Solve using division of rational numbers. If a car’s value decreases by $2,500 in the first 6 months, how much does the value decrease per month? (Round to the nearest hundredth.)
To find out how much the value of the car decreases per month, we need to divide the total decrease in value ($2,500) by the number of months (6).
$2,500 ÷ 6 ≈ $416.67
Therefore, the value of the car decreases by approximately $416.67 per month.
. 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.(1 point)
Responses
The quotient that describes the rate of change in the squirrel’s height above the ground is -19.05 feet/second.
The quotient that describes the rate of change in the squirrel’s height above the ground is 19.05 feet/second.
The quotient that describes the rate of change in the squirrel’s height above the ground is 10.48 feet/second.
The quotient that describes the rate of change in the squirrel’s height above the ground is -10.48 feet/second.
To determine 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 to make that change.
The squirrel starts at a height of 100 feet and moves down to a height of 45 feet in 5.25 seconds.
100 feet - 45 feet = 55 feet (change in height)
55 feet ÷ 5.25 seconds ≈ 10.48 feet/second
(The quotient is positive because the squirrel is moving downwards, so the rate of change is negative.)
Therefore, the quotient that describes the rate of change in the squirrel's height above the ground is -10.48 feet/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.(1 point)
Responses
The quotient that describes the rate of change in the dolphin’s position is -0.52 meters/second.
The quotient that describes the rate of change in the dolphin’s position is -0.52 meters/second.
The quotient that describes the rate of change in the dolphin’s position is 1.08 meters/second.
The quotient that describes the rate of change in the dolphin’s position is 1.08 meters/second.
The quotient that describes the rate of change in the dolphin’s position is -1.08 meters/second.
The quotient that describes the rate of change in the dolphin’s position is -1.08 meters/second.
The quotient that describes the rate of change in the dolphin’s position is 0.52 meters/second.
To determine the average rate of change in the dolphin's position, we need to divide the change in position by the time it takes to make that change.
The dolphin goes from an altitude of 3.5 meters above the water to a depth of 10 meters below the surface, which is a total change in position of 3.5 + 10 = 13.5 meters.
The time it takes for this change to occur is 12.5 seconds.
13.5 meters ÷ 12.5 seconds ≈ 1.08 meters/second
Since the dolphin is diving below the surface, the rate of change is negative.
Therefore, the quotient that describes the average rate of change in the dolphin's position is -1.08 meters/second.
The scuba diver was at a depth 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.
(1 point)
Responses
The quotient that scribes the average rate of change for the diver’s depth is -0.99 meters/second.
The quotient that scribes the average rate of change for the diver’s depth is -0.99 meters/second.
The quotient that scribes the average rate of change for the diver’s depth is 0.99 meters/second.
The quotient that scribes the average rate of change for the diver’s depth is 0.99 meters/second.
The quotient that scribes the average rate of change for the diver’s depth is -0.49 meters/second.
The quotient that scribes the average rate of change for the diver’s depth is -0.49 meters/second.
The quotient that scribes the average rate of change for the diver’s depth is -3.47 meters/second.
To determine the average rate of change in the diver's depth, we need to divide the change in depth by the time it takes to make that change.
The diver descends 10 meters in 10.1 seconds.
10 meters ÷ 10.1 seconds ≈ 0.99 meters/second
Since the diver is descending, the rate of change is negative.
Therefore, the quotient that describes the average rate of change in the diver's depth is -0.99 meters/second.
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 find out how much the value of the car decreases per month, we need to divide the total decrease in value ($4000) by the number of months (12).
$4000 ÷ 12 ≈ $333.33
Therefore, the value of the car decreases by approximately $333.33 per month.