Question

A road perpendicular to a highway leads to a farmhouse located 7 mile away. An automobile traveling on the highway passes through this intersection at a speed of 65 mph.
How fast is the distance between the automobile and the farmhouse increasing when the automobile is 6 miles past the intersection of the highway and the road?

Answer 1

\[y^2=x^2+49 \]Take the Total Derivative of the equation above and then solve for dy. The result is the following:\[dy=\frac{x dx}{y} \]Plug in the values for x, dx (speed), and y.

Answer 2

thank you very much!

Answer 3

You're welcome.