Question

If x^2 + y^2 = 289, find the value of dy/dt at (8,15)

Answer 1

Answer: a)

Explanation:

To find
`(dy)/(dx)`, we will have to use implicit differentiation, and because the base is
`dx`, we will take the deriviative of both sides with respect to
`x`.

To derive
`y` with respect to
`x`, just derive the term with respect to y then multiply the term with
`(dy)/(dx)`.

So
`(d)/(dx) x^(2)` is just
`2x`,
`(d)/(dx) y^(2)` is
`2y (dy)/(dx)`, and
`(d)/(dx) 289` is 0. Now substitue each term with it's deriviative.

`2x + 2y (dy)/(dx) = 0`

Now, just solve for
`(dy)/(dx)` when
`x` is 8 and
`y` is 15

`2(8) + 2(15)(dy)/(dx) = 0`

`16 + 30(dy)/(dx) = 0`

`(dy)/(dx) = (-16)/(30) = (-8)/(15)`

So the answer is choice a)