A squirrel has stored its acorns in a hole that is 45 feet from the ground in a 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
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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 its 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 dolphin’s position. Give your answer to the nearest hundredth
A scuba diver was at a depth of 15 meters below the surface when she saw something interesting about 10 meters lower. She made the descent in 10.1 seconds. Interpret the quotient to describe the rate of change in the diver’s depth. Give your answer to the nearest hundredth
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Solve using division of rational numbers. If a car’s value decreases by $4000 in the first 12 months, how much does the value decrease per month? (Round to the nearest hundredth.)
To interpret the quotient that describes 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 move.
In this case, the squirrel starts at a height of 100 feet and moves down to a height of 45 feet, which means the change in height is 100 - 45 = 55 feet.
The time it takes for the squirrel to move is given as 5.25 seconds.
To find the rate of change in the squirrel's height, we divide the change in height by the time it takes:
Rate of change = (Change in height) / (Time)
Rate of change = 55 feet / 5.25 seconds
Calculating this value, we get:
Rate of change = 10.48 feet per second (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.
To find the rate of change in the diver's depth, we divide the change in depth by the amount of time it takes for the diver to descend.
Change in depth = 15 m + 10 m = 25 m (since going lower is considered a negative change)
Time taken = 10.1 seconds
Rate of change = Change in depth / Time taken
Rate of change = 25 m / 10.1 sec
Dividing 25 by 10.1 gives us a rate of change of approximately 2.48 meters per second. Therefore, the diver's depth is changing at a rate of 2.48 meters per second.
To find the rate of change in the squirrel's height above the ground, we divide the change in height by the amount of time it takes for the squirrel to descend.
Change in height = 100 ft - 45 ft = 55 ft
Time taken = 5.25 seconds
Rate of change = Change in height / Time taken
Rate of change = 55 ft / 5.25 sec
Dividing 55 by 5.25 gives us a rate of change of approximately 10.48 feet per second. Therefore, the squirrel's height above the ground is decreasing at a rate of 10.48 feet per second.
To find the average rate of change in the dolphin's position, we divide the change in position by the amount of time it takes for the dolphin to go from its highest point above the water to its lowest depth.
Change in position = 3.5 m + 10 m = 13.5 m (since going below the surface is considered a negative change)
Time taken = 12.5 seconds
Average rate of change = Change in position / Time taken
Average rate of change = 13.5 m / 12.5 sec
Dividing 13.5 by 12.5 gives us an average rate of change of approximately 1.08 meters per second. Therefore, the dolphin's position is changing at an average rate of 1.08 meters per second.