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The force, F, needed to break a board varies inversely with the length, L, of the board. If it takes 24 pounds of pressure to break a board that is 2 feet long, how many pounds of pressure would it take to break a board that is 5 feet long?

Respuesta :

calculista

Answer:

9.6 pounds of pressure

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form [tex]y*x=k[/tex] or [tex]y=k/x[/tex]

so

In this problem

[tex]F*L=k[/tex]

step 1

Find the value of k

For [tex]F=24\ lb, L=2\ ft[/tex]

substitute

[tex]k=(24)(2)=48[/tex]

The equation is equal to

[tex]F*L=48[/tex]

step 2

For [tex]L=5\ ft[/tex]

Find the value of F

substitute the value of L in the equation

[tex]F*(5)=48[/tex]

[tex]F=48/5=9.6\ lb[/tex]

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