SOLUTION: if a, b, and c are sides of a right trinagle, where c is the hypotenuse and c is constant at 13cm, given that a is increasing at a rate of 3 cm/s, find the rate of change of b in c

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Question 408753: if a, b, and c are sides of a right trinagle, where c is the hypotenuse and c is constant at 13cm, given that a is increasing at a rate of 3 cm/s, find the rate of change of b in cm/s when b=5cm.
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
Since a is increasing at a constant rate, we can say that the rate of change of a is
da%2Fdt+=+3cm%2Fs

Since a%5E2+%2B+b%5E2+=+c%5E2+=+169 we can write b in terms of a:

b+=+sqrt%28169+-+a%5E2%29. Suppose we take the derivative of both sides (we can do this because we have equality for all a,b and their derivatives must be equal). Then,



When a+=+5,

db%2Fdt+=+%28-5%29%28144%29%5E%28-1%2F2%29%283cm%2Fs%29

db%2Fdt+=+-5%2F4 (cm/s)