Question 158168
Since the "distance, d, a string is stretched varies directly with the force, F", this means that we have the equation {{{d=kF}}}



{{{d=kF}}} Start with the given equation



{{{3=k(12)}}} Plug in {{{d=3}}} and {{{F=12}}}



{{{3/12=k}}} Divide both sides by 12 to isolate k



{{{1/4=k}}} Reduce



So the variation constant is {{{k=1/4}}} (or in decimal form {{{k=0.25}}})



{{{d=kF}}} Go back to the original equation



{{{d=(1/4)F}}} Plug in {{{k=1/4}}}



{{{d=(1/4)(30)}}} Since we want the distance when the "force of 30 pounds is applied", we need to plug in {{{F=30}}}



{{{d=30/4}}} Multiply



{{{d=15/2}}} Reduce



{{{d=7.5}}} Convert to decimal form



So the distance is 7.5 inches when a force of 30 pounds is applied.