This is a homework question.
The problem. I know the solution, but I don't know where it came from. The videos say nothing. The equation is $d(v) = (2.15v^2)/(64.4f)$ I need to solve for $f$, so I tried plugging in the numbers from the table into the equation and solving. I got approximately $0.018$ by solving, yet apparently the answer is $3.5$. How do I solve problems like this, and what was my mistake?
Let's try plugging in, for example, the values $v = 20$ and $d = 38$ from the table. This gives us $$ d = \frac{2.15 v^2}{64.4 f} \implies 38 = \frac{2.15 \cdot 20^2}{64.4 f}. $$ We now solve for $f$. Multiply both sides by the denominator, then divide both sides by the coefficient to solve for $f$. $$ 38 = \frac{2.15 \cdot 20^2}{64.4 f} \implies (38 \cdot 64.4) f = 2.15 \cdot 20^2 \implies f = \frac{2.15 \cdot 20^2}{38 \cdot 64.4} \approx 0.35. $$ If we forget the exponent attached to $v$, then we instead end up with $$ f = \frac{2.15 \cdot 20}{38 \cdot 64.4} \approx 0.018. $$ I suspect that this is the source of your error.
