4 months ago
Q:

IF ANYONE ANSWER THIS CORRECTLY I WILL GIVE THEM 43 POINTS AND THE BRAINLIEST ANSWERKen wants to build a table and put a border around it. The table and border must have an area of 3,276 square inches. The table is 36 inches wide and 72 inches long without the border. Which quadratic equation can be used to determine the thickness of the border, x? A. 4x² + 216x + 2,592 = 0 B. 4x² + 216x − 684 = 0 C. 2x² + 216x − 3,276 = 0 D. x² + 108x + 3,276 = 0Question 2(Multiple Choice Worth 2 points)(09.05)A particle is moving along a projectile path where the initial height is 96 feet with an initial speed of 16 feet per second. What is the maximum height of the particle?100 feet 96 feet 60 feet 56 feetQuestion 3(Multiple Choice Worth 2 points)(09.05)A golf ball is hit from the ground with an initial speed of 192 feet per second. Assume the starting height of the ball is 0 feet. How long will it take the golf ball to hit the ground? 39 secs 19 secs 12 secs 6 secsQuestion 4(Multiple Choice Worth 1 points)(09.05)Arianna kicks a soccer ball off the ground and into the air with an initial velocity of 42 feet per second. Assume the starting height of the ball is 0 feet. Approximately what maximum height does the soccer ball reach?1.3 ft 2.6 ft 26.0 ft 27.6 ftQuestion 5(Multiple Choice Worth 1 points)(09.05)Jules kicks a soccer ball off the ground and into the air with an initial velocity of 25 feet per second. Assume the starting height of the ball is 0 feet. Approximately how long does it take until the soccer ball hits the ground again? 0.6 sec 0.8 sec 1.6 secs 2.8 secsQuestion 6(Multiple Choice Worth 2 points)(09.05)Amir pitches a baseball at an initial height of 6 feet, with a velocity of 73 feet per second. If the batter misses, about how long does it take the ball hit the ground?Hint: Use H(t) = −16t² + vt + s. 4.64 seconds 2.94 seconds 2.28 seconds 0.08 second

Accepted Solution

A:
1. The overall width will be 36 +2x. The overall length will be 72 +2x. Then the area will be
.. (36 +2x)*(72 +2x) = 3276
.. 4x^2 + 216x +2592 = 3276
.. 4x^2 +216x -684 = 0 . . . . . . . . . . . . corresponding to selection B

2. h(t) = -16t^2 +16t +96
.. = -16(t^2 -t) +96
.. = -16(t^2 -t +1/4) +96 -(1/4)*(-16)
.. = -16(t -1/2)^2 +100 . . . . vertex y-coordinate is 100, matches 1st selection

3. h(t) = -16t^2 +192t = -16t(t -12)
.. The ball will again have a height of zero after 12 seconds, matches 3rd selection

4. h(t) = -16t^2 +42t = -16t(t -2.625)
The maximum height will be reached at t=1.3125. It will be
.. h(1.3125) = 16*1.3125^2 ≈ 27.6 . . . . . . corresponding to the 4th selection

5. h(t) = -16t^2 +25t = -16t(t -1.5625)
.. The ball will again have a height of zero after 1.5625 ≈ 1.6 seconds, matches 3rd selection

6. Assuming the ball is pitched horizontally, its vertical speed is zero.
.. h(t) = -16t^2 +6
.. t = √(6/16) ≈ 0.61 second

If Amir pitches the ball straight down, it will hit the ground in 0.08 seconds. If Amir pitches the ball straight up, it will take about 4.64 seconds to hit the ground. When pitched at any other angle, the time to hit the ground will be between these values.
.. no offered selection makes any sense