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andrew11 [14]
3 years ago
5

What is If a rectangular prism has a length, width, and height of centimeter, centimeter, and centimeter, respectively, then the

volume of the prism is _blank_ cubic centimeter pls if you really want a point don't put a random answer like 105/515 it's annoying ok
Mathematics
1 answer:
USPshnik [31]3 years ago
8 0

Answer:

The volume is 105/512 cubic inches

Step-by-step explanation:

Given [Missing from the question]

L = \frac{3}{8} cm -- Length

W=\frac{5}{8}cm -- Width

H = \frac{7}{8}cm -- Height

Required

Determine the volume.

The volume (V) is calculated as thus:

V = L *W *H

V = \frac{3}{8} cm* \frac{5}{8}cm * \frac{7}{8}cm

V = \frac{3}{8} * \frac{5}{8} * \frac{7}{8}cm^3

V = \frac{3*5*7}{8*8*8}cm^3

V = \frac{105}{512}cm^3

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3 years ago
Find the indefinite integral using the substitution provided.
Nady [450]

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

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

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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Step-by-step explanation:

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