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3 years ago

given: m<1=m<2,m<2=m<3. prove:m<1=m<3. write a two column proof ...geometic proof

Mathematics

1 answer:

Rufina [12.5K]3 years ago

4 0

M<1 = m<2, m<2 = m<3 reason: given
m<1 = m<3 reason: transitive property of equality

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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

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

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

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

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

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1 year ago

Use distributing property : (-11) x (-15) + (-11) x (-25) plzz answer fast

Semmy [17]

The answer is 440.
What I do is just take the -11 and -15 out of the parentheses so it is -11*-15 and the answer is 165. Then, you take -11 and -25 out of the parentheses and find the answer.
Add them together.
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2 years ago

What polynomial has a graph that passes through the given points?

Evgen [1.6K]

The answer is B. y = x^3 + 4x^2 + 2x - 2

A line that passes through all given point is the correct choice. Now, substitute x and y in all of the choices:

B. y = x³ + 4x² + 2x - 2
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x = -2
y = 2
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2 = (-2)³ + 4 *(-2)² + 2 * (-2) - 2
2 = -8 + 4 * 4 + (-4) - 2
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Point 2: (-1, -1)
x = -1
y = -1
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-1 = -1 + 4 * 1 + (-2) - 2
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So, line B passes through all choices.

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