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1 year ago

7

What values of a and b make this equation true?

1 answer:

Fynjy0 [20]1 year ago

5 0

Answer:

a = -4

b=-29

Step-by-step explanation:

<h3>Complex number:</h3>

First write the radicals in simplest form.

i² = -1

$\sf (4 + \sqrt{-49}) -2\left(\sqrt{(-4)^2}+\sqrt{-324}\right)=4 + \sqrt{49i^2} - 2\left(\\\sqrt{16}+\sqrt{324i^2}\right)$

$\sf =4 + \sqrt{7*7*i*i}-2\left(\sqrt{4*4}+\sqrt{18*18*i*i}\right)\\\\= 4 + 7i - 2(4 + 18i)\\\\= 4 + 7i - 2*4 - 2*18i\\\\= 4 + 7i -8-36i\\\\= 4 - 8 +7i - 36i\\\\= -4 - 29i$

$\sf \boxed{a = -4 }\\\\\boxed{b=-29}$

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

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Step-by-step explanation:

we know that

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Part 1) we have

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The area of the circle is equal to

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so

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For $r=18\ units$

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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

$r^{2}=36$

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Find the volume of the sphere

The volume of the sphere is

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

For $r=6\ units$

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

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

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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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For $r=12\ units$

substitute

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

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

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