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3 years ago

Please help, I've never gotten these and I still dont. this test is 95% of my grade

Mathematics

1 answer:

sweet-ann [11.9K]3 years ago

4 0

Answer:

-10

-4

-13

Step-by-step explanation:

this is how to do it.

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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

3 years ago

How many feet long is the fence ?

grandymaker [24]

Answer:

50 feet long

Step-by-step explanation:

Use the Pythagorean theorem to find the value of the missing side. The pythagoreon theorem only works with right triangles such as this one.

a²+b²=c²

Where a and b are length of legs (sides) of a triangle. And c is the length of the hypotenuse. The hypotenuse is the side across from the right angle.

We know by looking at the image posted in the question, that one leg of the triangle is 14 feet. And another leg is 48 feet. (Length of picnic area) (length of campground)

14²+48²=c²

Simplify

196+2304=2500

Find square root of 2500

√(2500)=50

So 14²+48²=50²

The missing side is 50 feet long. The fence is 50 feet long.

Attached is another example.

7 0

3 years ago

(-3) (4-5) I need help

-Dominant- [34]

Answer:

Step-by-step explanation:

I searched it up on the web

6 0

3 years ago

Read 2 more answers

Parcc chapter 7 pythagorean theorem

Bumek [7]

So, we know that a^2 + b^2 = c^2. Right? That is called the Pythagorean Theorem.

In this case. We can say that 39 is a, 40 is b, and x is c.
NOTE: It doesn't really matter whether 39 is a or b. a & b are just the two legs of the right triangle.

So, if we say that 39 is a, 40 is b, and x is c. We can plug it into the Pythagorean Theorem.

39^2 + 40^2 = x^2

I'll let you take it from there.

7 0

3 years ago

(2x^3+10x^2)/(x^2+x-20) divided by (2x^2)/(x-4)

Nutka1998 [239]

Answer:

Step-by-step explanation:

Who knew the answer would be 1 LOL

hope this helps :)

8 0

3 years ago

Please help, I've never gotten these and I still dont. this test is 95% of my grade​

Please help, I've never gotten these and I still dont. this test is 95% of my grade