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3 years ago

Will mark as Brainliest.

Mathematics

1 answer:

Ksivusya [100]3 years ago

4 0

3x^3+4x^2-15x-20

x^2(3x+4)-5(3x-4)

(3x+4)(x^2-5)

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JoAnn works in a publicity office at the state university. She is paid

sleet_krkn [62]

JoAnn works 43 hrs week.

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2 years ago

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$970 at 4 1/4% simple interest for 2 years

iogann1982 [59]

For simple interest
i=prn
where i= interest p=amount invested, r=rate n=time period
i= 970*4 and 1/4 * 2
i= $8245<span />

3 0

3 years ago

What is the antiderivative of 3x/((x-1)^2)

Maslowich

Answer:

$\int \:3\cdot \frac{x}{\left(x-1\right)^2}dx=3\left(\ln \left|x-1\right|-\frac{1}{x-1}\right)+C$

Step-by-step explanation:

Given

$\int \:\:3\cdot \frac{x}{\left(x-1\right)^2}dx$

$\mathrm{Take\:the\:constant\:out}:\quad \int a\cdot f\left(x\right)dx=a\cdot \int f\left(x\right)dx$

$=3\cdot \int \frac{x}{\left(x-1\right)^2}dx$

$\mathrm{Apply\:u-substitution:}\:u=x-1$

$=3\cdot \int \frac{u+1}{u^2}du$

$\mathrm{Expand}\:\frac{u+1}{u^2}:\quad \frac{1}{u}+\frac{1}{u^2}$

$=3\cdot \int \frac{1}{u}+\frac{1}{u^2}du$

$\mathrm{Apply\:the\:Sum\:Rule}:\quad \int f\left(x\right)\pm g\left(x\right)dx=\int f\left(x\right)dx\pm \int g\left(x\right)dx$

$=3\left(\int \frac{1}{u}du+\int \frac{1}{u^2}du\right)$

$\int \frac{1}{u}du=\ln \left|u\right|$ ∵ $\mathrm{Use\:the\:common\:integral}:\quad \int \frac{1}{u}du=\ln \left(\left|u\right|\right)$

$\int \frac{1}{u^2}du=-\frac{1}{u}$ ∵ $\mathrm{Apply\:the\:Power\:Rule}:\quad \int x^adx=\frac{x^{a+1}}{a+1},\:\quad \:a\ne -1$

$=3\left(\ln \left|u\right|-\frac{1}{u}\right)$

$\mathrm{Substitute\:back}\:u=x-1$

$=3\left(\ln \left|x-1\right|-\frac{1}{x-1}\right)$

$\mathrm{Add\:a\:constant\:to\:the\:solution}$

$=3\left(\ln \left|x-1\right|-\frac{1}{x-1}\right)+C$

Therefore,

$\int \:3\cdot \frac{x}{\left(x-1\right)^2}dx=3\left(\ln \left|x-1\right|-\frac{1}{x-1}\right)+C$

4 0

3 years ago

it costs luis $5 to park his car at a parking meter for 2 hours. what is the price to park for 1 hour? write and solve an equati

Sedbober [7]

So I did 5/2 and I got 2.5
5 divided by 2 = 2.5
Not 100% sure if I'm right though

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3 years ago

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10 points for answering!<br> What is the answer to 13, 14, and 15?

ki77a [65]

Step-by-step explanation:

$\implies\sf{ {x}^{2} = 144 } \\ \\ \implies\sf{ x = \pm \sqrt{144} } \\ \\ \implies\sf{ x = \pm 12 }$

$\implies\sf{ {x}^{2} = \dfrac{25}{289} } \\ \\ \implies\sf{ x = \pm \sqrt{ \frac{25}{289} } } \\ \\ \implies\sf{ x = \pm \frac{5}{17} }$

$\implies\sf{ {x}^{3} = 216 } \\ \\ \implies\sf{ x = \sqrt[3]{216} } \\ \\ \implies\sf{ x = 6 }$

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2 years ago