Question

A projectile is fired directly upward. The compound inequality 89 – 9.8t < 10.6 or 89 – 9.8t > 20.4 represents a projectile’s velocity that is less than 10.6 m/s or greater than 20.4 m/s. Solve the compound inequality. The solution to the inequality 89 – 9.8t < 10.6 is ? . The solution to the inequality 89 – 9.8t > 20.4 is? . To determine when the projectile hits the ground, solve 89 – 9.8t = 0 for t. Rounding to the nearest whole second, t is about ? seconds. The viable solution set is ?

Answer 1

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.

Note: Inequality sign get flip on dividing both side by a negative number.

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

Note: Inequality sign get flip on dividing both side by a negative number.

The solution to the inequality 89 – 9.8t < 10.6 is t > 8.

The solution to the inequality 89 – 9.8t > 20.4 is t < 7.

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

to the nearest whole second  t is about 9 seconds.

Therefore, variable solution set is {t < 7, t > 8, t = 9}.

Answer 2

Answer:

The solution to the inequality 89 – 9.8t < 10.6 is ?

t > 8

The solution to the inequality 89 – 9.8t > 20.4 is?

t < 7

To determine when the projectile hits the ground, solve 89 – 9.8t = 0 for t.

t = 9.08163265306

Rounding to the nearest whole second, t is about ?

9 seconds.

The viable solution set is ?

[0, 7) or (8, 9]