(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. 2. The speed v of an object being propelled through water is given by(2Pv(P,C) =kCwhere 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 r(with r 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+xP,C+yC) – v(P,C)v(P,C')1which then reduces to the function1+xf(r, y) =- 1.

Answered: Image /qna-images/answer/06092fc3-3c00-4b74-86bd-1cc725e2652c.jpg

(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 yersus a small fractional decrease in drag.

(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 yersus a small fractional decrease in drag.

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

(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.

2. The speed v of an object being propelled through water is given by
(2P
v(P,C) =
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 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+xP,C+yC) – v(P,C)
v(P,C')
1
which then reduces to the function
1+x
f(r, y) =
- 1.

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