applied problems

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applied problems

by neeg » Tue Mar 05, 2013 5:37 pm
An object thrown directly upward is at a height of h feet after t seconds, where h = -16(t-3)^2 + 150. At what height, in feet, is the object 2seconds after it reaches its maximuh height?

a)6
b)86
c)134
d)150
e)166

The solution goest on to explain that the minimum value of (t-3)^2 occurs when t = 3 and also the maximum value. I Can see that the minimum value would be at t= 3 as 3-3 =0 but not sure how the maximum also occurs at t= 3?
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by GMATGuruNY » Tue Mar 05, 2013 6:40 pm
An object thrown directly upward is at a height of h feet after t seconds, where h = -16 (t - 3)^2 +
150. At what height, in feet, is the object 2 seconds after it reaches its maximum height?
A. 6
B. 86
C. 134
D 150
E. 214

OA B
h = 150 -16(t - 3)².
To MAXIMIZE the value of h, we need to MINIMIZE 16(t-3)², the value being subtracted from 150.
Since (t-3)² cannot be negative, the smallest possible value of 16(t-3)² is 0.
16(t-3)² = 0 when t=3.
Thus, the MAXIMUM value of h occurs when t=3.

Two seconds later, t=5.
When t=5, h = 150 - 16(5-3)² = 150-64 = 86.

The correct answer is B.
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