An plane flies at a height of 5 miles to a point directly over an observer. Consider theta and x. Let x be the distance from the observer to the point directly below the plane. I made a picture of a right triangle.
The question tells me to write theta as a function of x. So, my answer is theta = arctan(5miles/x). Is this correct?
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?
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.
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.
Is this right?
This question is from my single variable calculus text, chapter on finding the derivative of inverse functions. Thanks....