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The speed v of an object being propelled through water is given by v(P,C) = where P is the power being used to propel the object, C is the drag coefficient, and k is a positive constant. Swimmers can therefore increase their swimming speeds by increasing their power or reducing their drag coefficients. To compare the effect of increasing power versus reducing drag, we need to somehow compare the two in common units. A frequently used approach is to determine the percentage change in speed that results from a given percentage change in power and in drag. If we work with percentages as fractions, then when power is changed by a fraction r (with r corresponding to 100r percent), P changes from P to P+rP. Likewise, if the drag coefficient is changed by a fraction y, then C changes from C to C+ yC. Then, the corresponding fractional change in speed is v(P+rP,C+ yC) – v(P,C) v(P,C) 1 which then reduces to the function 1+r f(r, y) = -1. + y

The speed v of an object being propelled through water is given by v(P,C) = where P is the power being used to propel the object, C is the drag coefficient, and k is a positive constant. Swimmers can therefore increase their swimming speeds by increasing their power or reducing their drag coefficients. To compare the effect of increasing power versus reducing drag, we need to somehow compare the two in common units. A frequently used approach is to determine the percentage change in speed that results from a given percentage change in power and in drag. If we work with percentages as fractions, then when power is changed by a fraction r (with r corresponding to 100r percent), P changes from P to P+rP. Likewise, if the drag coefficient is changed by a fraction y, then C changes from C to C+ yC. Then, the corresponding fractional change in speed is v(P+rP,C+ yC) – v(P,C) v(P,C) 1 which then reduces to the function 1+r f(r, y) = -1. + y

College Algebra
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter1: Equations And Graphs
Section1.3: Lines
Problem 92E
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The speed v of an object being propelled through water is given by 2P v(P,C) = G) kC where P is the power being used to propel the object, C is the drag coefficient, and k is a positive constant. Swimmers can therefore increase their swimming speeds by increasing their power or reducing their drag coefficients. To compare the effect of increasing power versus reducing drag, we need to somehow compare the two in common units. A frequently used approach is to determine the percentage change in speed that results from a given percentage change in power and in drag. If we work with percentages as fractions, then when power is changed by a fraction r (with r corresponding to 100r percent), P changes from P to P+xP. Likewise, if the drag coefficient is changed by a fraction y, then C changes from C to C+ yC. Then, the corresponding fractional change in speed is v(P+rP,C+ yC) – v(P,C) v(P,C) 1 which then reduces to the function 3(1+r - 1. 1+ y,
Transcribed Image Text:The speed v of an object being propelled through water is given by 2P v(P,C) = G) kC where P is the power being used to propel the object, C is the drag coefficient, and k is a positive constant. Swimmers can therefore increase their swimming speeds by increasing their power or reducing their drag coefficients. To compare the effect of increasing power versus reducing drag, we need to somehow compare the two in common units. A frequently used approach is to determine the percentage change in speed that results from a given percentage change in power and in drag. If we work with percentages as fractions, then when power is changed by a fraction r (with r corresponding to 100r percent), P changes from P to P+xP. Likewise, if the drag coefficient is changed by a fraction y, then C changes from C to C+ yC. Then, the corresponding fractional change in speed is v(P+rP,C+ yC) – v(P,C) v(P,C) 1 which then reduces to the function 3(1+r - 1. 1+ y,
(b) Based on the level curves of f (r, y) for the values c = -0.1,0,0.1,0.2,0.3, what can you say about the speed if we increase the power P by 50% while the drag C remains unchanged? What if we decrease the drag C by 50% while the power P remains unchanged? What can you conclude from these changes?
Transcribed Image Text:(b) Based on the level curves of f (r, y) for the values c = -0.1,0,0.1,0.2,0.3, what can you say about the speed if we increase the power P by 50% while the drag C remains unchanged? What if we decrease the drag C by 50% while the power P remains unchanged? What can you conclude from these changes?
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