Express the relationship between quantities A, B, and C, given that A varies directly as the square of B and…

Question

Express the relationship between quantities A, B, and C, given that A varies directly as the square of B and inversely as the square of C.

ScanSolve AI Tutor · Accepted Answer

Here's the solution to question 3:

The problem describes the relationship between three quantities A, B, and C.

Express the direct variation.
"A varies directly as the square of B" means that $A$ is proportional to $B^2$ .
$A \propto B^2$
Express the inverse variation.
"and inversely as the square of C" means that $A$ is proportional to $\frac{1}{C^2}$ .
$A \propto \frac{1}{C^2}$
Combine the variations into a single proportionality statement.
$A \propto \frac{B^2}{C^2}$
Introduce the constant of proportionality.
To convert the proportionality into an equation, we introduce a constant $k$ .
$A = k \frac{B^2}{C^2}$

Express the relationship between quantities A, B, and C, given that A varies directly as the square of B and inversely as the square of C.