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3 years ago

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Each number in a list of numbers can be found using the expression 6 − 23(n − 1), where n is a positive integer that gives the p

osition of the number in the list. What is the thirteenth number in the list?
A. −8
B. −2
C. 8
D. 13

1 answer:

sleet_krkn [62]3 years ago

7 0

Answer:

Step-by-step explanation:

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What is the area of this figure?

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Answer:

To solve, you must split the figure into 2 parts --> a rectangle and a trapezoid. The separating 'line' will be where the figure indents and starts to jut out. That separating 'line' will be 9 cm long.

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A = $\frac{a + b}{2}h$

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Match each spherical volume to the largest cross sectional area of that sphere

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Answer:

Part 1) $324\pi\ units^{2}$ ------> $7,776\pi\ units^{3}$

Part 2) $36\pi\ units^{2}$ ------> $288\pi\ units^{3}$

Part 3) $81\pi\ units^{2}$ ------> $972\pi\ units^{3}$

Part 4) $144\pi\ units^{2}$ ------> $2,304\pi\ units^{3}$

Step-by-step explanation:

we know that

The largest cross sectional area of that sphere is equal to the area of a circle with the same radius of the sphere

Part 1) we have

$A=324\pi\ units^{2}$

The area of the circle is equal to

$A=\pi r^{2}$

so

$324\pi=\pi r^{2}$

Solve for r

$r^{2}=324$

$r=18\ units$

Find the volume of the sphere

The volume of the sphere is

$V=\frac{4}{3}\pi r^{3}$

For $r=18\ units$

substitute

$V=\frac{4}{3}\pi (18)^{3}$

$V=7,776\pi\ units^{3}$

Part 2) we have

$A=36\pi\ units^{2}$

The area of the circle is equal to

$A=\pi r^{2}$

so

$36\pi=\pi r^{2}$

Solve for r

$r^{2}=36$

$r=6\ units$

Find the volume of the sphere

The volume of the sphere is

$V=\frac{4}{3}\pi r^{3}$

For $r=6\ units$

substitute

$V=\frac{4}{3}\pi (6)^{3}$

$V=288\pi\ units^{3}$

Part 3) we have

$A=81\pi\ units^{2}$

The area of the circle is equal to

$A=\pi r^{2}$

so

$81\pi=\pi r^{2}$

Solve for r

$r^{2}=81$

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Find the volume of the sphere

The volume of the sphere is

$V=\frac{4}{3}\pi r^{3}$

For $r=9\ units$

substitute

$V=\frac{4}{3}\pi (9)^{3}$

$V=972\pi\ units^{3}$

Part 4) we have

$A=144\pi\ units^{2}$

The area of the circle is equal to

$A=\pi r^{2}$

so

$144\pi=\pi r^{2}$

Solve for r

$r^{2}=144$

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The volume of the sphere is

$V=\frac{4}{3}\pi r^{3}$

For $r=12\ units$

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$V=\frac{4}{3}\pi (12)^{3}$

$V=2,304\pi\ units^{3}$

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Answer:

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Step-by-step explanation:

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