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Given f (x) = - x2 + 6 x -11 determine each of the following.
(a) f ( 2)
(b) f ( -10)
(c) f (t )
Solution
(a) f ( 2) = - ( 2)2 + 6(2) -11 = -3
(b) f ( -10) = - ( -10)2 + 6 ( -10) -11 = -100 - 60 -11 ) -171
Be careful while squaring negative numbers!
(c ) f (t ) = -t 2 + 6t -11
Recall that we substitute for the x's whatever is in the parenthesis on the left. Frequently this will be something other than a number. Thus, in this case we put t's into for all the x's on the left.
If the hight of pipe is 18 inches, what is the volume of the shaded region in terms of π? a. 31.5π in 3 b. 126π in 3 c. 157.5 in 3 d. 58.5 in 3
2
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