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s2008m [1.1K]
3 years ago
10

17=3(g+3)-g. I also need the math

Mathematics
2 answers:
Feliz [49]3 years ago
4 0
Let's solve your equation step-by-step.<span>17=<span><span>3<span>(<span>g+3</span>)</span></span>−g</span></span>
Step 1: Simplify both sides of the equation.<span>17=<span><span>3<span>(<span>g+3</span>)</span></span>−g</span></span><span>
Simplify: (Show steps)</span><span>17=<span><span>2g</span>+9</span></span>
Step 2: Flip the equation.<span><span><span>2g</span>+9</span>=17</span>
Step 3: Subtract 9 from both sides.<span><span><span><span>2g</span>+9</span>−9</span>=<span>17−9</span></span><span><span>2g</span>=8</span>
Step 4: Divide both sides by 2.<span><span><span>2g</span>2</span>=<span>82</span></span><span>g=4</span>
Answer:<span>g=<span>4</span></span>
IgorC [24]3 years ago
4 0
Do you need it simplified if you do then:

you multiply 3 into the parentheses 17=3(g+3)-g
                                                              17=3g+9-g
then add like terms 17=3g+9-g meaning g
                                          17=3g+9
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<img src="https://tex.z-dn.net/?f=%5Cbegin%7Bequation%7D%5Ctext%20%7B%20Question%3A%20If%20%7D%20%5Cint_%7B%5Cfrac%7B-1%7D%7B%5C
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We want to evaluate

\displaystyle \int_{-\frac1{\sqrt2}}^{\frac1{\sqrt2}} \sqrt{\left(\frac{x-1}{x+1}\right)^2 + \left(\frac{x+1}{x-1}\right)^2 - 2} \, dx

First we note that the integrand is even (replacing x with -x doesn't fundamentally alter the function being integrated), so this is equal to

\displaystyle 2 \int_0^{\frac1{\sqrt2}} \sqrt{\left(\frac{x-1}{x+1}\right)^2 + \left(\frac{x+1}{x-1}\right)^2 - 2} \, dx

The radicand reduces significantly to

\displaystyle \left(\frac{x-1}{x+1}\right)^2 + \left(\frac{x+1}{x-1}\right)^2 - 2 = \frac{16x^2}{(1-x^2)^2}

so that taking the square root, we simplify the integral to

\displaystyle 8 \int_0^{\frac1{\sqrt2}} \frac x{1-x^2} \, dx

which is trivially computed with a substitution of y = 1 - x^2 and dy=-2x\,dx:

\displaystyle -4 \int_1^{\frac12} \frac{dy}y = 4 \int_{\frac12}^1 \frac{dy}y = -4 \ln\left(\frac12\right) = \ln(2^4) = \boxed{\ln(16)}

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2 years ago
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