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2 years ago

Find the value of x that makes m || n x=

Mathematics

1 answer:

kogti [31]2 years ago

4 0

180-73
=107
X would equal 107

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What is 8,663,943,526 rounded to the nearest hundred thousand?

Sloan [31]

8,663,900,000
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3 years ago

If S_1=1,S_2=8 and S_n=S_n-1+2S_n-2 whenever n≥2. Show that S_n=3⋅2n−1+2(−1)n for all n≥1.

Snezhnost [94]

You can try to show this by induction:

• According to the given closed form, we have $S_1=3\times2^{1-1}+2(-1)^1=3-2=1$ , which agrees with the initial value S₁ = 1.

• Assume the closed form is correct for all n up to n = k. In particular, we assume

$S_{k-1}=3\times2^{(k-1)-1}+2(-1)^{k-1}=3\times2^{k-2}+2(-1)^{k-1}$

and

$S_k=3\times2^{k-1}+2(-1)^k$

We want to then use this assumption to show the closed form is correct for n = k + 1, or

$S_{k+1}=3\times2^{(k+1)-1}+2(-1)^{k+1}=3\times2^k+2(-1)^{k+1}$

From the given recurrence, we know

$S_{k+1}=S_k+2S_{k-1}$

so that

$S_{k+1}=3\times2^{k-1}+2(-1)^k + 2\left(3\times2^{k-2}+2(-1)^{k-1}\right)$

$S_{k+1}=3\times2^{k-1}+2(-1)^k + 3\times2^{k-1}+4(-1)^{k-1}$

$S_{k+1}=2\times3\times2^{k-1}+(-1)^k\left(2+4(-1)^{-1}\right)$

$S_{k+1}=3\times2^k-2(-1)^k$

$S_{k+1}=3\times2^k+2(-1)(-1)^k$

$\boxed{S_{k+1}=3\times2^k+2(-1)^{k+1}}$

which is what we needed. QED

6 0

2 years ago

What information is needed in order to solve problems using the Pythagorean theorem?

gladu [14]

You would need to know the length of two sides either a2, b2, c2. you would also need to know what sides you are solving for, either one of the legs or hypotenuse. hope this helps, if you know how to solve a Pythagorean theorem problem this should be easy to answer

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3 years ago

Jason collects baseball cards. He bought one card for $25. Its current value is represented by the expression 25(1.02)t, where t

IrinaVladis [17]

This one isn’t really that hard. the answer is 24.

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2 years ago

Perpendicular lines are always, sometimes , never coplanar

daser333 [38]

They are always on a coplanar

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3 years ago

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