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Marta_Voda [28]
3 years ago
8

What is the volume of the cylinder?

Mathematics
1 answer:
elena-s [515]3 years ago
3 0
Volume = pi×r^2×h
= 64 × 4 × pi
= 256pi units^3
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Please solve the following quadratic equation and show your work: x^2 -x =30
saveliy_v [14]
Rewriting the equation as a quadratic equation equal to zero:
     x^2 - x - 30 = 0
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3 years ago
The population of a community is known to increase at a rate proportional to the number of people present at time t. If the popu
Lady bird [3.3K]

Answer:

P(t) = P(0)e^{0.0693t}

Step-by-step explanation:

The population of a community is known to increase at a rate proportional to the number of people present at time t.

This means that the population growth is modeled by the following differential equation:

\frac{dP(t)}{dt} = rP(t)

Which has the following solution:

P(t) = P(0)e^{rt}

In which P(t) is the population after t years, P(0) is the initial population and r is the growth rate.

The population has doubled in 10 years

This means that P(10) = 2P(0). We use this to find r.

P(t) = P(0)e^{rt}

2P(0) = P(0)e^{10r}

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10r = \ln{2}

r = \frac{\ln{2}}{10}

r = 0.0693

So the equation that will estimate the population of the community in t years is:

P(t) = P(0)e^{0.0693t}

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Cos x is the derivative of sin x.
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