a pilot is flying an airplane at an average altitude of 60,000 feet above the ground. due to strong winds, the pilot decides to fly 5,000 feet love to avoid excessive turbulence. it takes the pilot 4.5 minutes to make this adjustment. interpret the quotient to describe the rate of the change in the plane's altitude. give your answer to the nearest hundredth.
To interpret the quotient describing the rate of change in the plane's altitude, we need to find the rate of change or the derivative of the altitude with respect to time.
Since the pilot lowers the plane's altitude by 5,000 feet in 4.5 minutes, we can find the rate of change as:
Rate of Change = Change in altitude / Change in time
Rate of Change = 5000 feet / 4.5 minutes
Rate of Change ≈ 1111.11 feet/minute
Therefore, the quotient describing the rate of change in the plane's altitude is approximately 1111.11 feet/minute, rounded to the nearest hundredth.
Okay, now show your work for it
Sure! Let's break down the calculation step by step:
Given:
Change in altitude = 5,000 feet
Change in time = 4.5 minutes
To find the rate of change, we can use the formula:
Rate of Change = Change in altitude / Change in time
Plugging in the values:
Rate of Change = 5,000 feet / 4.5 minutes
To divide these two values, we consider the fraction:
Rate of Change = (5,000 feet) / (4.5 minutes)
Now, let's simplify:
Rate of Change = 1,111.11 feet/minute
So, the rate of change in the plane's altitude is approximately 1,111.11 feet/minute, rounded to the nearest hundredth.
Okay, now simplify the whole thing and break it down into small steps
Certainly! Here's a step-by-step breakdown:
1. Given:
- Change in altitude = 5,000 feet
- Change in time = 4.5 minutes
2. Use the formula for rate of change:
Rate of Change = Change in altitude / Change in time
3. Substitute the given values:
Rate of Change = 5,000 feet / 4.5 minutes
4. Divide the numerator and denominator:
Rate of Change = 1,111.11 feet/minute
Therefore, the rate of change in the plane's altitude is approximately 1,111.11 feet/minute, rounded to the nearest hundredth.
To find the rate of change in the plane's altitude, we need to divide the change in altitude by the time it takes.
The change in altitude is 5,000 feet, and the time it takes is 4.5 minutes.
So, the rate of change in the plane's altitude is:
Rate of change = Change in altitude / Time
= 5,000 feet / 4.5 minutes
To find the answer to the nearest hundredth, we can divide 5,000 by 4.5 using a calculator:
Rate of change = 5,000 / 4.5 ≈ 1,111.11
Therefore, the rate of change in the plane's altitude is approximately 1,111.11 feet per minute.
To find the rate of change in the plane's altitude, we need to calculate the change in altitude per unit of time. In this case, the change in altitude is 5,000 feet, and the time taken is 4.5 minutes.
To calculate the rate of change, we use the formula:
Rate of change = Change in altitude / Time taken
Substituting the given values:
Rate of change = 5,000 feet / 4.5 minutes
To calculate this, we need to convert the units of time into hours since we are given the altitude change in feet. There are 60 minutes in an hour, so:
Time taken in hours = 4.5 minutes / 60 minutes per hour
Time taken in hours = 0.075 hours
Let's substitute this back into the formula:
Rate of change = 5,000 feet / 0.075 hours
Rate of change ≈ 66,666.67 feet per hour
Therefore, the rate of change in the plane's altitude is approximately 66,666.67 feet per hour.