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3 years ago

Which long division problem can be used to prove the formula for factoring the difference of two perfect cubes?

Mathematics

1 answer:

worty [1.4K]3 years ago

4 0

Answer:

a-b divided into $a^{3} + 0a^{2} b + 0 ab^{2} - b^{3}$

the reason is that the (a-b) vs (a+b) in the "SOAP"

same, opposite, always a plus the "-" in the "a-b" has to match the

sign between the two cubes

Step-by-step explanation:

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Solve the system below by substitution. write the solution as a coordinate pair.

bonufazy [111]

Answer:

x = 4 y = 7

Step-by-step explanation:

x + 3 = -1/2x + 9

x = -1/2x + 6

3/2x = 6

x = 4

y = (4) + 3

y = 7

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3 years ago

I have no idea what to do. (It’s #15 part A btw) please help me!

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3 years ago

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mote1985 [20]

The answer is
5r3s2t−4r2s2t2+2rs2t3

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4 years ago

The set of all numbers that can be written as a fraction. The decimals will either terminate or repeat.

jeka94

It’s C I just took the test!!!!!

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4 years ago

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The volume of a sphere is decreasing at a constant rate of 9988 cubic centimeters per minute. At the instant when the volume of

Inessa05 [86]

Using implicit differentiation, it is found that the rate of change of the surface area of the sphere -2201.293 square centimeters per second.

<h3>What is the volume of a sphere?</h3>

The volume of a sphere, of radius r, is given by:

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

<h3>What is the surface area of a sphere?</h3>

The surface area of a sphere, of radius r, is given by:

$S = 4\pi r^2$

<h3>What is the rate of change?</h3>

Applying implicit differentiation, the rate of change of both the volume and the surface area can be found, as follows:

$\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt}$

$\frac{dS}{dt} = 8\pi r\frac{dr}{dt}$

Volume of 3131 cubic centimeters, hence:

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

$\frac{4\pi r^3}{3} = 3131$

$4\pi r^3 = 3(3131)$

$r = \sqrt[3]{\frac{3(3131)}{4\pi}}$

$r = 9.0754$

The volume of a sphere is decreasing at a constant rate of 9988 cubic centimeters per minute, hence:

$\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt}$

$-9988 = 4\pi (9.0754)^2\frac{dr}{dt}$

$\frac{dr}{dt} = -\frac{9988}{4\pi (9.0754)^2}$

$\frac{dr}{dt} = -9.651$

Then, the rate of change of the surface area of the sphere is given by:

$\frac{dS}{dt} = 8\pi (9.0754)(-9.651) = -2201.293$

The rate of change of the surface area of the sphere -2201.293 square centimeters per second.

To learn more about implicit differentiation, you can take a look at brainly.com/question/25608353

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3 years ago