Answer:
The answer is below
Step-by-step explanation:
The linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time, x, measured in seconds: A linear model with ordered pairs at 0, 60 and 2, 75 and 4, 75 and 6, 40 and 8, 20 and 10, 0 and 12, 0 and 14, 0. The x axis is labeled Time in seconds, and the y axis is labeled Height in feet. Part A: During what interval(s) of the domain is the water balloon's height increasing? (2 points) Part B: During what interval(s) of the domain is the water balloon's height staying the same? (2 points) Part C: During what interval(s) of the domain is the water balloon's height decreasing the fastest? Use complete sentences to support your answer. (3 points) Part D: Use the constraints of the real-world situation to predict the height of the water balloon at 16 seconds.
Answer:
Part A:
Between 0 and 2 seconds, the height of the balloon increases from 60 feet to 75 feet at a rate of 7.5 ft/s
Part B:
Between 2 and 4 seconds, the height stays constant at 75 feet.
Part C:
Between 4 and 6 seconds, the height of the balloon decreases from 75 feet to 40 feet at a rate of -17.5 ft/s
Between 6 and 8 seconds, the height of the balloon decreases from 40 feet to 20 feet at a rate of -10 ft/s
Between 8 and 10 seconds, the height of the balloon decreases from 20 feet to 0 feet at a rate of -10 ft/s
Hence it fastest decreasing rate is -17.5 ft/s which is between 4 to 6 seconds.
Part D:
From 10 seconds, the balloon is at the ground (0 feet), it continues to remain at 0 feet even at 16 seconds.
Answer:
- 3, - 1, 1
Step-by-step explanation:
To find the first 3 terms substitute n = 1, 2, 3 into the formula
a₁ = 2(1) - 5 = 2 - 5 = - 3
a₂ = 2(2) - 5 = 4 - 5 = - 1
a₃ = 2(3) - 5 = 6 - 5 = 1
The first 3 terms are - 3, - 1, 1
X-2y = 3
-2y=3-x move the x over to the other side
-y=3/2 -1/2x divide both sides by 2
y=1/2x - 3/2 divide both sides by -1
8 foot path
1st step = 8/2 = 4ft
2nd step = 4/2 = 2ft
3rd step = 2/2 = 1ft
4th step = 1/2 = 1/2ft
So he covered 7 1/2 ft (or 7.5ft)
