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Chapter 8: Q. 8.184 (page 1017)

The force needed to break a board varies inversely with its length. Richard uses 24pounds of pressure to break a 2-foot long board.

a Write the equation of variation.

b How many pounds of pressure is needed to break a 5-foot long board?

Short Answer

Expert verified
  1. The equation of variation is, F=48l.
  2. 9.6pounds of pressure is needed to break a5-foot long board.

Step by step solution

01

Part a Step 1. Given information

The force needed to break a board varies inversely with its length.

Force =24

Length =2

02

Part a Step 2. Let us consider F be the force and l be the length.

The formula for inverse variation is, y=kx.

We will use Fin place of yand lin place of x.

Substitute the given values in the equation.

F=kl24=k2

Solve for the constant of variation.

k=24脳2k=48

03

Part a Step 3. Substitute k=48 in the equation.

F=klF=48l

04

Part b Step 1. Given information

Length,l=5

05

Part b Step 2. From the part a, the obtained equation is, F=48l.

Substitute the known value in the equation.

F=485F=9.6

The required force is, 9.6pounds of pressure.

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