2. The speed v of an object being propelled through water is given by3(2PkC.v(P, C) =where P is the power being used to propel the object, C is the drag coefficient, andk is a positive constant. Swimmers can therefore increase their swimming speeds byincreasing their power or reducing their drag coefficients.To compare the effect of increasing power versus reducing drag, we need to somehowcompare the two in common units. A frequently used approach is to determine thepercentage change in speed that results from a given percentage change in power andin drag.If we work with percentages as fractions, then when power is changed by a fraction x(with x corresponding to 100x percent), P changes from P to P+xP. Likewise, if thedrag coefficient is changed by a fraction y, then C changes from C to C + yC. Then,the corresponding fractional change in speed isv(P+zР,С +УС) — v(Р,С)v(P,C) which then reduces to the function1+xf(x, y)1.+ y(a)Suppose that the changes in power x and drag y are small. Use thelinear approximation of f to describe the effect of a small fractional increase inpower versus a small fractional decrease in drag.(b)Based on the level curves of f(x, 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 thedrag C remains unchanged? What if we decrease the drag C by 50% while thepower P remains unchanged? What can you conclude from these changes?

Answered: Image /qna-images/answer/0f22a63c-9548-4d39-8bea-8824bcb8b35b.jpg

which then reduces to the function 1+x f(x, y) = 1. + y (a) Suppose that the changes in power x and drag y are small. Use the linear approximation of f to describe the effect of a small fractional increase in power versus a small fractional decrease in drag. (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?

which then reduces to the function 1+x f(x, y) = 1. + y (a) Suppose that the changes in power x and drag y are small. Use the linear approximation of f to describe the effect of a small fractional increase in power versus a small fractional decrease in drag. (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?

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

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2. The speed v of an object being propelled through water is given by
3(2P
kC.
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 x
(with x corresponding to 100x 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+zР,С +УС) — v(Р,С)
v(P,C)

which then reduces to the function
1+x
f(x, y)
1.
+ y
(a)
Suppose that the changes in power x and drag y are small. Use the
linear approximation of f to describe the effect of a small fractional increase in
power versus a small fractional decrease in drag.
(b)
Based on the level curves of f(x, 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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