The equation d = 23 · t2 represents the distance in feet, d, the ball travels in t seconds.
Part A
How far does the ball travel in 5 seconds?200 feet in 5 seconds. Show your work.
Part B
How many seconds would it take for the ball to travel 25 feet? Show your work.
Part C
If the ball traveled for 9 seconds, what would be the distance it traveled? Show your work.
Part D
In the inequality shown below, x and y are consecutive, positive integers.
If T is the time it takes for the ball to travel 1,000 feet, what are the values of x and y? Explain your answer.
The interger is x<t<y
Part A:
To find the distance the ball travels in 5 seconds, we can substitute t = 5 into the equation d = 23 · t^2.
d = 23 · (5)^2 = 23 · 25 = 575 feet
Therefore, the ball travels 575 feet in 5 seconds.
Part B:
To find the number of seconds it would take for the ball to travel 25 feet, we need to rearrange the equation d = 23 · t^2 to solve for t.
d = 23 · t^2
25 = 23 · t^2
Divide both sides by 23:
25/23 = t^2
Take the square root of both sides:
√(25/23) = t
Simplify the square root:
t ≈ 1.063
Therefore, it would take approximately 1.063 seconds for the ball to travel 25 feet.
Part C:
To find the distance the ball would travel in 9 seconds, we can substitute t = 9 into the equation d = 23 · t^2.
d = 23 · (9)^2 = 23 · 81 = 1863 feet
Therefore, the ball would travel 1863 feet in 9 seconds.
Part D:
To find the values of x and y in the inequality, we need to solve for T in the equation d = 23 · t^2 and set it equal to 1000.
d = 23 · t^2
1000 = 23 · t^2
Divide both sides by 23:
1000/23 ≈ t^2
Take the square root of both sides:
√(1000/23) ≈ t
Simplify the square root:
t ≈ 6.619
Since x and y are consecutive positive integers in the inequality, we can set them to be the closest whole numbers above and below t.
x = 6
y = 7
Therefore, the values of x and y are 6 and 7 respectively.