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3 years ago

Sorry if its blurry im on my laptop

Mathematics

1 answer:

Kamila [148]3 years ago

6 0

Answer:

Step-by-step explanation:

1 in=2 ft

Bedroom 1

scale

17.5 in ×12.5in

actual

(17.5×2)×(12.5×2)

35 ft×25 ft

Living Room

scale

17.5 in×17.5 in

actual

35 ft×35 ft

Bathroom 1

scale

12.5 in×12.5 in

actual

25 ft×25 ft

Kitchen

scale

17.5 in ×12.5 in

actual

35 ft×35 ft

Bedroom2

scale

12.5 in ×12.5 in

actual

25 ft×25 ft

Entryway

scale

12.5 in×12.5 in

actual

25 ft×25 ft

Bathroom 2

scale

12.5 in×5 in

actual

25 ft×10 ft

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Kobotan [32]

In order to find the answer to this question, you need to multiply the fractions. But before we do that, we need to turn the mixed fraction into a proper fraction. 1 3/4 would turn into 7/4 because you multiply the denominator by the whole number and add the numerator. So we come out with:

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2 years ago

Find the indefinite integral using the substitution provided.

Nady [450]

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

This is the same as writing 7*Ln( e^(2x) + 10) + C

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

Explanation:

Start with the equation $u = e^{2x}+10$

Apply the derivative and multiply both sides by 7 like so

$u = e^{2x}+10\\\\\frac{du}{dx} = 2e^{2x}\\\\7\frac{du}{dx} = 7*2e^{2x}\\\\7\frac{du}{dx} = 14e^{2x}\\\\7du = 14e^{2x}dx\\\\$

The "multiply both sides by 7" operation was done to turn the 2e^(2x) into 14e^(2x)

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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1 year ago