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2 years ago

The large sphere has a diameter of 12 feet.

Mathematics

1 answer:

stiks02 [169]2 years ago

6 0

Answer:

C. 288π ft³

Step-by-step explanation:

V(Sphere) = 4/3πr³

V(Sphere) = 4/3π(6)³

V(Sphere) = 4/3π(216)

V(Sphere) = 288π ft³

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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

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

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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 measure of an exterior angle at n measures 99�. m�l � __1 3 x� and m�m � __2 3 x�. find m�l, m�m, and m�lnm.

kirill [66]

You should ask your parent/guardian
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3 years ago

Chang drove 420 miles using 18 gallons of gas. At this rate, how many gallons of gas would he need to drive 357 miles?

qwelly [4]

Answer:

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Step-by-step explanation:

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4 0

3 years ago

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svetoff [14.1K]

Answer:

C, E

Step-by-step explanation:

A. INCORRECT

A is wrong because a reflection across the x-axis DOES move the position of the figure (as it is flipped, so the position changes), but it DOES NOT change the angle (since a shift in position doesn't equal to a change in angle measure)

B. INCORRECT

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C. CORRECT

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D. INCORRECT

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E. CORRECT

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3 years ago

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horrorfan [7]

Answer:

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Step-by-step explanation:

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3 years ago

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