question 4\nheight of a rocket\na toy rocket is shot from a platform 21 feet above the ground. the rocket…

question 4\nheight of a rocket\na toy rocket is shot from a platform 21 feet above the ground. the rocket flies into the air, reaches a\nmaximum height of 48 feet, then falls to the ground. the graph of h(t) below shows the height of this\nrocket (in feet) t seconds after launch.\napproximate the average rates of change over\neach of the following time intervals. round to\ntwo decimal places.\n0 seconds to 30 seconds:\nselect an answer\n30 seconds to 70 seconds:\nselect an answer\n0 seconds to 70 seconds:\nselect an answer\ncomplete the statement to explain the meaning of the rate of change in this situation.\non average, the height of the rocket is select an answer at an select an answer rate.\nwhat do the values above tell you about the rate of change of h(t)?\nthe rate of change for h(t) is select an answer.

question 4\nheight of a rocket\na toy rocket is shot from a platform 21 feet above the ground. the rocket flies into the air, reaches a\nmaximum height of 48 feet, then falls to the ground. the graph of h(t) below shows the height of this\nrocket (in feet) t seconds after launch.\napproximate the average rates of change over\neach of the following time intervals. round to\ntwo decimal places.\n0 seconds to 30 seconds:\nselect an answer\n30 seconds to 70 seconds:\nselect an answer\n0 seconds to 70 seconds:\nselect an answer\ncomplete the statement to explain the meaning of the rate of change in this situation.\non average, the height of the rocket is select an answer at an select an answer rate.\nwhat do the values above tell you about the rate of change of h(t)?\nthe rate of change for h(t) is select an answer.

Answer

Explanation:

Step1: Recall the formula for average rate of change

The formula for the average rate of change of a function (y = H(t)) over the interval ([a,b]) is (\frac{H(b)-H(a)}{b - a}).

Step2: Find (H(0)), (H(30)) and (H(70))

From the graph, when (t = 0), (H(0)=21); when (t = 30), (H(30) = 48); when (t=70), (H(70)=0).

Step3: Calculate the average rate of change from (t = 0) to (t = 30)

Substitute (a = 0), (b = 30), (H(a)=21), (H(b)=48) into the formula (\frac{H(b)-H(a)}{b - a}). [ \frac{48 - 21}{30-0}=\frac{27}{30}=0.90 ]

Step4: Calculate the average rate of change from (t = 30) to (t = 70)

Substitute (a = 30), (b = 70), (H(a)=48), (H(b)=0) into the formula (\frac{H(b)-H(a)}{b - a}). [ \frac{0 - 48}{70 - 30}=\frac{-48}{40}=-1.20 ]

Step5: Calculate the average rate of change from (t = 0) to (t = 70)

Substitute (a = 0), (b = 70), (H(a)=21), (H(b)=0) into the formula (\frac{H(b)-H(a)}{b - a}). [ \frac{0 - 21}{70-0}=\frac{-21}{70}=- 0.30 ]

Answer:

0 seconds to 30 seconds: (0.90) 30 seconds to 70 seconds: (-1.20) 0 seconds to 70 seconds: (-0.30)