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ioda
2 years ago
5

A cylinder has a height of 14 centimeters and a radius of 17 centimeters. What is its volume? Use ​ ≈ 3.14 and round your answer

to the nearest hundredth.
Mathematics
1 answer:
9966 [12]2 years ago
6 0
<h2><u>Answer</u></h2>

Volume = \sf{\pi r^2 h}

= \sf{3.14 \times {17}^{2} \times 14 } = \sf{12704.45~cm^3}

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Answer:

P(t)=3,000,000-3,000,000e^{0.0138t}

Step-by-step explanation:

Since P(t) increases at a rate proportional to the number of people still unaware of the product, we have

P'(t)=K(3,000,000-P(t))

Since no one was aware of the product at the beginning of the campaign and 50% of the people were aware of the product after 50 days of advertising

<em>P(0) = 0 and P(50) = 1,500,000 </em>

We have and ordinary differential equation of first order that we can write

P'(t)+KP(t)= 3,000,000K

The <em>integrating factor </em>is

e^{Kt}

Multiplying both sides of the equation by the integrating factor

e^{Kt}P'(t)+e^{Kt}KP(t)= e^{Kt}3,000,000*K

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(e^{Kt}P(t))'=3,000,000Ke^{Kt}

Integrating both sides

e^{Kt}P(t)=3,000,000K \int e^{Kt}dt +C

e^{Kt}P(t)=3,000,000K(\frac{e^{Kt}}{K})+C

P(t)=3,000,000+Ce^{-Kt}

But P(0) = 0, so C = -3,000,000

and P(50) = 1,500,000

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e^{-50K}=\frac{1}{2}\Rightarrow K=-\frac{log(0.5)}{50}=0.0138

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P(t)=3,000,000-3,000,000e^{0.0138t}

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