QUESTION 18 Convert the following binary numbers to a hexadecimal number. (You need to show only the final answer. Do not round your answer.) a. 100111010101.010111102 = 16 16 b. 10100111110011.0100112=

A box with a square base and open top must have a volume of 108 cm. We wish to find the dimensions of the box that minimize the amount of material used. First, find a formula for the surface area of the box in terms of only x, the length of one side of the square base. Simplify your formula as much as possible. A(z) = Next, find the derivative, A’(x). A' (x) = Now, calculate when the derivative equals zero, that is, when A'(x) = 0. A' (x) = 0 when x = We next have to make sure that this value of x gives a minimum value for the surface area. Let's use the second derivative test. Find A"(x). A"(x) = Evaluate A"(x) at the x-value you gave above. NOTE: Since your last answer is positive, this means that the graph of A(x) is concave up around that value, so the zero of A'(x) must indicate a local minimum for A(x).

Find the prime factorization of each of the following numbers. a. 14^4 22^22 25^11 b. 400^50 4500^23 c. 2.3^4 5^109.7+4.3^4.5^109 d. 2.3.5.7.11.13+1