Question

an ant moves along the x-axis from left to right at 5 inches per second. a spider moves upward along the y-axis at 3 inches per second. at a certain instant, the ant is 4 inches to the right of the origin and the spider is 8 units above the origin. at this instant, how fast is the distance between the spider and the ant changing?

Answer 1

here is a sketch

Do you know how to use implicit differentiation ?
As the first step, take the derivative with respect to "t" (time)
of the equation
\[ x^2 + y^2 = r^2\]