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Kobotan [32]
4 years ago
7

2×5/14 write your answer as afraction in simplest form​

Mathematics
1 answer:
Mashutka [201]4 years ago
7 0

Answer: 5/7

\(๑╹◡╹๑)ノ♬

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Which of the following is the solution to the differential equation dP/dt+P=10 with the initial condition P(0)=4
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  •    Option C.    P=10-6e^{-t}

Explanation:

<u>1. Separate variables:</u>

      \dfrac{dP}{dt}+P=10\\ \\ \\ \\\dfrac{dP}{dt}=-P+10\\ \\ \\ \dfrac{dP}{-P+10}=dt

<u></u>

<u>2. Find the indefinite integrals</u>

    -\ln{(10-P)}=t+C

<u></u>

<u>3. Solve for P</u>

      10-P=e^{-t+C}\\ \\ 10-P=Ke^{-t}\\ \\ P=10-Ke^{-t}

<u></u>

<u>4. Use the initial condition, P(0) = 4, to find K:</u>

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  • 4 = 10 - K
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  • K = 6

<u></u>

<u>5. Substitute K = 6 into the integrated equation:</u>

       P=10-6e^{-t}

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