Pre-Calc Homework Solutions 13

Pre-Calc Homework Solutions 13 - Section 1.3 66. (a) Note...

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66. (a) Note that 2 mi 5 10,560 ft, so there are ˇ 8 w 0 w 0 w 2 w 1 w x w 2 w feet of river cable at $180 per foot and (10,560 2 x ) feet of land cable at $100 per foot. The cost is C ( x ) 5 180 ˇ 8 w 0 w 0 w 2 w 1 w x w 2 w 1 100(10,560 2 x ) (b) C (0) 5 $1,200,000 C (500) < $1,175,812 C (1000) < $1,186,512 C (1500) 5 $1,212,000 C (2000) < $1,243,732 C (2500) < $1,278,479 C (3000) < $1,314,870 Values beyond this are all larger. It would appear that the least expensive location is less than 2000 ft from point P. 67. (a) [ 2 3, 3] by [ 2 1, 3] (b) Domain of y 1 : [0, ) Domain of y 2 :( 2‘ ,1] Domain of y 3 : [0, 1] (c) The functions y 1 2 y 2 , y 2 2 y 1 , and y 1 ? y 2 all have domain [0, 1], the same as the domain of y 1 1 y 2 found in part (b). Domain of } y y 1 2 } : [0, 1) Domain of } y y 2 1 } : (0, 1] (d) The domain of a sum, difference, or product of two functions is the intersection of their domains. The domain of a quotient of two functions is the
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