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# At time t = 0, a projectile was fired upward from an initial

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At time t = 0, a projectile was fired upward from an initial [#permalink]  15 May 2019, 05:25
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100% (03:25) correct 0% (00:00) wrong based on 2 sessions
At time t = 0, a projectile was fired upward from an initial height of 10 feet. Its height after t seconds is given by the function $$h(t) = p−10(q −t)^2$$ , where p and q are positive constants. If the projectile reached a maximum height of 100 feet when t = 3, then what was the height, in feet, of the projectile when t = 4 ?

(A) 62

(B) 70

(C) 85

(D) 89

(E) 90
[Reveal] Spoiler: OA

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Re: At time t = 0, a projectile was fired upward from an initial [#permalink]  19 May 2019, 04:45
At t=3, h(3) = p-10(q-3)^2. We are given that height is 100 when t=3
100 = p-10(q-3)^2
100 = p – 10(q^2-6q+9)
100 = p - 10q^2+60q -90--------EQ1
At t =0, we are given that the height is 10
10 = p - 10q^2----Eq2
(EQ1)-(EQ2)
90 = 60q-90
180 = 60Q
q= 3
Lets substititute q in EQ2
10-p = -90
-p=-100
P = 100
H(4) = 100-10(3-4)^2
H(4) = 100-10 = 90
Re: At time t = 0, a projectile was fired upward from an initial   [#permalink] 19 May 2019, 04:45
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