Pre-Calc Homework Solutions 177

Pre-Calc Homework Solutions 177 - Section 4.6(d Note that V...

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(d) Note that V 5 IR gives 12 5 2 R , so R 5 6 ohms. Now substitute the known values into the equation in (c). 1 5 2 } d d R t } 1 6 1 2 } 1 3 } 2 3 5 2 } d d R t } } d d R t } 5 } 3 2 } ohms/sec R is changing at the rate of } 3 2 } ohms/sec. Since this value is positive, R is increasing. 8. Step 1: r 5 radius of plate A 5 area of plate Step 2: At the instant in question, } d d r t } 5 0.01 cm/sec, r 5 50 cm. Step 3: We want to find } d d A t } . Step 4: A 5 p r 2 Step 5: } d d A t } 5 2 p r } d d r t } Step 6: } d d A t } 5 2 p (50)(0.01) 5 p cm 2 /sec At the instant in question, the area is increasing at the rate of p cm 2 /sec. 9. Step 1: l 5 length of rectangle w 5 width of rectangle A 5 area of rectangle P 5 perimeter of rectangle D 5 length of a diagonal of the rectangle Step 2: At the instant in question, } d d l t } 5 2 2 cm/sec, } d d w t } 5 2 cm/sec, l 5 12 cm, and w 5 5 cm. Step 3: We want to find } d d A t } , } d d P t } , and } d d D t } . Steps 4, 5, and 6: (a) A 5 lw } d d A t } 5 l } d d w t } 1 w } d d l t } } d d A t } 5 (12)(2) 1 (5)( 2 2) 5 14 cm 2 /sec The rate of change of the area is 14 cm 2 /sec.
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