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N76 [4]
3 years ago
7

after 1 second the ball is 76 feet in the air: after 2 seconds it is 144 feet in the air. Find the height of the function. h(x)=

?
Mathematics
1 answer:
MArishka [77]3 years ago
4 0
General equation for height, h
h = ut + 0.5gt^2

at t=1s, h = 76 feet
76 = u*1 + 0.5*a*1^2
76 = u + 0.5a

at t=2s, h = 144 feet
144 = u*2 + 0.5*a*2^2
144 = 2u + 2a
72 = u + a

Subtract 2 equations
0.5a = -4
a = -8
u = 80

So the equation,
h(x) = 80t + 0.5*(-8) t^2
h(x) = 80t - 4t^2
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Step-by-step explanation:

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Help me!!!<br> Is for today!!!<br> And what is its congruency?
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Step-by-step explanation:

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How do I solve this?
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3 years ago
The perimeter of a rectangle is 300 feet. The width of the rectangle is 10 feet more than the length. What is the width of the r
gavmur [86]
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3 years ago
I'm studying a new bacteria that doubles in numbers every 25 minutes. If i start with 50 bacteria, how long until i have 5 milli
dimaraw [331]

Answer:

415.63 minutes

Step-by-step explanation:

Growth can be represented by the equation A=A_0e^{rt}. We can find the rate at which it grows by using t=25 minutes and \frac{A_{0}}{A} =2 or double the amount at that time. The first step we always take is to divide A_0 by A.

[tex]\frac{A_{0}}{A}=e^{rt}\\2=e^{r(25)}

2=e^{(25)r}

To solve for r, we will take the natural log of both sides and use log rules to isolate r.

ln 2=ln e^{(25)r}\\ln 2=25r (ln e)\\\frac{ln2}{25} =r

We know lne=1 so we were able to cancel it out and divide both sides by 25.

We solve with a calculator \frac{ln2}{25} =r\\0.0277=r

We change 0.0277 into a percent by multiplying by 100 to get 2.77% as the rate.

The equation is A=A_0e^{0.0277t} .

We repeat the step above substituting A=5,000,000, A_0=50, and r=0.02777. Then solve for t.

5000000=50e^{0.0277t}\\\frac{5000000}{50} =e^{0.0277t}\\100000=e^{0.0277t}\\ln100000=lne^{0.0277t}\\ln100000=0.02777t(lne)\\\frac{ln100000}{0.0277} =t

t=415.63 minutes

6 0
3 years ago
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