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2 years ago

8

Harish's soccer team is trying to raise $5,092 to travel to a tournament in Florida, so they decided to host a pancake breakfast

. Each person must pay $38 for the breakfast. How many people need to attend their breakfast in order to raise $5,092?

1 answer:

Gre4nikov [31]2 years ago

7 0

Answer: 134 people

Step-by-step explanation:

Data: The soccer team needs to raise <u>$5,092</u>

They are hosting a pancake breakfast to do so and are charging <u>$38</u> to do so

The number of people they need to attend their breakfast for the money to be raised: $x

Step one, make the equation

$38x=$5,092

Reason: Since we know that the number of people(x) times $38 will equal $5,092 so to put it into an equation will make it easier to solve.

Step two, Isolate x by dividing by 38 on both sides

$38x/38=$5,092/38=x=134

Reason: Since you are trying to find the number of people(x) you have to isolate it. the way to do that is by getting rid of the 38 next to it and by dividing, you cancel out the multplication and get rid of the 38. However, since what you do to one side you do to the other, you divide 5,092 by 38 to get the answer of 134.

Answer: 134 people

I hope this helps!

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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

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

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

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

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

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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, $h = D = 2r$

$h = 2r$

Substitute 2r for h in equation 1

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

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

$V = 14$

Hence, the volume of the sphere is 14m³

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3 years ago

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