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3 years ago

Choose all the numbers that could be common denominators for 2/3 and 3/4. 8, 12, 16, 36, 48

Mathematics

1 answer:

Ksivusya [100]3 years ago

7 0

Answer: 12 36 and 48

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Just 7 and 8 please!!

77julia77 [94]

Just multiply it so multiply 59.89 x 4 and then for number 8 multiply 88.70 x 4

4 0

4 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

3 years ago

You randomly choose one butterfly from a group. There are 3 blue, 2 red, 1 green, and 1 yellow butterflies.

valentinak56 [21]

Answer:

2 ways or 2/7

Step-by-step explanation:

There are 2 red butterflies in a group and there are 7 butterflies total.

7 0

3 years ago

What is 2x+4+3x=14 ?

fenix001 [56]

Answer is provided in the image attached.

8 0

3 years ago

Read 2 more answers

The volume of a cylinder is 64 cubic feet, and the height of the cylinder is 8 feet. What is the radius of the cylinder?

antoniya [11.8K]

Answer:

V = pi R^2 * h volume of cylinder (area of base * height)

pi R^2 = 64 / 8 = 8

R^2 = 8 / pi = 2.865

R = 1.69 ft

5 0

3 years ago