Solve the rational inequality. Write the solution set in interval notation.
-The profit made when t units are sold, t > 0, is given by $\mathrm { P } = \mathrm { t } ^ { 2 } - 30 \mathrm { t } + 216$ Determine the number of units to be sold in order for P > 0 (a profit is made) .

Question

Solve the rational inequality. Write the solution set in interval notation.
-The profit made when t units are sold, t > 0, is given by

\mathrm { P } = \mathrm { t } ^ { 2 } - 30 \mathrm { t } + 216

Determine the number of units to be sold in order for P > 0 (a profit is made) .

Quizplus · Accepted Answer

To solve the inequality $P = t^2 - 30t + 216 > 0$, we first find the roots of the quadratic equation $t^2 - 30t + 216 = 0$. Factoring the quadratic, we get $(t-18)(t-12) = 0$, which gives us the roots $t = 18$ and $t = 12$. The inequality $P > 0$ is satisfied when $t$ is outside the interval [12, 18], meaning $t > 18$ or $t < 12$.

Solve the Rational Inequality P=t2−30t+216\mathrm { P } = \mathrm { t } ^ { 2 } - 30 \mathrm { t } + 216P=t2−30t+216

Solve the Rational Inequality $\mathrm { P } = \mathrm { t } ^ { 2 } - 30 \mathrm { t } + 216$