401 Test 4: Chapter 7 Applications of Differentiation Description: 25 questions. 1) Asum = 19.689in2 Asum = 10.768in2 Asum = 8.922in2 Asum = 3.282in2 2) Little Louie is making a diorama for his 2nd grade teacher and you are going to help him. Unfortunately, you have no shoeboxes. In fact, the only material you have for the box itself is a pizza box left over from last week's midnight munchie run. After cutting away the parts of the box that are too greasy to use, you are left with a sheet of cardboard with dimensions 14 8 in inches. How big must the squares you cut out of the sheet of cardboard be in order to maximize Little Louie's diorama? 2.612 by 1.388 inches 4.722 by 8.722 inches 1.639 by 1.639 inches 5.694 by 5.694 inches 3) Suppose the position of a particle on a number line is given by p( t) = 3t3 3t, where t is in minutes and p is in meters. Which of the following equations represents the acceleration of the object? a(t) = 18 a(t) = 9t2 a(t) = 9t2 3 a(t) = 18t 4) A television camera at ground level is filming at the lift-off of a space shuttle that is rising vertically according to the position equation S = 50t2, where S is measured in feet and t is measured in seconds. The camera is 2000 ft from the launch pad. What is the rate of change in the angle of elevation of the camera 10 4) seconds after lift-off? 5) The area of a rectangle is given by the functionA(x) = 8x x 2 , where x is the length of one of the sides. What is the maximum area of this rectangle? 4 8 16 28 6) Suppose a particle is moving from left to right along the graph of y = x2. Find the rate of change of the distance between the particle and the origin at the instant x = 5 if the particle moves horizontally at a constant rate of 10 units/ second. (In other words, dx/dt = 10) 10 units/second 4 units/second 100 units/second 364 units/second 7) Suppose you are told that z = x2y3, where x and y are changing with time. Suppose also that x is increasing at a constant rate of 3 units/second and that y is decreasing at a constant rate of 2 units/second. What is the rate of change ofz with respect to time when x = 5 and y = 7? 2,940 units/second 17,640 units/second 7,105 units/second 8,575 units/second 8) a(t) = 3 a(t) = 3 8) a(t) = 65 a(t) = t 9) True or false? The largest rectangle with a given perimeter p units is a square. true false 10) A cartoon cat lights a bomb and tosses it into the air. The bomb is set to detonate in 8 seconds. The altitude of the bomb is given by the function P(t) = 9t2 + 72t with P( t) in feet and t in seconds. What is the altitude of the bomb when it explodes? 144 feet 0 feet 144 feet 572 feet 11) A farmer is building a chicken pen in the shape of a rectangle and has 100 feet of fencing material. If a chicken needed 2 square feet to live, what would be the maximum number of chickens the farmer could keep alive in the pen? 625 chickens 313 chickens 312 chickens 0 chickens 12) 13) Suppose that a certain clock has a minute hand that is 4 inches long and an hour hand that is 3 inches long. What is the rate of change of the distance between the tips of the minute and hour hands at 2:00? 18.1 inches/hour 950 inches/hour 16.6 inches/hour 4.6 inches/hour 14) 0 1 15) Jim, who is 6 ft tall, is walking directly away from a 15 ft lamppost at a rate of 4 ft per sec. What is the rate of change in the length of Jim's shadow when he is 8 ft from the base of the lamppost? 16) 16) 17) Use the linear approximation formula to approximate 18) An object is dropped off a tower. Its height h (in feet) above the ground after t seconds is given by h( t) = 576 16t 2 .Which of the following is the velocity when it strikes the ground? 6 ft/sec 32 ft/sec 192 ft/sec 192 ft/sec 19) 20) 20) The distance between home plate and first base on a baseball diamond is 90 ft. A runner is moving towards first base at 24 ft/sec. What is the rate of change in the distance between the runner and second base at the instant the runner is 60 ft away from first base? 21) 144 feet 432 feet 4 seconds 8 seconds 22) Use the linear approximation formula to approximate ln 1.1. 23) 23) Complete two interations of Newton's method for the given function and indicated initial guess. 127/48 129/48 Which of the following is equal to x3? 10/3 8/3 24) 25) A pebble is dropped into a pool of water, generating circular ripples. The radius of the largest ripple is increasing at a constant rate of 3 inches per second. By how many inches did the circumference of the ripple increase between 0 and 2 seconds? 12 in. 6 in. 2 in. 3 in