A squirrel has stored its acorns in a hole that
is 45 feet from the ground in tall tree. The squirrel starts on a perch 100 feet above the ground. The squirrel moves from the perch down to its stored Acorns in 5.25 seconds. Interpret the quotient to describe the rate of change in the squirrel's height above the ground. Give your answer to the nearest hundredth.
To find the rate of change in the squirrel's height above the ground, we need to divide the change in height by the time taken.
The squirrel starts on a perch 100 feet above the ground and moves down to the acorns stored 45 feet from the ground. This means the change in height is 100 - 45 = 55 feet.
The time taken is 5.25 seconds.
To find the rate of change, we divide the change in height by the time taken:
Rate of change = Change in height / Time taken
Rate of change = 55 feet / 5.25 seconds
Rate of change ≈ 10.48 feet per second
So, the rate of change in the squirrel's height above the ground is approximately 10.48 feet per second.
A dolphin jumped above the surface of the water it reached an altitude of 3.5 meters above the surface of the water and then dove 10 meters below the surface of the water it went from the highest point above the water to its lowest depth in 12.5 seconds interpret the quotient to describe the average rate of change in the dolphins position give your answer to the nearest hundredth
To find the average rate of change in the dolphin's position, we need to divide the change in position by the time taken.
The dolphin jumped from an altitude of 3.5 meters above the surface of the water to a depth of 10 meters below the surface. This means the change in position is 3.5 + 10 = 13.5 meters.
The time taken is 12.5 seconds.
To find the average rate of change, we divide the change in position by the time taken:
Average rate of change = Change in position / Time taken
Average rate of change = 13.5 meters / 12.5 seconds
Average rate of change ≈ 1.08 meters per second
So, the average rate of change in the dolphin's position is approximately 1.08 meters per second.
To interpret the quotient to describe the rate of change in the squirrel's height above the ground, we need to divide the change in height by the time it took. The change in height is obtained by subtracting the final height from the initial height.
The initial height of the squirrel's perch is 100 feet, and the final height when it reaches the stored acorns is 45 feet. Therefore, the change in height is 100 - 45 = 55 feet.
The time it took for the squirrel to move from the perch to the stored acorns is given as 5.25 seconds.
To find the rate of change, we divide the change in height by the time it took:
Rate of change = Change in height / Time
Rate of change = 55 feet / 5.25 seconds
Simplifying this division gives:
Rate of change = 10.4761 feet per second.
Rounding this answer to the nearest hundredth gives:
Rate of change ≈ 10.48 feet per second.
Therefore, the rate of change in the squirrel's height above the ground is approximately 10.48 feet per second.
To interpret the quotient and describe the rate of change in the squirrel's height above the ground, we need to divide the change in height by the time it takes for the squirrel to make that change.
Given:
Initial height (perch): 100 feet
Final height (acorns in the hole): 45 feet
Time taken: 5.25 seconds
To calculate the change in height, we subtract the final height from the initial height:
Change in height = Final height - Initial height
= 45 ft - 100 ft
= -55 ft
The negative sign indicates that the squirrel moves downward (since it is descending from the perch).
To determine the rate of change in height, we divide the change in height by the time taken:
Rate of change = Change in height / Time taken
= -55 ft / 5.25 seconds
Calculating this quotient gives us:
Rate of change = -10.48 ft/sec (rounded to the nearest hundredth)
Therefore, the rate of change in the squirrel's height above the ground is approximately -10.48 feet per second.