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Pre-Calc Homework Solutions 83

# Pre-Calc Homework Solutions 83 - Section 3.4 9 Q(t 200(30...

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9. Q ( t ) 5 200(30 2 t ) 2 5 200(900 2 60 t 1 t 2 ) 5 180,000 2 12,000 t 1 200 t 2 Q 9 ( t ) 5 2 12,000 1 400 t The rate of change of the amount of water in the tank after 10 minutes is Q 9 (10) 5 2 8000 gallons per minute. Note that Q 9 (10) , 0, so the rate at which the water is running out is positive. The water is running out at the rate of 8000 gallons per minute. The average rate for the first 10 minutes is } Q (1 1 0 0 ) 2 2 Q 0 (0) } 5 } 80,000 2 10 180,000 } 5 2 10,000 gallons per minute. The water is flowing out at an average rate of 10,000 gallons per minute over the first 10 min. 10. (a) Average cost 5 } c ( 1 1 0 0 0 0) } 5 } 11 1 , 0 0 0 00 } 5 \$110 per machine (b) c 9 ( x ) 5 100 2 0.2 x Marginal cost 5 c 9 (100) 5 \$80 per machine (c) Actual cost of 101st machine is c (101) 2 c (100) 5 \$79.90, which is very close to the marginal cost calculated in part (b). 11. (a) [0, 50] by [ 2 500, 2200] The values of x which make sense are the whole numbers, x \$ 0. (b) Marginal revenue 5 r 9 ( x ) 5 } d d x } 3 2000 1 1 2 } x 1 1 1 } 24 5 } d d x } 1 2000 2 } x 20 1 00 1 } 2 5 0 2 5 } ( x 2 1 00 1 0 ) 2 } (c) r 9 (5) 5 } (5 2 1 00 1 0 ) 2 } 5 } 20 3 0 6 0 } < 55.56 The increase in revenue is approximately \$55.56.
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