This lesson draws on and extends the concepts from the preceding lesson, Direct and Inverse Variation.
$\displaystyle A = k\cdot \frac{t^2}{x^3}$ |
Write the equation that describes the relationship between the variables, using the information from Direct and Inverse Variation. Don't forget the constant of proportionality! |
$\displaystyle 3 = k\cdot\frac{1^2}{2^3}\,$, $\displaystyle 3 = \frac{k}{8}$ |
substitute the known values of $\,A\,$, $\,t\,$ and $\,x\,$; simplify |
$k = 24$ | solve for the constant of proportionality, $\,k\,$ |
$\displaystyle A = 24\cdot\frac{t^2}{x^3}\,$, $\displaystyle A= \frac{24t^2}{x^3}$ | the final equation can be written in slightly different ways |
$\displaystyle A = \frac{24\cdot (-1)^2}{4^3} = \frac{24}{64} = \frac{3}{8}$ |
now, whenever any two of the three variables are known, the remaining variable can be determined |