Solve the rational inequality. Write the solution set in interval notation.
-The profit made when t units are sold, t > 0, is given by $\mathrm { P } = \mathrm { t } ^ { 2 } - 33 \mathrm { t } + 270$ Determine the number of units to be sold in order for P < 0 (a loss is taken) .

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 } - 33 \mathrm { t } + 270

Determine the number of units to be sold in order for P < 0 (a loss is taken) .

Quizplus · Accepted Answer

To find the values of $t$ for which $P < 0$, we first need to factor the quadratic equation $P = t^2 - 33t + 270$. Factoring gives us $(t - 15)(t - 18) = 0$, so the roots are $t = 15$ and $t = 18$. For $P < 0$, $t$ must be between these two roots, so the solution is $15 < t < 18$, which corresponds to option D.

Solve the Rational Inequality P=t2−33t+270\mathrm { P } = \mathrm { t } ^ { 2 } - 33 \mathrm { t } + 270P=t2−33t+270

Solve the Rational Inequality $\mathrm { P } = \mathrm { t } ^ { 2 } - 33 \mathrm { t } + 270$