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Unformatted text preview: Math 1650 Homework Solutions Jason Snyder, PhD. Page 1 of 10 2.6 2 30 (even, except 12) 1 18 In these exercises you are asked to find a function that models a reallife situation. Use the guidelines for modeling described in the text to help you. 2) Area A poster is 10 inches longer than it is wide. Find a function that models its area in terms of its width ? . The area of the poster is given by area = width height. Let ? be the width of the poster, and we express height in terms of ? . In Words In Algebra Width ? Height ? + 10 Thus we have area = width height ( ? ) = ? ( ? + 10) ( ? ) = ? 2 + 10 ? 4) Volume The height of a cylinder is four times its radius. Find a function that models the volume of the cylinder in terms of its radius . The volume of a cylinder is given by volume = radius 2 height. Let be the radius of the cylinder, and we express height in terms of . In Words In Algebra Radius Height 4 Thus we have Math 1650 Homework Solutions Jason Snyder, PhD. Page 2 of 10 volume = radius 2 height ( ) = 2 (4 ) ( ) = 4 3 6) Perimeter A rectangle has an area of 16 m 2 . Find a function that models its perimeter in terms of the length ? of one of its sides. The perimeter of a rectangle is given by Perimeter = 2(length + width). Let ? be the length of the rectangle, and we express width in terms of ? . In Words In Algebra Length ? Width 16 ? Thus we have perimeter = 2(length + width) ( ? ) = 2 ? + 16 ? ( ) = 2 ? 2 + 16 ? 8) Area Find a function that models the surface area of a cube in terms of its volume . The surface area of a cube is given by surface area = 6(length of one side) 2 . Let be the length of one side of the cube. We therefore need to express , the volume of the cube, in terms of . The formula that relates and is = 3 . Solving for , we get = 3 . Math 1650 Homework Solutions Jason Snyder, PhD. Page 3 of 10 Thus we get surface area = 6(length of one side) 2 ( ) = 6 2 ( ) = 6 3 2 10) Area Find a function that models the area of a circle in terms of its circumference ....
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 Spring '06
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