Solve the rational inequality. Write the solution set in interval notation.
-If a rocket is propelled upward from ground level, its height in meters after t seconds is given by $\mathrm { h } = - 9.8 \mathrm { t } ^ { 2 } + 78.4 \mathrm { t }$ . During what interval of time will the rocket be higher than 147 m?
A) 3

Question

Solve the rational inequality. Write the solution set in interval notation.
-If a rocket is propelled upward from ground level, its height in meters after t seconds is given by $\mathrm { h } = - 9.8 \mathrm { t } ^ { 2 } + 78.4 \mathrm { t }$ . During what interval of time will the rocket be higher than 147 m?
A) 3 < t < 5
B) 6 < t < 8
C) 0 < t < 3
D) 5 < t < 6

Quizplus · Accepted Answer

To find when the rocket is higher than 147 m, we set the height equation greater than 147 and solve for t: $-9.8t^2 + 78.4t > 147$. Rearranging gives $-9.8t^2 + 78.4t - 147 > 0$. Factoring or using the quadratic formula, we find the roots of the equation, which represent the times when the rocket is exactly 147 m high. Solving this inequality shows that the rocket is higher than 147 m between 3 and 5 seconds.

Solve the Rational Inequality h=−9.8t2+78.4t\mathrm { h } = - 9.8 \mathrm { t } ^ { 2 } + 78.4 \mathrm { t }h=−9.8t2+78.4t

Solve the Rational Inequality $\mathrm { h } = - 9.8 \mathrm { t } ^ { 2 } + 78.4 \mathrm { t }$