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3 years ago

How to simplify expressions

Mathematics

1 answer:

Vadim26 [7]3 years ago

7 0

Answer:

on https://www.storyofmathematics.com it says

To simplify any algebraic expression, the following are the basic rules and steps:

Remove any grouping symbol such as brackets and parentheses by multiplying factors.

Use the exponent rule to remove grouping if the terms are containing exponents.

Combine the like terms by addition or subtraction.

Combine the constants.

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What is the exact value of tan -13pi/6 and also the explanation

mihalych1998 [28]

$tan\left(-\frac{13\pi}{6}\right)=-tan\left(2\frac{1}{6}\pi\right)=-tan\left(2\pi+\frac{1}{6}\piright)=-tan\frac{1}{6}\pi=-\frac{\sqrt3}{3}$

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3 years ago

Read 2 more answers

A sphere is inscribed in a cube with a surface area of 216 square centimeters. What is the volume of the sphere

pentagon [3]

Answer:

$V=298.5cm^3$

Step-by-step explanation:

To find the volume of the sphere we need to know its radius.

And the radius can be found with the information we have about the surface area.

The formula for the surface area is as follows:

$SA=4\pi r^2$

from this formula we clear the radius r:

$r^2=\frac{SA}{4\pi}\\ \\r=\sqrt{\frac{SA}{4\pi} }$

and we substitute the known value of the surface area, and also the value of $\pi$ :

$r=\sqrt{\frac{216cm^2}{4(3.1416)} }\\ \\r=\sqrt{\frac{216cm^2}{12.5664} }\\ \\r=\sqrt{17.1887cm^2}\\ \\r=4.146cm$

and now that we know the radius we find the volume:

$V=\frac{4\pi r^3}{3} \\\\V=\frac{4(3.1416)(4.146cm)^3}{3}\\ \\V=\frac{895.521cm^3}{3}\\ \\V=298.5cm^3$

the volume of the sphere is $298.5cm^3$

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