Question

What is the length of a rope if the mass of a rope is 4.25

Answer 1

Using a regression calculator, the line of best fit for the given set of data is:

`y=0.34121x+0.168088`

where y = mass of the rope and x = length of the rope.

To estimate the length of the rope if its mass is 4.25 kilograms, let's replace "y" in the equation above with 4.25, and then solve for x.

`4.25=0.34121x+0.168088`

Subtract 0.168088 on both sides of the equation.

`4.25-0.168088=0.34121x+0.168088-0.168088`
`4.081912=0.34121x`

Then, divide both sides of the equation by 0.34121.

`(4.081912)/(0.34121)=(0.34121x)/(0.34121)`
`\begin{gathered} 11.963049=x \\ 11.96\approx x \end{gathered}`

Therefore, the length of the rope having a mass of 4.25 kilograms is approximately 11.96 meters.