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f(x,y) = √(1+1)-1. By using the level curves of f(x, y), display your ability to describe the changes in speed relative to the changes in power z and drag y.

f(x,y) = √(1+1)-1. By using the level curves of f(x, y), display your ability to describe the changes in speed relative to the changes in power z and drag y.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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3. The speed of an object being propelled through water is given by v(P, C) = (2P 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.
Transcribed Image Text:3. The speed of an object being propelled through water is given by v(P, C) = (2P 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 a (with a corresponding to 100 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 fractional change in speed resulting from both effects is v(P+ TP, C+yC) − v(P.C) v(P, C) which then reduces to the function f(x, y) = √(1) - 1. By using the level curves of f(x, y), display your ability to describe the changes in speed relative to the changes in power z and drag y.
Transcribed Image Text:If we work with percentages as fractions, then when power is changed by a fraction a (with a corresponding to 100 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 fractional change in speed resulting from both effects is v(P+ TP, C+yC) − v(P.C) v(P, C) which then reduces to the function f(x, y) = √(1) - 1. By using the level curves of f(x, y), display your ability to describe the changes in speed relative to the changes in power z and drag y.
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