Four identical circles of radius r are inscribed (as shown) in a square of side x feet. (a) Express the total area of the four circles, T, as a function of x. T(x) = (b) Consider the region inside the square, but outside the four circles. Find a formula for the area of this region, A, as a function of x. A(x) =

Find a formula for the described function and state its domain Express the surface area of a cube as a function of its volume.

During Ricardo noticed an ink stain with a diameter of about 3 cm on the front of his teacher’s shirt. He then noticed that there was a pen in the pocket and that the ink blot was continuing to spread across the front of the teacher’s shirt. He estimated that the diameter of the ink blot seemed to be growing by about 0.5 cm every 2 minutes. a) Write an equation for the RADIUS, r, of the ink stain, as a function of time, t. Assume that t = 0 represents the time that Ricardo first noticed the ink stain. b) Write an equation showing the AREA, A, of the ink stain as a function of the time t. (Hint: It might help to first write A as a function of r. ) c) Draw a graph of the function A(t) for 10 minutes. d) At what time is the area of the ink stain about 25 square centimeter? Show how you answer this question. (i.e. ”I found it using desmos” is not sufficient)

Find and simplify the difference quotientfor the given function.f(x) = 1 /x