No, the answer must be in radians per hour (or in terms of an angle measure over a time measure) because you area asked for the rate of change of theta.Part B: The speed of the plane is 400 mph. Find d(theta)/dt when x is 10 miles and when x is 3 miles.
The answer must be in radians because I am searching for angle theta. Is this right?
No, that is not correct. You have missed one important point.I found d(theta)/dt to be -5/x^2 divided by 1 + (25/x^2). Is this the correct function? It is a complex fraction.
You have correctly written theta= arctan(5/x). The derivative of arctan(u) is . Here, so so, the derivative of arctan(5/x) with respect to x is . It might be better to multiply both numerator and denominator by to get .
However, the crucial point is that , which is what was asked, is .
If x= 10, so . However, that is , not ! You have not used the fact that dx/dt= 400 mph.Afterward, I simply plugged x = 10 and x = 3 individually and simplified.
For x = 10, my answer is -1/25.
For x = 3, my answer is -5/34.
No. It isn't. You did all of the calculations correctly but you did not answer the question that was asked!Is this right?
This question is from my single variable calculus text, chapter on finding the derivative of inverse functions. Thanks....