Solve the rational inequality. Write the solution set in interval notation.
-A coin is tossed upward from a balcony $320 \mathrm { ft }$ high with an initial velocity of $32 \mathrm { ft } / \mathrm { sec }$. During what interval of time will the coin be at a height of at least $80 \mathrm { ft }$ ? $\left( h = - 16 t ^ { 2 } + v _ { 0 } t + h _ { 0 } \right.$. $)$
A) $0 \leq t \leq 1$
B) $4 \leq t \leq 5$
C) $5 \leq t \leq 10$
D) $0 \leq t \leq 5$

Question

Quizplus · Accepted Answer

To find the interval of time during which the coin will be at a height of at least $80 \mathrm { ft }$, we use the given equation for the height of the coin $h = - 16 t ^ { 2 } + 32 t + 320$, and set it greater than or equal to $80$: $-16t^2 + 32t + 320 \geq 80$. Simplifying this inequality gives us a quadratic equation whose solutions can be found using the quadratic formula or factoring, leading to the determination that the coin is at least $80 \mathrm { ft }$ high between $t = 0$ and $t = 5$ seconds.

Solve the Rational Inequality 320ft320 \mathrm { ft }320ft High with an Initial Velocity Of

Solve the Rational Inequality $320 \mathrm { ft }$ High with an Initial Velocity Of