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yarga [219]
3 years ago
10

Simplify (10–2) 4. A) 10^-8 B)10^-6 C)-10^-6 D)-10^8

Mathematics
2 answers:
Hatshy [7]3 years ago
8 0

Answer:

A

Step-by-step explanation:

(10^{-2})^{4}

Apply the law of exponents.

10^{-2 \times 4}

=10^{-8}

ololo11 [35]3 years ago
5 0

Answer:

= {10}^{ - 8}  \\

Answer A is correct.

Step-by-step explanation:

{( {10}^{ - 2}) }^{4}  \\  {10}^{ - 2 \times 4}  \\   = {10}^{ - 8}

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Why is the answer to this integral's denominator have 1+pi^2
ss7ja [257]

It comes from integrating by parts twice. Let

I = \displaystyle \int e^n \sin(\pi n) \, dn

Recall the IBP formula,

\displaystyle \int u \, dv = uv - \int v \, du

Let

u = \sin(\pi n) \implies du = \pi \cos(\pi n) \, dn

dv = e^n \, dn \implies v = e^n

Then

\displaystyle I = e^n \sin(\pi n) - \pi \int e^n \cos(\pi n) \, dn

Apply IBP once more, with

u = \cos(\pi n) \implies du = -\pi \sin(\pi n) \, dn

dv = e^n \, dn \implies v = e^n

Notice that the ∫ v du term contains the original integral, so that

\displaystyle I = e^n \sin(\pi n) - \pi \left(e^n \cos(\pi n) + \pi \int e^n \sin(\pi n) \, dn\right)

\displaystyle I = \left(\sin(\pi n) - \pi \cos(\pi n)\right) e^n - \pi^2 I

\displaystyle (1 + \pi^2) I = \left(\sin(\pi n) - \pi \cos(\pi n)\right) e^n

\implies \displaystyle I = \frac{\left(\sin(\pi n) - \pi \cos(\pi n)\right) e^n}{1+\pi^2} + C

6 0
2 years ago
The portions of a house that need to be heated can be modeled by one rectangular prism with a length of 45 feet, a width of 20 f
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Answer:

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Step-by-step explanation:

= (45)(20)(10) + (350)(9)

= 9000 + 3150

= 12150 ft^3

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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