A pilot is flying an airplane. Due to strong winds, the pilot decides to fly 4,000 feet lower to avoid excessive 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.(1 point)
The quotient is the rate of change in the plane's altitude. To find it, we divide the change in altitude (4,000 feet) by the time it takes to make the adjustment (3.5 minutes):
Rate of change = Change in altitude / Time taken
Rate of change = 4000 feet / 3.5 minutes
Calculating this, we find:
Rate of change = 1142.86 feet per minute
Therefore, the rate of change in the plane's altitude is approximately 1142.86 feet per 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?(1 point)
To find the change in the amount of water in 1 minute, we need to divide the change in water (250 gallons) by the time taken (5 minutes):
Change in water in 1 minute = Change in water / Time taken
Change in water in 1 minute = 250 gallons / 5 minutes
Calculating this, we find:
Change in water in 1 minute = 50 gallons
Therefore, the change in the amount of water in 1 minute is 50 gallons.
Use the properties of operations and rules for multiplying and dividing signed numbers to solve:
(−4)×(75)×(−34)÷(715)
Using the properties of operations and rules for multiplying and dividing signed numbers, we can solve the expression:
(−4)×(75)×(−34)÷(715)
First, we can start by multiplying the numbers:
(−4)×(75)×(−34) = 10,200
Next, we divide by 715:
10,200 ÷ 715 = 14.29 (rounded to the nearest hundredth)
Therefore, the value of the expression (−4)×(75)×(−34)÷(715) is approximately 14.29.
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 a sentence to explain what your answer means.(4 points)
To find how long it will take for the fish to reach a depth of −37.8 meters, we can use the equation:
Time = (Final depth - Initial depth) / Rate of change
The initial depth is −10.8 meters, the final depth is −37.8 meters, and the rate of change is 1.5 meters every 2 minutes.
Time = (−37.8 - (−10.8)) / 1.5
Simplifying this expression, we get:
Time = −27 / 1.5
Time = −18
Therefore, it will take the fish −18 minutes to reach a depth of −37.8 meters.
The negative sign indicates that the fish is swimming deeper into the water and the time given is in reference to reaching a depth below sea level. So, the fish will take 18 minutes to descend 37.8 meters deeper into the water beyond its current position of 10.8 meters below sea level.
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?(1 point)
Responses
−15
negative 15
15
15
−50
negative 50
50
To interpret the quotient that describes the rate of change in the plane's altitude, we need to express this as a ratio of two different quantities:
Rate of change in altitude = Change in altitude / Time taken
In this case, the change in altitude is 4,000 feet (negative since the plane is descending) and the time taken is 3.5 minutes.
Now we can calculate the rate of change:
Rate of change in altitude = -4,000 feet / 3.5 minutes
Dividing -4,000 by 3.5 gives us approximately -1142.86 feet per minute. Remember that the plane is descending, so the rate is negative.
Therefore, the rate of change in the plane's altitude is approximately -1142.86 feet per minute, to the nearest hundredth.