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mixer [17]
2 years ago
8

B. Write the following in exponential notation.then identity the base and the exponent.

Mathematics
1 answer:
Alchen [17]2 years ago
8 0

Answer:

1. 8^5, base is 8 and exponent is 5

2. (-1)^7, the base is -1 and the exponent is 7

3. -2 * a^3, the base is a and the exponent is 3

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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
Somebody please prove if a triangle with side length of 6,8,10 is a right triangle using the Pythagorean theorem!! Will mark Bra
BabaBlast [244]
Answer:
Pythagorean’s theorem states that if a^2 + b^2 = c^2 where c is the hypotenuse and a and b are the side lengths of the right triangle

Given that we can plug in
a= 6 , b = 8 , c = 10

We get an equation:

6^2 + 8^2 = 10^2
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What is the nearest one to 43.568
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3 years ago
Drew invests $70.00. It earns 50% interest annually.
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Step-by-step explanation:

50% interest annually.

that means he gets 50% interest of the invested capital every year.

and that means he gets 50% of $70 in one year.

70 = 100%

1% = 100%/100 = 70/100 = $0.70

50% = 1%×50 = 0.7 × 50 = $35

he will earn $35 interest in one year.

as you noticed: 50% simply means 1/2 (as 100% stands for the whole).

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1 year ago
a scanner scanned 72 photos in 8 minutes if it scans photos at a constant rate it can scan ___ photos in 23 minutes
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If it can scan 72 photos in 8 minutes, it can scan 72/8 = 9 photos per minute.
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