the table represents the height of a ball thrown up from the roof of a building, h(t), in meters, t seconds…

the table represents the height of a ball thrown up from the roof of a building, h(t), in meters, t seconds after it is thrown upward.\n|t|h(t)|\n|0|0|\n|2|60.4|\n|4|81.6|\n|6|63.6|\n|8|6.4|\n|10|-90|\n|12|-225.6|\nwhich statements are true? check all that apply.\nthe ball is at the same height as the building between 8 and 10 seconds after it is thrown.\nthe height of the ball decreases and then increases.\nthe ball reaches its maximum height about 4 seconds after it is thrown.\nthe ball hits the ground between 8 and 10 seconds after it is thrown.\nthe height of the building is 81.6 meters.

the table represents the height of a ball thrown up from the roof of a building, h(t), in meters, t seconds after it is thrown upward.\n|t|h(t)|\n|0|0|\n|2|60.4|\n|4|81.6|\n|6|63.6|\n|8|6.4|\n|10|-90|\n|12|-225.6|\nwhich statements are true? check all that apply.\nthe ball is at the same height as the building between 8 and 10 seconds after it is thrown.\nthe height of the ball decreases and then increases.\nthe ball reaches its maximum height about 4 seconds after it is thrown.\nthe ball hits the ground between 8 and 10 seconds after it is thrown.\nthe height of the building is 81.6 meters.

Answer

Explanation:

Step1: Analyze initial height

At $t = 0$, $h(0)=0$. This means the starting - point (height of the building) is at height $0$ meters.

Step2: Observe height changes

The height values are $h(2) = 60.4$, $h(4)=81.6$, $h(6)=63.6$, $h(8)=6.4$, $h(10)= - 90$, $h(12)=-225.6$. The height first increases from $t = 0$ to $t = 4$ (from $0$ to $81.6$ meters) and then decreases.

Step3: Check statements

  • For the statement "The ball is at the same height as the building between 8 and 10 seconds after it is thrown": The height of the building is $0$ (at $t = 0$). Between $t = 8$ ($h(8)=6.4$) and $t = 10$ ($h(10)=-90$), the ball is not at height $0$, so this statement is false.
  • For the statement "The height of the ball decreases and then increases": The height first increases from $t = 0$ to $t = 4$ and then decreases, so this statement is false.
  • For the statement "The ball reaches its maximum height about 4 seconds after it is thrown": Since $h(4)=81.6$ and $h(2)=60.4$, $h(6)=63.6$, the maximum height in the given data is at $t = 4$ seconds, so this statement is true.
  • For the statement "The ball hits the ground between 8 and 10 seconds after it is thrown": The ground level is considered $h = 0$. At $t = 8$, $h(8)=6.4$ and at $t = 10$, $h(10)=-90$. Since the height changes sign between $t = 8$ and $t = 10$, the ball hits the ground in this interval, so this statement is true.
  • For the statement "The height of the building is 81.6 meters": At $t = 0$, $h(0)=0$, so the height of the building is $0$ meters, not $81.6$ meters, so this statement is false.

Answer:

The ball reaches its maximum height about 4 seconds after it is thrown; The ball hits the ground between 8 and 10 seconds after it is thrown.