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enot [183]
4 years ago
11

Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth.

Mathematics
2 answers:
DaniilM [7]4 years ago
7 0
A ) h = -16 t² + 135 t + 76
Let : h = 0
0 = - 16 t² + 135 t + 76
B ) t 1/2 = (-b+/- √ ( b² - 4 ac ) / ( 2 a )
t 1/2 = (-135 - √(18,225 + 4,864))/ (-32) = ( - 135 - 151.95) / (- 32)=
= (-286.95) / (- 32) = 9.967 ≈ 9.0 s ( other solution is negative )
Answer:
2)  0 = -16 t² + 135 t + 76;  9 s 

drek231 [11]4 years ago
6 0

Answer:

The answer is 2.) 0=-16t^{2}+135t+76;9 s

Step-by-step explanation:

Given initial velocity=135 ft/s

& cliff=76 foot

Given quadratic equation

0=-16t^{2}+vt+c

⇒   0=-16t^{2}+135t+76                    (let h=0 it is given)

⇒   t=\frac{-135\pm\sqrt ((135)^{2}-4(-16)(76))}{2(-16)}

⇒   t=\frac{-135\pm151.951}{-32}

⇒    t=8.96≈9 s (the other root is negative)

Hence, rocket will take 9 s to hit the ground after launched.


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A bacteria colony increases in size at a rate of 4.0581e1.6t bacteria per hour. If the initial population is 36 bacteria, find t
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Answer:

1560

Step-by-step explanation:

The rate of Increase of the population (P) of the bacteria is given as:

\frac{dP}{dt} =4.058e^{1.6t}

dP =4.058e^{1.6t}}dt\\Taking\: Integrals\\\int dP =4.058 \int e^{1.6t}dt\\P(t)=\frac{4.058}{1.6} (e^{1.6t} +K)\\P(t)=2.53625 (e^{1.6t} +K)

Where k is a constant of Integration.

At t=0, P(t)=36

36=2.53625 (e^{1.6*0} +K)\\36=2.53625 (e^{0} +K)\\36=2.53625 (1 +K)\\36=2.53625 +2.53625K\\K=13.19

Therefore:

P(t)=2.53625 (e^{1.6t} +13.19)\\At \: t=4\\P(4)=2.53625 (e^{1.6*4} +13.19)\\=1559.88\\P(4)=1560

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