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Pre-Calc Homework Solutions 292

Pre-Calc Homework Solutions 292 - 292 Section 7.1 7 19(a...

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19. (a) Final position 5 2 1 E 7 0 v ( t ) dt 5 2 2 } 1 2 } (1)(2) 1 } 1 2 } (1)(2) 1 1(2) 1 } 1 2 } (2)(2) 2 } 1 2 } (2)(1) 5 5; ends at x 5 5. (b) E 7 0 ) v ( t ) ) dt 5 } 1 2 } (1)(2) 1 } 1 2 } (1)(2) 1 1(2) 1 } 1 2 } (2)(2) 1 } 1 2 } (2)(1) 5 7 meters 20. (a) Final position 5 2 1 E 10 0 v ( t ) dt 5 2 1 } 1 2 } (2)(3) 2 } 1 2 } (1)(3) 2 (3)(3) 2 } 1 2 } (1)(3) 1 } 1 2 } (3)(3) 5 2 2.5; ends at x 5 2 2.5. (b) Distance 5 E 10 0 ) v ( t ) ) dt 5 } 1 2 } (2 ? 3) 1 } 1 2 } (1)(3) 1 3(3) 1 } 1 2 } (1)(3) 1 } 1 2 } (3)(3) 5 19.5 meters 21. E 10 0 27.08 ? e t /25 dt 5 27.08 3 25 e t /25 4 5 27.08[25 e 0.4 2 25] < 332.965 billion barrels 22. E 24 0 3 3.9 2 2.4 sin 1 } 1 p 2 t } 24 dt 5 3 3.9 t 1 } 28 p .8 } cos 1 } 1 p 2 t } 24 5 31 93.6 1 } 28 p .8 } 2 2 } 28 p .8 } 4 5 93.6 kilowatt-hours 23. (a) Solve 10,000(2 2 r ) 5 0: r 5 2 miles. (b) Width 5 D r , Length 5 2 p r: Area 5 2 p r D r (c) Population 5 Population density 3 Area (d) E 2 0 10,000(2 2 r )(2 p r ) dr 5 20,000 p E 2 0 (2 r 2 r 2 ) dr 5 20,000 p 3 r 2 2 } 1 3 } r 3 4 5 20,000 p 31 4 2 } 8 3 } 2 2 0 4 5 } 80, 3 000 } p < 83,776 24. (a) Width 5 D r , Length 5 2 p r : Area 5 2 p r D r (b) Volume per second 5 Inches per second 3 Cross section area 8(10 2 r 2 ) } s i e n c . } ? (2 p r ) D r in 2 5 flow in } s in ec 3 } (c) E 3 0 8(10 2 r 2 )(2 p r ) dr 5 16 p E 3 0 (10 r 2 r 3 ) dr 5 16 p 3 5 r 2 2 } 1 4 } r 4
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