A pilot is flying an airplane. Due to strong winds, the pilot decides to fly 4,000 feet lower to avoid excess turbulence. It takes the pilot 3.5 minutes to make this adjustment. Interpret the quotient to describe the rate of change in the plane's altitude. Give your answer to the nearest hundredth, and remember the plane is descending.
The quotient that best represents the rate of change in the plane's altitude is __ feet/minute
The quotient that best represents the rate of change in the plane's altitude is 1142.86 feet/minute.
A fire engine's water tank holds 750 gallons of water. If the pump removes 250 gallons of water in 5 minutes, what is the change in the amount of water in gallons in 1 minute?
A. 50
B. -15
C. -50
D. 15
To find the change in the amount of water in gallons in 1 minute, we need to divide the change in gallons by the change in minutes.
The change in gallons is -250 (since the water is being removed from the tank).
The change in minutes is 5.
So, the change in the amount of water in gallons in 1 minute is -250/5 = -50.
Therefore, the correct option is C. -50.
Solve the following word problem. A fish is swimming at -10.8 meters, or 10.8 meters below sea level. Every 2 minutes it descends another 1.5 meters. How long will it take for the fish to reach a depth of -37.8 meters? Show your work and write 1 short sentence explaining your answer.
To find the time it will take for the fish to reach a depth of -37.8 meters, we need to divide the total change in depth (-37.8 - (-10.8) = -37.8 + 10.8 = -27) by the rate of descent (1.5 meters per 2 minutes) and multiply by 2 to find the time for a depth change of 1 meter.
Time = (Total depth change / Rate of descent) * 2
Time = (-27 / 1.5) * 2
Time = -18 * 2
Time = 36 minutes.
The fish will take 36 minutes to reach a depth of -37.8 meters.
Explanation: By calculating the time for a depth change of 1 meter using the given rate of descent, we can then determine the total time needed for a change in depth of 27 meters.
To find the quotient that describes the rate of change in the plane's altitude, we need to divide the change in altitude by the time it takes to make this adjustment.
The change in altitude is 4,000 feet (since the pilot decided to fly 4,000 feet lower).
The time it takes to make this adjustment is 3.5 minutes.
Dividing the change in altitude by the time gives us:
Rate of change in altitude = Change in altitude / Time
Rate of change in altitude = 4,000 feet / 3.5 minutes
Using a calculator, we can find that:
Rate of change in altitude ≈ 1142.86 feet/minute
Rounding to the nearest hundredth, the quotient that represents the rate of change in the plane's altitude is approximately 1142.86 feet/minute.
To find the rate of change in the plane's altitude, we need to divide the change in altitude by the time it takes to make that change. The change in altitude is given as 4,000 feet. The time taken to make this adjustment is given as 3.5 minutes.
So, to find the rate of change, we divide the change in altitude (4,000 feet) by the time taken (3.5 minutes):
Rate of change = Change in altitude / Time taken
Rate of change = 4,000 feet / 3.5 minutes
Calculating this division, we get:
Rate of change = 1142.8571428571427 feet/minute
Rounded to the nearest hundredth, the rate of change in the plane's altitude is approximately 1142.86 feet/minute.