A squirrel has stored its acorns in a hole that is 45 feet from the ground in a tall tree. The squirrel moved from a perch 100 feet above the ground to get 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 can divide the change in height by the time it took to make that change.
The squirrel moved from a perch 100 feet above the ground to its stored acorns in a hole 45 feet from the ground. This is a change in height of 100 - 45 = 55 feet.
The squirrel took 5.25 seconds to make this change in height.
So, the rate of change in the squirrel's height above the ground is 55 feet / 5.25 seconds = 10.48 feet per second.
Therefore, the quotient describes the rate of change in the squirrel's height above the ground as 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 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.
To find the average rate of change in the dolphin's position, we can divide the change in position by the time it took for that change.
The dolphin went from an altitude of 3.5 meters above the surface of the water to a depth of 10 meters below the surface of the water. This is a change in position of 3.5 + 10 = 13.5 meters.
The dolphin took 12.5 seconds to make this change in position.
So, the average rate of change in the dolphin's position is 13.5 meters / 12.5 seconds = 1.08 meters per second.
Therefore, the quotient describes the average rate of change in the dolphin's position as approximately 1.08 meters per second.
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.
To find the rate of change in the diver's depth, we can divide the change in depth by the time it took to make that change.
The diver went from a depth of 15 meters below the surface to a depth of 10 meters lower, which is 15 + 10 = 25 meters below the surface.
The diver took 10.1 seconds to make this change in depth.
So, the rate of change in the diver's depth is 25 meters / 10.1 seconds = 2.48 meters per second.
Therefore, the quotient describes the rate of change in the diver's depth as approximately 2.48 meters per second.
Solve using division of rational numbers. If a car’s value decreases by $4,000 in the first 12 months, how much does the value decrease per month? (Round to the nearest hundredth.)
To find the value by which the car's value decreases per month, we need to divide the total decrease in value by the number of months.
The car's value decreases by $4,000 in the first 12 months.
So, the value that the car decreases per month is $4,000 / 12 months = $333.33 (rounded to the nearest hundredth).
Therefore, the car's value decreases approximately by $333.33 per month.
It is recommended that hikers drink 24 ounces of water an hour. If a canteen has 24 ounces of water, how much should the amount of water in the canteen change every 10 minutes?
To find the amount by which the water in the canteen should change every 10 minutes, we need to divide the recommended amount of water per hour by the number of 10-minute intervals in an hour.
The recommended amount of water for an hour is 24 ounces.
There are 6 10-minute intervals in an hour (60 minutes divided by 10 minutes).
So, the amount of water that should change every 10 minutes is 24 ounces / 6 intervals = 4 ounces.
Therefore, the amount of water in the canteen should change by 4 ounces every 10 minutes.
To find the rate of change in the squirrel's height above the ground, we need to calculate the difference in its height and divide it by the time it took.
The squirrel moved from a perch 100 feet above the ground to get to its stored acorns in 5.25 seconds. Therefore, the difference in height is 100 feet.
To find the rate of change, we divide the difference in height (100 feet) by the time (5.25 seconds):
Rate of change = Difference in height / Time = 100 feet / 5.25 seconds = 19.05 feet/second.
Therefore, the rate of change in the squirrel's height above the ground is approximately 19.05 feet/second.