A mountain goat is climbing to the top of a large cliff. The cliff is 50 feet higher than its starting point. If it takes the goat 22 minutes to climb this cliff, interpret the quotient to describe the rate of change in the goat’s elevation. Give your answer to the nearest hundredth.
The quotient is obtained by dividing the change in elevation, 50 feet, by the time it takes to climb the cliff, 22 minutes.
Rate of change in elevation = $\dfrac{50 \text{ feet}}{22 \text{ minutes}} = \dfrac{25}{11} \approx \boxed{2.27 \text{ feet per minute}}$.
A bird is flying at an average altitude of 10 meters above the ground. After 3 seconds, it settles on a branch that is 3 meters above the ground. Interpret the quotient to describe the rate of change in the bird’s altitude. Give your answer to the nearest hundredth and remember that the bird is descending.
To interpret the quotient to describe the rate of change in the goat's elevation, we need to divide the change in the goat's elevation by the time it took to climb.
The change in elevation is given as 50 feet, and the time it took to climb is given as 22 minutes.
Therefore, the rate of change in the goat's elevation is calculated by dividing 50 feet by 22 minutes:
Rate of change = 50 feet / 22 minutes
To find the answer to the nearest hundredth, divide 50 by 22 and round to two decimal places.
Rate of change ≈ 2.27 feet/minute
To interpret the quotient that describes the rate of change in the goat's elevation, we need to find the rate at which the goat is climbing the cliff. The rate of change, in this case, is the change in elevation (in feet) divided by the time taken (in minutes).
Given that the cliff is 50 feet higher than the starting point, we know that the change in elevation is +50 feet. And since it takes the goat 22 minutes to climb the cliff, the time taken is 22 minutes.
To find the rate of change, we divide the change in elevation by the time taken:
Rate of change = Change in elevation / Time taken.
Rate of change = 50 feet / 22 minutes.
To express the rate of change to the nearest hundredth, we can calculate this division:
Rate of change ≈ 50 / 22 ≈ 2.27 feet/minute.
So, the quotient, which describes the rate of change in the goat's elevation, is approximately 2.27 feet/minute.