Question

The distance traveled, in meters, of a coin dropped from a tall building is modeled by the equation d(t) = 4.9t2 where d equals the distance traveled at time t seconds and t equals the time in seconds. What does the average rate of change of d(t) from t = 3 to t = 6 represent?

The coin travels an average distance of 44.1 meters from 3 seconds to 6 seconds.
The coin falls down with an average speed of 14.7 meters per second from 3 seconds to 6 seconds.
The coin falls down with an average speed of 44.1 meters per second from 3 seconds to 6 seconds.
The coin travels an average distance of 14.7 meters from 3 seconds to 6 seconds.


PLEASE HELP!!

Answer 1

Explanation:

PART A: Parallel lines are two lines that never meet. Find an example that contradicts this definition. How would you change the definition to make...

Answer 2

The average rate of change of d(t) from t = 3 to t = 6 represent: A. The coin travels an average distance of 44.1 meters from 3 seconds to 6 seconds.

In Mathematics and Geometry, the average rate of change (ARoC) of a function f(x) on a closed interval [a, b] can be calculated by using this mathematical equation (formula):

Average rate of change (ARoC) =
`(f(b) - f(a))/((b - a))`

Based on the given quadratic function, we can reasonably infer and logically deduce the following:

`d(t)=4.9t^2\\\\d(3)=4.9(3)^2`

f(a) = d(3) = 44.1

`d(t)=4.9t^2\\\\d(6)=4.9(6)^2`

f(a) = d(3) = 176.4

Next, we would determine the average rate of change (ARoC) of the function over the interval [3, 6]:

Average rate of change (ARoC) =
`(176.4 - 44.1)/((6 - 3))`

Average rate of change (ARoC) = 44.1 meters.

In this context, we can logically deduce that the coin travels an average distance of 44.1 meters from 3 seconds to 6 seconds.