1. Elena needs to find a table that will fit three cube-shaped cases, each containing a frog. If the volume of each case is 1,000 cubic inches, could she use a table with a top that measures 30 inches long and 18 inches wide? Explain and show your work. ( 3 points) a) Find the length of the side of each case.

b) Is the length of the table enough for the 3 cases? Explain

c) Is the width of the table enough for the 3 cases? Explain

Does the function satisfy the hypotheses of the mean value theorem on the given interval? f(x) = 4x^2 + 3x + 4, [−1, 1] no, f is continuous on [−1, 1] but not differentiable on (−1, 1). no, f is not continuous on [−1, 1]. yes, f is continuous on [−1, 1] and differentiable on (−1, 1) since polynomials are continuous and differentiable on . there is not enough information to verify if this function satisfies the mean value theorem. yes, it does not matter if f is continuous or differentiable; every function satisfies the mean value theorem.

Consider the polynomials given below. p(x) = x4 + 3x3 + 2x2 – x + 2 q(x) = (x3 + 2x2 + 3)(x2 – 2) determine the operation that results in the simplified expression below. 35 + x4 – 573 - 3x2 + x - 8 a. p+q b. pq c.q-p d. p-q

An octagonal prism has jow many lateral faces?