We have the following equation:
h (t) = - 16t ^ 2 + 161t + 128
We substitute the value of h (t) = 170:
170 = -16t ^ 2 + 161t + 128
We rewrite the equation:
-16t ^ 2 + 161t + 128 - 170 = 0
-16t ^ 2 + 161t - 42 = 0
We look for the roots of the equation:
t1 = (161/32) + root (23233) / 32
t2 = (161/32) - root (23233) / 32
Answer:
The object is 170 feet off the ground at the following times:
t1 = (161/32) + root (23233) / 32
t2 = (161/32) - root (23233) / 32
Answer:
Uniform is when you dress properly and working atire non uniform is when you dress freely
This problem is an example of solving equations with variables on both sides. To solve, we must first set up an equation for both the red balloon and the blue balloon.
Since the red balloon rises at 2.6 meters per second, we can represent this part of the equation as 2.6s. The balloon is already 7.3 meters off of the ground, so we just add the 7.3 to the 2.6s:
2.6s + 7.3
Since the blue balloon rises at 1.5 meters per second, we can represent this part of the equation as 1.5s. The balloon is already 12.4 meters off of the ground, so we just add the 12.4 to the 1.5:
1.5s + 12.4
To determine when both balloons are at the same height, we set the two equations equal to each other:
2.6s + 7.3 = 1.5s + 12.4
Then, we solve for s. First, the variables must be on the same side of the equation. We can do this by subtracting 1.5s from both sides of the equation:
1.1s + 7.3 = 12.4
Next, we must get s by itself. We work towards this by subtracting 7.3 from both sides of the equation:
1.1s = 5.1
Last, we divide both sides by 1.1. So s = 4.63.
This means that it will take 4.63 seconds for both balloons to reach the same height. If we want to know what height that is, we simply plug the 4.63 back into each equation:
2.6s + 7.3
= 2.6 (4.63) + 7.3
= 19.33
1.5s + 12.4
= 1.5 (4.63) + 12.4
= 19.33
After 4.63 seconds, the balloons will have reached the same height: 19.33 meters.
190 min.................................
