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Applications and Extensions (a) When will the object be 15 meters above the ground? 103. Dimensions of a Window The function A (x) = x(x + 2) (b) When will it strike the ground? describes the area A of the opening of a rectangular window in which the length is 2 feet more than the width, x. Find the (c) Will the object reach a height of 100 meters. dimensions of the window if the area of the opening is to be 109. Consecutive Integers The sum S of the consecutive integers 143 square feet by solving A (x) = 143. 1, 2, 3, . . ., n is given by the function S (n) = In(n + 1). 104. Dimensions of a Window The function A (x) = x(x + 1) describes the area A of the opening of a rectangular window Determine the number of consecutive integers, starting in which the length is 1 centimeter more than the width, x. with 1, that must be added to get a sum of 210. . 20 Find the dimensions of the window if the area of the opening 110. Geometry The number of diagonals D of a polygon with is to be 306 square centimeters by solving A (x) = 306. 105. Constructing a Box An open box is to be constructed from n sides is given by the function D (n) = in(n -3). a square sheet of sheet metal with dimensions x feet by Determine the number of sides a polygon with 65 diagonals x feet by removing a square of side 1 foot from each corner will have. Is there a polygon with 80 diagonals? and turning up the edges. The volume V of the box is V(x) = (x - 2) 2. Find the dimensions of the sheet metal 111.) Show that the sum of the roots of a quadratic equation needed to make a box that will hold 4 cubic feet by solving is b the equation V (x) = 4. 4ft by aft 106. Constructing a Box Rework Problem 105 if the box needs 112. Show that the product of the roots of a quadratic equation to hold 16 cubic feet. is 107. Physics A ball is thrown vertically upward from the top of a a building 96 feet tall with an initial velocity of 80 feet per 113. Find k such that the function f(x) = kx2 + x + k = 0 has second. The distance s (in feet) of the ball from the ground a repeated real zero. after t seconds is s ( t) = 96 + 80t - 16t. (a) After how many seconds does the ball strike the ground? 114. Find k such that the function f(x) = x2 - kx + 4 = 0 has a repeated real zero. (b) After how many seconds will the ball pass the top of the building on its way down? 115. Show that the real zeros of the function f(x) = ax2 + bx + c 108. Physics An object is propelled vertically upward with an are the negatives of the real zeros of the function initial velocity of 20 meters per second. The distance s (in g (x) = ax - bx + c. Assume that b2 - 4ac 2 0. meters) of the object from the ground after t seconds is 116. Show that the real zeros of the function f(x) = ax + bx + c s (t) = -4.912 + 20t. are the reciprocals of the real zeros of the function g (x) = cx2 + bx + a. Assume that b2 - 4ac 2 0