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Umnica [9.8K]
3 years ago
5

-4/5(-8x+6)=1+7 Please Help

Mathematics
1 answer:
bagirrra123 [75]3 years ago
8 0

Answer:

x = 2

Step-by-step explanation:

-4/5(-8x + 6) = 1 + 7 (distribute first)

6.4x -4.8 = 8 (add 4.8 on both sides)

6.4x = 12.8 (divide by 6.4)

x = 2

PLUG IN

-4/5(-8(2) + 6) = 1 + 7

-4/5(-16 + 6) = 8

-4/5(-10) = 8

8 = 8

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Evaluate using integration by parts ​
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I(n)=\displaystyle\int x^ne^x\,\mathrm dx

One round of IBP, setting

u=x^n\implies\mathrm du=nx^{n-1}\,\mathrm dx

\mathrm dv=e^x\,\mathrm dx\implies v=e^x

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\displaystyle I(n)=x^ne^x-n\int x^{n-1}e^x\,\mathrm dx

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This is called a power-reduction formula. We could try solving for I(n) explicitly, but no need. n=5 is small enough to just expand I(5) as much as we need to.

I(5)=x^5e^x-5I(4)

I(5)=x^5e^x-5(x^4e^x-4I(3))=(x-5)x^4e^x+20I(3)

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I(5)=(x^2-5x+20)x^3e^x-60(x^2e^x-2I(1))=(x^3-5x^2+20x-60)x^2e^x+120I(1)

I(5)=(x^3-5x^2+20x-60)x^2e^x+120(xe^x-I(0))

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