Question 1097414
When a variable (like braking distance, d, in feet)
varies directly with some other variable (like the square of the speed, with r=speed measured in mph),
as one variable changes by a factor, so does the other.
As the speed doubles, from 50 mph to 110 mph,
the square of the speed quadruples.
It changes from {{{50^2=2500}}} to {{{100^2=10000}}} ,
but we do not need to calculate to know
that when one number doubles its square quadruples.
The square of the speed quadrupled,
and so does the breaking distance,
from {{{110ft}}} to {{{4*(110ft)=highlight(440ft)}}} .
Easy mental math.
 
If you were asked to write it as a function,
you would define {{{k}}} as a positive constant,
say that
{{{d=k*r^2}}} ,
and substituting {{{110}}} for the distance and {{{50}}} for the speed,
you would find {{{k}}} :
{{{110=k*50^2}}} --> {{{110=k*2500}}} --> {{{110/2500=k}}} --> {{{k=0.044}}} .
Then, the function,would be
{{{d=0.044*r^2}}} .
Then, you could use that function,
substituting {{{100}}} for {{{r}}} ,
to calculate the answer as
{{{d=0.044*100^2=0.044*10000=440}}} .
That would require a lot more writing and calculating.