 - Prob. 35RECh. 12 - Prob. 36RECh. 12 - Prob. 37RECh. 12 - Prob. 38RECh. 12 - Prob. 39RECh. 12 - Slopes of tangent lines a. Find all points where...Ch. 12 - Slopes of tangent lines a. Find all points where...Ch. 12 - Prob. 42RECh. 12 - Prob. 43RECh. 12 - Prob. 44RECh. 12 - Prob. 45RECh. 12 - Prob. 46RECh. 12 - Prob. 47RECh. 12 - Prob. 48RECh. 12 - The area that is inside the cardioid r = 1 + cos ...Ch. 12 - Prob. 50RECh. 12 - Prob. 51RECh. 12 - Prob. 52RECh. 12 - Prob. 53RECh. 12 - Prob. 54RECh. 12 - Prob. 55RECh. 12 - Prob. 56RECh. 12 - Prob. 57RECh. 12 - Prob. 58RECh. 12 - Prob. 59RECh. 12 - Prob. 60RECh. 12 - Prob. 61RECh. 12 - Prob. 62RECh. 12 - Prob. 63RECh. 12 - Prob. 64RECh. 12 - Prob. 65RECh. 12 - Prob. 66RECh. 12 - Prob. 67RECh. 12 - Prob. 68RECh. 12 - Prob. 69RECh. 12 - Prob. 70RECh. 12 - Prob. 71RECh. 12 - Prob. 72RECh. 12 - Prob. 73RECh. 12 - Prob. 74RECh. 12 - Lam curves The Lam curve described by...Ch. 12 - Prob. 76RE
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