7_Cal_Solution of Calculus_6e

7_Cal_Solution of Calculus_6e - r= 1 2 S ; V= Answer: V (S...

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r = 1 2 r S π ; V = 4 3 πr 3 = 4 3 π · 1 8 µ S π ± 3 / 2 = 1 6 π µ S π ± 3 / 2 . Answer: V ( S )= 1 6 π µ S π ± 3 / 2 , 0 5 S< + . C01S01.039: To avoid decimals, we note that a change of 5 C is the same as a change of 9 F, so when the temperature is 10 Citis32+18=50 F; when the temperature is 20 C then it is 32 + 2 · 18 = 68 F. In general we get the Fahrenheit temperature F by adding 32 to the product of 1 10 C and 18, where C is the Celsius temperature. That is, F =32+ 9 5 C, and therefore C = 5 9 ( F 32). Answer: C ( F 5 9 ( F 32) ,F> 459 . 67 . C01S01.040: Suppose that a rectangle has base length x and perimeter 100. Let h denote the height of such a rectangle. Then 2 x +2 h = 100, so that h =50 x . Because x = 0 and h = 0, we see that 0 5 x 5 50. The area A of the rectangle is xh , so that A ( x x (50 x ) , 0 5 x 5 50 . C01S01.041: Let y denote the height of such a rectangle. The rectangle is inscribed in a circle of diameter 4, so the bottom side x and the left side y are the two legs of a right triangle with hypotenuse 4. Consequently x 2 + y 2 = 16, so y = 16 x 2 (not 16 x 2 because y = 0). Because x = 0 and y = 0, we see that 0 5 x 5 4. The rectangle has area A = xy ,so A ( x x p 16 x 2 , 0 5 x 5 4 . C01S042.042: We take the problem to mean that current production is 200 barrels per day per well, that
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