Express the relationship between S, t, and r in an equation, given that S varies directly as the square of t…

Question

Express the relationship between S, t, and r in an equation, given that S varies directly as the square of t and inversely as the cube root of r.

ScanSolve AI Tutor · Accepted Answer

The problem describes a relationship of variation between variables $S$ , $t$ , and $r$ .

Identify the direct and inverse variations.
"S varies directly as the square of t" means $S \propto t^2$ .
"S varies inversely as the cube root of r" means $S \propto \frac{1}{\sqrt[3]{r}}$ .
Combine these variations into a single equation using a constant of proportionality, $k$ .
Combining the direct and inverse variations, we get:
$S = k \frac{t^2}{\sqrt[3]{r}}$
where $k$ is the constant of proportionality.

Express the relationship between S, t, and r in an equation, given that S varies directly as the square of t and inversely as the cube root of r.