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3 years ago

Tell whether each equation represents a direct variation. if so, identify the constant of variation.

Mathematics

1 answer:

Ivenika [448]3 years ago

7 0

Answer:

1. Not a direct variation

2. Direct variation (constant= -4)

3. Direct variation (constant= -1)

Step-by-step explanation:

A direct variation is a function of the type

y = k*x, where k can be any real number

First case

1. y=4x+9

The term 9 interferes with the expression (it creates an offset for the value)

2. 2y=-8x

It is a direct variation, y = -4x

3. x+y=0

It is a direct variation, y = -x

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

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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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