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2 years ago

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Kristoff rents a kiosk in the mall to open an umbrella stand. He pays $3 to the mall owner for each umbrella he sells. The amoun

t Kristoff pays is given by f(x) = 3x, where x is the number of umbrellas sold. Graph the function and give its domain and range.

1 answer:

jeka57 [31]2 years ago

3 0

Answer:

Coolman2131231 avatar

Coolman2131231

23 seconds ago

Mathematics

College

Kristoff rents a kiosk in the mall to open an umbrella stand. He pays $3 to the mall owner for each umbrella he sells. The amount Kristoff pays is given by f(x) = 3x, where x is the number of umbrellas sold. Graph the function and give its domain and range.

Step-by-step explanation:

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A sphere and a cylinder have the same radius and height. The volume of the cylinder is 21m. what is the volume of the sphere.

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Answer:

The volume of the sphere is 14m³

Step-by-step explanation:

Given

Volume of the cylinder = $21m^3$

Required

Volume of the sphere

Given that the volume of the cylinder is 21, the first step is to solve for the radius of the cylinder;

<em>Using the volume formula of a cylinder</em>

The formula goes thus

$V = \pi r^2h$

Substitute 21 for V; this gives

$21 = \pi r^2h$

Divide both sides by h

$\frac{21}{h} = \frac{\pi r^2h}{h}$

$\frac{21}{h} = \pi r^2$

The next step is to solve for the volume of the sphere using the following formula;

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

Divide both sides by r

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

Expand Expression

$\frac{V}{r} = \frac{4}{3}\pi r^2$

Substitute $\frac{21}{h} = \pi r^2$

$\frac{V}{r} = \frac{4}{3} * \frac{21}{h}$

$\frac{V}{r} = \frac{84}{3h}$

$\frac{V}{r} = \frac{28}{h}$

Multiply both sided by r

$r * \frac{V}{r} = \frac{28}{h} * r$

$V = \frac{28r}{h}$ ------ equation 1

From the question, we were given that the height of the cylinder and the sphere have equal value;

This implies that the height of the cylinder equals the diameter of the sphere. In other words

$h = D$ , where D represents diameter of the sphere

Recall that $D = 2r$

So, $h = D = 2r$

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Substitute 2r for h in equation 1

$V = \frac{28r}{2r}$

$V = \frac{28}{2}$

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3 years ago

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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