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tensa zangetsu [6.8K]
3 years ago
13

Lynnette can wash 959595 cars in 5 days. How many cars can Lynnette wash in 11 days?

Mathematics
1 answer:
aleksley [76]3 years ago
6 0

Answer:

Lynnette can wash 2111109 in 11 days

Step-by-step explanation:

Have a good day :)

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Answer:  7\text{Ln}\left(e^{2x}+10\right)+C

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=======================================================

Explanation:

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This way we can do the following substitutions:

\displaystyle \int \frac{14e^{2x}}{e^{2x}+10}dx\\\\\\\displaystyle \int \frac{1}{e^{2x}+10}14e^{2x}dx\\\\\\\displaystyle \int \frac{1}{u}7du\\\\\\\displaystyle 7\int \frac{1}{u}du\\\\\\

Integrating leads to

\displaystyle 7\int \frac{1}{u}du\\\\\\7\text{Ln}\left(u\right)+C\\\\\\7\text{Ln}\left(e^{2x}+10\right)+C\\\\\\

Be sure to replace 'u' with e^(2x)+10 since it's likely your teacher wants a function in terms of x. Also, do not forget to have the plus C at the end. This is a common mistake many students forget to do.

To verify the answer, you can apply the derivative to it and you should get back to the original integrand of \frac{14e^{2x}}{e^{2x}+10}

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