Given compound inequality 89 – 9.8t < 10.6 or 89 – 9.8t > 20.4.
Let us solve them one by one.
89 – 9.8t < 10.6
Subtracting 89 from both sides, we get
89-89 – 9.8t < 10.6 - 89
-9.8t < -78.4
Dividing both sides by -9.8, we get
t > 8.
<em>Note: Inequality sign get flip on dividing both side by a negative number.</em>
89 – 9.8t > 20.4
Subtracting 89 from both sides, we get
89-89 – 9.8t < 20.4 - 89
-9.8 t < - 68.6.
Dividing both sides by -9.8, we get
t < 7
<em>Note: Inequality sign get flip on dividing both side by a negative number.</em>
<h3><em> The solution to the inequality 89 – 9.8t < 10.6 is </em>t > 8. </h3><h3> The solution to the inequality 89 – 9.8t > 20.4 is t < 7.</h3>
When the projectile hits the ground:
89 – 9.8t = 0
Subtracting 89 from both sides, we get
89 - 89 – 9.8t = 0 -89.
-9.8t = -89.
Dividing both sides by 9.8, we get
<h3>to the nearest whole second t is about 9 seconds.</h3><h3>Therefore, variable solution set is {t < 7, t > 8, t = 9}.</h3><h3 />
= 3.142 x 3 x 3 = 28.278 square units ≈ 28.28 square units