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otez555 [7]
3 years ago
12

What the height of a cube if the volume is 729centimeters to the third power

Mathematics
1 answer:
LenKa [72]3 years ago
3 0

Answer:

387420489

Step-by-step explanation:

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Which of the following geometric series converges?
Artist 52 [7]

All three series converge, so the answer is D.

The common ratios for each sequence are (I) -1/9, (II) -1/10, and (III) -1/3.

Consider a geometric sequence with the first term <em>a</em> and common ratio |<em>r</em>| < 1. Then the <em>n</em>-th partial sum (the sum of the first <em>n</em> terms) of the sequence is

S_n=a+ar+ar^2+\cdots+ar^{n-2}+ar^{n-1}

Multiply both sides by <em>r</em> :

rS_n=ar+ar^2+ar^3+\cdots+ar^{n-1}+ar^n

Subtract the latter sum from the first, which eliminates all but the first and last terms:

S_n-rS_n=a-ar^n

Solve for S_n:

(1-r)S_n=a(1-r^n)\implies S_n=\dfrac a{1-r}-\dfrac{ar^n}{1-r}

Then as gets arbitrarily large, the term r^n will converge to 0, leaving us with

S=\displaystyle\lim_{n\to\infty}S_n=\frac a{1-r}

So the given series converge to

(I) -243/(1 + 1/9) = -2187/10

(II) -1.1/(1 + 1/10) = -1

(III) 27/(1 + 1/3) = 18

8 0
3 years ago
The pair of values below is from a direct variation. Find the missing number.
NISA [10]

Answer:

The answer is 2.

2  since 6/4=3/2

Step-by-step explanation:

Since your relation is a direct variation then the points on your line are of the form y=kx where k is the constant of variation (also called constant of proportionality)

If y=kx then y/x=k.

So all the points in this relation since it is a direct variation will be equal to y-coordinate/x-coordinate.

So we are going to solve this proportion:

\frac{6}{4}=\farc{3}{x}

Again I put y/x from each point. They should have same ratio because this is a direct variation.

Cross multiply:

6(x)=4(3)

6x=12

Divide boht sides by 6:

x=\frac{12}{6}

x=2

6 0
3 years ago
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What is f(2) = 2x -6
Dennis_Churaev [7]

Answer:

f(2) = -2

Step-by-step explanation:

f(2) = 2x - 6

f(2) = 2(2) - 6

f(2) = 4 - 6

f(2) = -2

4 0
3 years ago
Tanvi is a kickboxing instructor who will be teaching classes at a local gym. To get certified as an instructor, she spent a tot
DENIUS [597]

Answer:

I think the answer is 4. if my math is correct

5 0
3 years ago
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What is the slope of the line that passes through the points (3, -2) and (9, -2)?
ICE Princess25 [194]

m=(-2+2)/(9-6)=0/3=0

m=0

7 0
3 years ago
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