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28. A 1600-lb elevator is suspended by a 200-ft cable that weighs 10 lb/ft. How much work is required to raise the elevator from the basement to the third floor, a distance of 30 ft?

28. A 1600-lb elevator is suspended by a 200-ft cable that weighs 10 lb/ft. How much work is required to raise the elevator from the basement to the third floor, a distance of 30 ft?

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.2: Determinants
Problem 8AEXP
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Hello, I need help with question 28.

23. The base of a solid is a circular disk with radius 3. Find the volume of the solid if parallel cross-sections perpendicular to the base are isosceles right triangles with hypotenuse lying along the base. 24. The base of a solid is the region bounded by the parabolas y = x² and y = 2 – x². Find the volume of the solid if the cross-sections perpendicular to the x-axis are squares with one side lying along the base. 25. The height of a monument is 20 m. A horizontal cross- section at a distance x meters from the top is an equilateral triangle with side x meters. Find the volume of the monument. 26. (a) The base of a solid is a square with vertices located at (1, 0), (0, 1), (–1, 0), and (0, – 1). Each cross-section perpendicular to the x-axis is a semicircle. Find the volume of the solid. (b) Show that by cutting the solid of part (a), we can rearrange it to form a cone. Thus compute its volume more simply. 27. A force of 30 N is required to maintain a spring stretched from its natural length of 12 cm to a length of 15 cm. How much work is done in stretching the spring from 12 cm to 20 cm? 28. A 1600-lb elevator is suspended by a 200-ft cable that weighs 10 lb/ft. How much work is required to raise the elevator from the basement to the third floor, a distance of 30 ft? 29. A tank full of water has the shape of a paraboloid of revo- lution as shown in the figure; that is, its shape is obtained
Transcribed Image Text:23. The base of a solid is a circular disk with radius 3. Find the volume of the solid if parallel cross-sections perpendicular to the base are isosceles right triangles with hypotenuse lying along the base. 24. The base of a solid is the region bounded by the parabolas y = x² and y = 2 – x². Find the volume of the solid if the cross-sections perpendicular to the x-axis are squares with one side lying along the base. 25. The height of a monument is 20 m. A horizontal cross- section at a distance x meters from the top is an equilateral triangle with side x meters. Find the volume of the monument. 26. (a) The base of a solid is a square with vertices located at (1, 0), (0, 1), (–1, 0), and (0, – 1). Each cross-section perpendicular to the x-axis is a semicircle. Find the volume of the solid. (b) Show that by cutting the solid of part (a), we can rearrange it to form a cone. Thus compute its volume more simply. 27. A force of 30 N is required to maintain a spring stretched from its natural length of 12 cm to a length of 15 cm. How much work is done in stretching the spring from 12 cm to 20 cm? 28. A 1600-lb elevator is suspended by a 200-ft cable that weighs 10 lb/ft. How much work is required to raise the elevator from the basement to the third floor, a distance of 30 ft? 29. A tank full of water has the shape of a paraboloid of revo- lution as shown in the figure; that is, its shape is obtained
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