You are given the following equation. 16x2 + 25y2 = 400 (a) Find dy / dx by implicit differentiation. dy / dx = Correct: Your answer is correct. (b) Solve the equation explicitly for y and differentiate to get dy / dx in terms of x. (Consider only the first and second quadrants for this part.) dy / dx = Incorrect: Your answer is incorrect. (c) Check that your solutions to parts (a) and (b) are consistent by substituting the expression for y into your solution for part (a). (Do this on paper. Your teacher may ask you to turn in this work.)

a)

b)

c) The two expressions match

a)

The equation in this problem is

Here, we want to find by implicit differentiation.

To do that, we apply the operator on each term of the equation. We have:

(by applying composite function rule)

Therefore, the equation becomes:

And re-arranging for dy/dx, we get:

b)

Now we want to solve the equation explicitly for y and then differentiate to find dy/dx. The equation is:

First, we isolate y, and we find:

And taking the square root,

Here we are told to consider only the first and second quadrants, so those where y > 0; so we only take the positive root:

Now we differentiate this function to find dy/dx; using the chain rule, we get:

(2)

c)

Now we want to check if the two solutions are consistent.

To do that, we substitute the expression that we found for y in part b:

Into the solution found in part a:

Doing so, we find:

(1)

We observe that expression (1) matches with expression (2) found in part b: therefore, we can conclude that the two solutions are coeherent with each other.

the radius is 2 times the diameter.

step-by-step explanation: