KFS

Thanks for the answer DrP. But please explain it more clear. I know nothing about similar triangles. Thank you.

Hello. This is not even a problem but an example my book gives, but I want to understand it in order to do the exercises. It is as follows: A light L is being raised up a pole. The light shines on the object Q, casting a shadow on the ground. At a certain moment the light is 40 meters off the ground, rising at 5 meters per minute. How fast is the shadow shrinking at that instant? Then the book gives the answer that I don't understand. It reads: Let the height be y at time t and the lenght of the shadow be x. By similiar triangles, x/10=(x+20)/y; i.e., xy=10(x+20).The explanation goes on but I only want to know about the similar triangles part. I don't know where the equation and the 10 and 20 come from. Just that, I have no problem with the rest. Thank you in advance.

Hello. My problem is as follows: Suppose x^4+y^2+y-3=0. a) Compute dy/dx by implicit differentiation. b) What is dy/dx when x=1 and y=1? c) Solve for y in terms of x (by the quadratic formula) and compute dy/dx directly. Compare with your answer in part a).I solved a) and b). a)=-4x^3/(2y + 1), and b)=-4/3. I'm stuck at c). This is what I've been doing: Using the quadratic formula to solve for y in x^4+y^2+y-3=0 gives y=-1±√-4x^4+13/(2). Then applying the chain rule in the result of y gives -4x^3/(√-4x^4+13). But it must give the same as a)=-4x^3/(2y + 1) . Where am I failing at? How can I solve it?Thank you for your time.