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3 years ago

If two lines are skew lines, then they are noncoplanar. True or false

Mathematics

1 answer:

Anika [276]3 years ago

7 0

Answer:

Two lines that both lie in the same plane must either cross each other or be parallel, so skew lines can exist only in three or more dimensions. Two lines are skew if and only if they are not coplanar.

Step-by-step explanation:

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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

Please help Me with this

ratelena [41]

I belive that it would be 40% or .4

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3 years ago

Yul has lunch at a restaurant. The bill is $14.50 and the sales tax amount is 5%. If he wants to leave a 20% tip after the sales

jek_recluse [69]

Answer:

The tip will be $3.05.

The bill will cost $18.28 with the tip and tax.

Step-by-step explanation:

14.50 + 5% (or 0.73) = 15.23

15.23 + 20% (or 3.05) = 18.28

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2 years ago

What is the absolute value equation that has the solution x= -10 and x= -5

Anna11 [10]

the answer is
-10 times- 5

3 0

3 years ago

drek231 [11]

Answer:

sub to graec franz

Step-by-step explanation:

6.72 4893,.43

7 0

2 years ago