Question

In kickboxing, it is found that the pressure, p, needed to break a board varies inversely with the length of the board.If it takes 5 lbs of pressure to break a board that is 2 feet long, how long is the board that requires 18 lbs of pressureto break?

Answer 1

The pressure, p, needed to break a board varies inversely with the length of the board.

Formula for a inverse variation:

`y=(k)/(x)`

In the given situation the variable p is the dependent variable (y) and the variable l (length) is the independt variable (x).

Use the given data to find the value of the constant k:

`k=y\cdot x`

if it takes 5 lbs of pressure to break a board that is 2 feet long:

`\begin{gathered} k=5\cdot2 \\ k=10 \end{gathered}`

Using the value of k you get the next equation for the given varation:

`p=(10)/(l)`

How long is the board that requires 18 lbs of pressure to break?

Find l when p is 18:

`18=(10)/(l)`

solve l:

`\begin{gathered} 18\cdot l=10 \\ l=(10)/(18) \\ \\ l=0.55 \end{gathered}`Then, the board that requires 18lbs of pressure to break has a length of 0.55 feet