To store his art supplies, kyle buys a cube-shapped box with 8-inches sides. his longest paintbrush is 13.5 inches long. explain how kyle determined that the 13.5 inch brush could fit in the box. (show mathematical, explain in words, solve mathematically and draw diagram)

Suppose that f(0) = −3 and f '(x) ≤ 8 for all values of x. how large can f(4) possibly be? solution we are given that f is differentiable (and therefore continuous) everywhere. in particular, we can apply the mean value theorem on the interval [0, 4] . there exists a number c such that

Afarmer has a large field that is x feet in length. he wants to fence in a rectangular section in the middle of the field , leaving a length of 100 feet of open field behind each end of the fenced rectangle.he also wants the width of the fenced-in space to be 100 feet less than its length. find the expressions to represent the length and width of the fenced section of the field

Interpret the following expression (5y^2-7)^3/(2y)^2