Pre-Calc Homework Solutions 182

Pre-Calc Homework Solutions 182 - 182 Section 4.6 25. Step...

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24. (a) Note that the level of the coffee in the cone is not needed until part (b). Step 1: V 1 5 volume of coffee in pot y 5 depth of coffee in pot Step 2: } d d V t 1 } 5 10 in 3 /min Step 3: We want to find the value of } d d y t } . Step 4: V 1 5 9 p y Step 5: } d d V t 1 } 5 9 p } d d y t } Step 6: 10 5 9 p } d d y t } } d d y t } 5 } 9 1 p 0 } < 0.354 in./min The level in the pot is increasing at the rate of approximately 0.354 in./min. (b) Step 1: V 2 5 volume of coffee in filter r 5 radius of surface of coffee in filter h 5 depth of coffee in filter Step 2: At the instant in question, } d d V t 2 }52 10 in 3 /min and h 5 5 in. Step 3: We want to find 2} d d h t } . Step 4: Note that } h r } 5 } 3 6 } , so r 5 } h 2 } . Then V 2 5 } 1 3 } p r 2 h 5 } p 1 h 2 3 } . Step 5: } d d V t 2 } 5 } p 4 h 2 } } d d h t } Step 6: 2 10 5 } p ( 4 5) 2 } } d d h t } } d d h t }52} 5 8 p } in./min Note that } d d h t } , 0, so the rate at which the level is falling is positive. The level in the cone is falling at the rate of } 5 8 p } < 0.509 in./min. 25. Step 1: Q 5 rate of CO 2 exhalation (mL/min) D 5 difference between CO 2 concentration in blood pumped to the lungs and CO 2 concentration in blood returning from the lungs (mL/L) y 5 cardiac output Step 2:
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