Respuesta :
Since the distance varies directly as the square of time, then its expression looks like this:
[tex]d\text{ = k}\cdot t^2[/tex]Where d is the distance, "k" is the proportionality constant and t is the time the object is falling. We know that after 6 seconds the stone travels 304 feet. With this information we can determine the value of "k".
[tex]\begin{gathered} 304=k\cdot(6)^2 \\ 304=k\cdot36 \\ k=\frac{304}{36} \\ k=8.44 \end{gathered}[/tex]Therefore the complete expression is:
[tex]d=8.44\cdot t^2[/tex]We want to know the distance after 7 seconds, therefore t = 7.
[tex]\begin{gathered} d=8.44\cdot(7)^2 \\ d=8.44\cdot49=413.56\text{ feet} \end{gathered}[/tex]The stone will travell approximatelly 314 feet in 7 seconds.
