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3 years ago

The volume of a cube is 1 cubic meter. What is the length of of each side of the cube

1 answer:

4 0

1 Metre is the length of each side of the cube.

To example, here is the Volume Of Cube Equation:

V = a^3

We are given the value for V, so just take the cube root of 1, which equates to 1.

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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 What is the value of x?

KonstantinChe [14]

Side JL is 4√2 recall that in a 30-60-90 right triangle the hypotenuse is 2 times the size of the short leg.

JL also serves as the hypotenuse of the 45-45-90 triangle JML. The ratio of side lengths in this triangle is 1:1:√2

So we can see that the value of x = 4

7 0

3 years ago

what is the width of a rectangular prism when the surface area is 904 square feet, and it has a height of 10 feet and a length o

k0ka [10]

Answer:

The answer

Step-by-step explanation:

the width of a rectangular prism which has a height of 10 feet and a length of 14 feet should be 140 square feet

7 0

3 years ago

PLEASE HELP WILL MARK BRAINLIEST!

pantera1 [17]

Answer:

Make a coordinate plane and you have to solve around the origin say 4,4 and 4,1.

Step-by-step explanation:

8 0

3 years ago

What were some of the challenges pilgrims faced on their journey

EleoNora [17]

On the ocean Pilgrims encounter fierce storms, disease, and their ship falls into disrepair. During the first winter they lack shelter, warmth, and food.

The Pilgrims struggled to build homes, and many families crowded into the few homes that were built. Food was scarce, and many Pilgrims starved to death that first winter.

Hope this helped

3 0

3 years ago