Let P = (x,y) be a point on the graph of y = x2 - 3. (a) Express the distance d from P to the origin as a function of x. d(x) = (b) What is d if x = 0? d(0) (Round to two decimal places.) (c) What is d if x = 1? d(1) = (Round to two decimal places.) Use a graphing utility to graph d = d(x) in order to answer the following question. (d) For what positive value of x is d smallest? XE (Round to two decimal places.)A rectangle has one corner in quadrant I on the graph of y = 16 -x, another at the origin, a third on the positive y-axis, and 20- the fourth on the positive x-axis (see the figure) (a) Express the area A of the rectangle as a function of x. 12 (b) What is the domain of A? (c) Graph A = A(x). For what value of x is A largest? (d) What is the largest area? (0,0) - 2 2 6 (a) The area A of the rectangle as a function of x is A(x) = (Simplify your answer.) (b) The domain is (Type your answer in interval notation.) (c) Graph A = A(x). Choose the correct graph below. O A. O B. O c. OD. Xmin = 0, Xmax = 4, Xscl = 1, Xmin = 0, Xmax = 4, Xscl = 1, Xmin = 0, Xmax = 4, Xscl = 1, Xmin = 0, Xmax = 4, Xscl = 1, Ymin = 0, Ymax = 30, Yscl = 5 Ymin = 0, Ymax = 30, Yscl = 5 Ymin = 0, Ymax = 30, Yscl = 5 Ymin = 0, Ymax = 30, Yscl = 5 A is largest for x = (1) (Round to two decimal places as needed.) (d) The largest area is 7(2) (Round to two decimal places as needed.) (1) O cubic unit(s). (2) O cubicunit(s). O unit(s). O unit(s). O square unit(s). O square unit(s).An open box with a square base is to be made from a square piece of cardboard 27 inches on a side by cutting out a square from each corner and turning up the sides. See the figure. X Answers parts (a) through (e). 27 in. XY -27 in. (a) Express the volume V of the box as a function of the length x of the side of the square cut from each corner. V= (Simplify your answer.) (b) What is the volume if a 4-inch square is cut out? The volume is (1 ) (Simplify your answer.) (c) What is the volume if a 12-inch square is cut out? The volume is (2) (Simplify your answer.) (d) Graph V = V(x). For what value of x is V largest? Choose the correct graph below. O A. O B. O c. OD. Xmin = 0, Xmax = 13.5, Xmin = 0, Xmax = 13.5, Xmin = 0, Xmax = 13.5, Xmin = 0, Xmax = 13.5, Xscl = 0.5, Ymin = 0, Xscl =0.5, Ymin = 0, Xscl = 0.5, Ymin = 0, Xscl = 0.5, Ymin = 0, Ymax = 800, Yscl = 100 Ymax = 1500, Yscl = 250 Ymax = 1500, Yscl = 250 Ymax = 1500, Yscl = 250 For what value of x is V largest? K= (3) (e) What is the largest volume? The largest volume is (4) (1) O inches. (2) O cubic inches. (3) O square inches (4) O square inches. square inches. square inches. inches inches OO O cubic inches. O cubic inches O cubic inches.In parts (a) and (b), use the given gure. (a) For what value of x does f(x) = 90:)? (a) Solve the equation: f(x) = 900. x = 4 (b) Solve the inequality f(x) > 900. (b) For which values of x is too > 90:)? For every x in the interval _ f(x) > 900. (Type your answer in interval notation.)