Question

A road perpendicular to a highway leads to a farmhouse located 9 mile away. An automobile traveling on the highway passes through this intersection at a speed of 45mph. How fast is the distance between the automobile and the farmhouse increasing when the automobile is 7 miles past the intersection of the highway and the road?

Answer 1

27.63 mph

Explanation:

credit to guy above he is my best friend and he helped answer this question. guy above even though your name is weird we still love you. everybody thank him

Answer 2

27.63 mph

Explanation:

First we find the distance, p between the Car and the house using Pythagoras theorem.

`p^2=x^2+y^2\\p^2=7^2+9^2\\p^2=49+81=130\\p=√(130) miles`

Taking derivatives of:

`p^2=x^2+y^2\\2p (dp)/(dt) =2x (dx)/(dt) + 2y (dy)/(dt)`

Since the farmhouse does not move, its speed
`(dy)/(dt)=0`

Therefore:

`2*√(130) *(dp)/(dt) =2*7*45 + 2y*0\\2*√(130) *(dp)/(dt)=630\\(dp)/(dt)=(630)/(2√(130))\\(dp)/(dt)=27.63 mph`

The distance between the automobile and the farmhouse is increasing at a rate of 27.63mph.