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.
Remember, the nearest hundredth. Not the exact answer.
The quotient to describe the rate of change in the plane's altitude is the change in altitude divided by the time taken to make the adjustment.
In this case, the change in altitude is 4,000 feet (as the plane descended) and the time taken is 3.5 minutes.
So, the rate of change in the plane's altitude is approximately -1142.86 feet per minute (rounded to the nearest hundredth).
Can you please explain how you got your answer?
Certainly! To find the rate of change in the plane's altitude, we need to divide the change in altitude by the time taken.
The change in altitude is given as 4,000 feet.
The time taken is given as 3.5 minutes.
Therefore, the rate of change in the plane's altitude can be calculated as:
Rate of change = Change in altitude / Time taken
Rate of change = 4,000 feet / 3.5 minutes
Simplifying this division, we get:
Rate of change = 1,142.857142857143 feet per minute
Rounding this to the nearest hundredth, we get:
Rate of change ≈ 1,142.86 feet per minute
Since the plane is descending, the negative sign is implied. So, the rate of change in the plane's altitude is approximately -1142.86 feet per minute.
A recipe calls for 2 1/3 cups of oatmeal. You double the recipe and then divide it evenly into 14 servings. How much oatmeal is in each serving?
To find out how much oatmeal is in each serving, we first need to find the total amount of oatmeal in the doubled recipe.
The original recipe calls for 2 1/3 cups of oatmeal. When doubled, this becomes:
2 1/3 cups x 2 = 4 2/3 cups
Now, we need to divide the total amount of oatmeal (4 2/3 cups) evenly into 14 servings. To do this, we divide the total amount by the number of servings:
4 2/3 cups ÷ 14 servings
To simplify this division, we can convert 4 2/3 to an improper fraction:
4 2/3 = (4 x 3 + 2) / 3 = 14/3
Now, we can divide 14/3 by 14:
(14/3) cups ÷ 14 = (14/3) / 14 = 14/3 * 1/14 = 2/3 cups
So, there is approximately 2/3 cup of oatmeal in each serving.
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.
To find out how long it will take for the fish to reach a depth of -37.8 meters, we need to calculate the number of descents of 1.5 meters the fish needs to make.
First, let's find the difference between the initial depth of -10.8 meters and the target depth of -37.8 meters:
-37.8 meters - (-10.8 meters) = -37.8 meters + 10.8 meters = -27 meters
The fish needs to descend -27 meters.
Since the fish descends 1.5 meters every 2 minutes, we can divide the total descent by the descent per interval:
-27 meters ÷ 1.5 meters = -18
The fish needs to make 18 descents of 1.5 meters each to reach a depth of -37.8 meters.
Since each descent takes 2 minutes, we can multiply the number of descents by the time per descent:
18 descents x 2 minutes = 36 minutes
Therefore, it will take 36 minutes for the fish to reach a depth of -37.8 meters.
This means that if the fish continues to descend for 36 minutes at a rate of 1.5 meters every 2 minutes, it will reach a depth of -37.8 meters.