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5 A trough has a trapezoidal cross section with a height of 5 m and horizontal sides of width m and 2 5 m. Assume the length of the trough is 14 m. See the figure to the right. Complete parts (a) and (b) below. ... 5 m 5 m 2.5 m 14 m a. How much work is required to pump the water out of the trough (to the level of the top of the trough) when it is full? Use 1000 kg/m³ for the density of water and 9.8 m/s² for the acceleration due to gravity. Draw a y-axis in the vertical direction (parallel to gravity) and use the midpoint of the bottom of one edge of the trough as the location of the origin. For 0 ≤ y ≤5, find the cross-sectional area A(y) in terms of y. A(y) = (Simplify your answer. Use integers or fractions for any numbers in the expression.) Set up the integral that gives the work required to pump the water out of the tank. Use increasing limits of integration. Select the correct choice below and fill in the answer boxes to complete your choice.

5 A trough has a trapezoidal cross section with a height of 5 m and horizontal sides of width m and 2 5 m. Assume the length of the trough is 14 m. See the figure to the right. Complete parts (a) and (b) below. ... 5 m 5 m 2.5 m 14 m a. How much work is required to pump the water out of the trough (to the level of the top of the trough) when it is full? Use 1000 kg/m³ for the density of water and 9.8 m/s² for the acceleration due to gravity. Draw a y-axis in the vertical direction (parallel to gravity) and use the midpoint of the bottom of one edge of the trough as the location of the origin. For 0 ≤ y ≤5, find the cross-sectional area A(y) in terms of y. A(y) = (Simplify your answer. Use integers or fractions for any numbers in the expression.) Set up the integral that gives the work required to pump the water out of the tank. Use increasing limits of integration. Select the correct choice below and fill in the answer boxes to complete your choice.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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A trough has a trapezoidal cross section with a height of 5 m and horizontal sides of width 5 2 5 m. Assume the length of the trough is 14 m. See the figure to the right. Complete parts (a) and (b) below. JOdx OA. S S m and a. How much work is required to pump the water out of the trough (to the level of the top of the trough) when it is full? Use 1000 kg/m³ for the density of water and 9.8 m/s² for the acceleration due to gravity. Draw a y-axis in the vertical direction (parallel to gravity) and use the midpoint of the bottom of one edge of the trough as the location of the origin. For 0 ≤ y ≤5, find the cross-sectional area A(y) in terms of y. A(y) = (Simplify your answer. Use integers or fractions for any numbers in the expression.) OB. S 5 m Set up the integral that gives the work required to pump the water out of the tank. Use increasing limits of integration. Select the correct choice below and fill in the answer boxes to complete your choice. (Type exact answers.) dy 5 m 2.5 m 14 m
Transcribed Image Text:A trough has a trapezoidal cross section with a height of 5 m and horizontal sides of width 5 2 5 m. Assume the length of the trough is 14 m. See the figure to the right. Complete parts (a) and (b) below. JOdx OA. S S m and a. How much work is required to pump the water out of the trough (to the level of the top of the trough) when it is full? Use 1000 kg/m³ for the density of water and 9.8 m/s² for the acceleration due to gravity. Draw a y-axis in the vertical direction (parallel to gravity) and use the midpoint of the bottom of one edge of the trough as the location of the origin. For 0 ≤ y ≤5, find the cross-sectional area A(y) in terms of y. A(y) = (Simplify your answer. Use integers or fractions for any numbers in the expression.) OB. S 5 m Set up the integral that gives the work required to pump the water out of the tank. Use increasing limits of integration. Select the correct choice below and fill in the answer boxes to complete your choice. (Type exact answers.) dy 5 m 2.5 m 14 m
5 2 A trough has a trapezoidal cross section with a height of 5 m and horizontal sides of width 5 m. Assume the length of the trough is 14 m. See the figure to the right. Complete parts (a) and (b) below. O B. Jody m and 5 m 5 m 2.5 m 14 m Approximately of work is required to pump the water out of the trough. (Use scientific notation. Use the multiplication symbol in the math palette as needed. Round to six decimal places as needed.) b. If the length is doubled, is the required work doubled? Explain. O A. No. If the length of the trough is doubled, the required work is less than twice the required work to empty the original trough. B. Yes. The length of the trough is a constant term that can be moved outside of the work integral. C. Yes. This is true only for figures with trapezoidal cross sections. D. No. If the length of the trough is doubled, the required work is more than twice the required work to empty the original trough.
Transcribed Image Text:5 2 A trough has a trapezoidal cross section with a height of 5 m and horizontal sides of width 5 m. Assume the length of the trough is 14 m. See the figure to the right. Complete parts (a) and (b) below. O B. Jody m and 5 m 5 m 2.5 m 14 m Approximately of work is required to pump the water out of the trough. (Use scientific notation. Use the multiplication symbol in the math palette as needed. Round to six decimal places as needed.) b. If the length is doubled, is the required work doubled? Explain. O A. No. If the length of the trough is doubled, the required work is less than twice the required work to empty the original trough. B. Yes. The length of the trough is a constant term that can be moved outside of the work integral. C. Yes. This is true only for figures with trapezoidal cross sections. D. No. If the length of the trough is doubled, the required work is more than twice the required work to empty the original trough.
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