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The force, F, needed to break a board in a martial arts class varies inversely with the length, L, of the board. If it takes 24 pounds of pressure to break a board 2.5 feet long, how many pounds of pressure would it take to break a board that is 18 inches long?

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Answer:

it would take 40 pounds of pressure to break the board.

Step-by-step explanation:

[tex]F = \frac{x}{L}[/tex]

Now we plug in the numbers of force and length

[tex]24 =\frac{k}{2.5}[/tex]

Now we multiply both sides by 2.5 to get rid of the fraction.

[tex]60=x[/tex]

Now we plug in our variation constant

[tex]F=\frac{60}{L}[/tex]

So we convert the length of 2.5 feet into inches. This is 18 inches. Since there are 12 inches in one foot, we have that 18 inches is equal to 18 divided by 12.

18÷12=1.5

We get that 18 inches is equal to 1.5 feet

we plug L = 1.5 into our inverse variation equation and solve for F.

[tex]F=\frac{60}{1.5}[/tex]

This simplifies to F = 40

If you have any questions feel free to ask in the comments - Mark

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