Pre-Calc Homework Solutions 315

# Pre-Calc Homework Solutions 315 - Section 7.5 315 15(a From...

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15. (a) From the equation x 5 } 3 8 } y , it follows that a thin horizontal rectangle has area } 3 4 } y D y, where y is the distance from the top of the triangle, the pressure is 62.4( y 2 3). The total force is approximately n k 5 1 62.4( y k 2 3) 1 } 3 4 } y k 2 D y 5 n k 5 1 46.8( y k 2 2 3 y k ) D y . (b) E 8 3 46.8( y 2 2 2 3 y ) dy 5 3 15.6 y 3 2 70.2 y 2 4 5 3494.4 2 ( 2 210.6) 2 3705 lb 16. (a) From the equation y 5 } x 2 2 } , it follows that a thin horizontal rectangle has area 2 ˇ 2 w y w D y , where y is distance from the bottom, and pressure 62.4(4 2 y ). The total force is approximately Σ n k 5 1 62.4(4 2 y k )(2 ˇ 2 w y k w ) D y 5 Σ n k 5 1 124.8 ˇ 2 w (4 ˇ y k w 2 y k 3/2 ) D y . (b) E 4 0 124.8 ˇ 2 w (4 ˇ y w 2 y 3/2 ) dy 5 124.8 ˇ 2 w 3 } 8 3 } y 3/2 2 } 2 5 } y 5/2 4 5 1064.96 ˇ 2 w < 1506.1 lb 17. (a) Work to raise a thin slice 5 62.4(10 3 12)( D y ) y. Total work
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