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Volume of a Box An open box is constructed from a 6 in. by 10 in sheet of cardboard by cutting a square piece from each corner and then folding up the sides, as shown in the figure.
The volume of the box is
(a) Explain how the expression for V is obtained.
(b) Expand the expression for V. What is the degree of the resulting polynomial?
(c) Find the volume when
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Chapter P Solutions
College Algebra
- Building Envelope The building code in a certain town requires that a house be at least 10 ft from the boundaries of the lot. The buildable area or building envelope for the rectangular lot shown in the following figure is given by A=(x20)(y20) a Explain how the expression for A is obtained. b Expand to express A as a polynomial in x and y. c A contractor has a choice of purchasing one of two rectangular lots, each having the same area. One lot measures 100 ft by 400 ft; the other measures 200 ft by 200 ft. Which lot has the larger building envelope?arrow_forwardVolume of Concrete A culvert is constructed out of large cylindrical shells cast in concrete, as shown in the figure. Using the formula for the volume of a cylinder given on the inside back cover of this book, explain why the volume of the cylindrical shell is v=R2hr2h Factor to show that v=2averageradiusheightthickness Use the ‘unrolled” diagram to explain why this makes sense geometrically.arrow_forwardFabricating sheet metal The open tray shown in the illustration is to be manufactured from a 12-by-14-inch rectangular sheet of metal by cutting squares from each corner and folding up the sides. If the volume of the tray is to be 160 cubic inches and x is to be an integer, what size squares should be cut from each corner?arrow_forward
- Population The table shows the U.S. populations for the years 1970,1980,1990 and 2000. Source: U.S. Census Bureau Year Population in millions 1970 1980 1990 2000 205 227 249 282 a Find a cubic polynomial that fits the data and use it to estimate the population in 2010. b The actual population in 2010 was 309 million. How does your estimate compare?arrow_forwardFind the image of the square in Example 6 after a vertical stretch by a factor of k=2.arrow_forwardError Analysis Describe the error. Use synthetic division to find the remainder when x2+3x5is divided by x+1.arrow_forward
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