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olya-2409 [2.1K]

3 years ago

11

Three friends buy one pack of 80 stickers. T hey divide the stickers equally and give the remainder to their teacher. How many w

ill each friend get?

1 answer:

Anestetic [448]3 years ago

8 0

Answer:

26

Step-by-step explanation:

80 divided by three = 26.666666

26 times 3 = 78

2 leftover

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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

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Recall the IBP formula,

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

Let

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Then

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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

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

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

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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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2. Solve each equation separately

(a) Equation (1)

$\begin{array}{rcl}x - 3 & < & x - 3\\x & < & x\\\end{array}\\\text{This is impossible. No solutions exist.}$

(b) Equation (2)

$\begin{array}{rcl}x - 3 & < & -(x - 3)\\x - 3 & < & -x + 3\\x &$

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