Use the graph of f(x) to solve the inequality.
-The profit made when $t$ units are sold, $t > 0$ , is given by $P = t ^ { 2 } - 34 t + 285$ . Determine the number of units to be sold in order for $\mathrm { P } > 0$ (a profit is made) .

Question

Use the graph of f(x) to solve the inequality. -The profit made when $t$ units are sold, $t > 0$, is given by $P = t ^ { 2 } - 34 t + 285$. Determine the number of units to be sold in order for $\mathrm { P } > 0$ (a profit is made). A) $t = 19$ units or $t = 15$ units B) $t > 19$ units or $t < 15$ units C) $t = 34$ units D) 19 units $< t < 15$ units

Quizplus · Accepted Answer

To solve the inequality $P > 0$, we first find the roots of the quadratic equation $t^2 - 34t + 285 = 0$. Factoring or using the quadratic formula, we find the roots to be $t = 19$ and $t = 15$. Since $P(t)$ is a parabola opening upwards (the coefficient of $t^2$ is positive), $P(t) > 0$ outside the interval between the roots. Therefore, the correct answer is $t > 19$ units or $t < 15$ units.

Use the Graph of F(x) to Solve the Inequality ttt Units Are Sold

Use the Graph of F(x) to Solve the Inequality $t$ Units Are Sold