Answer: A. 40
Step-by-step explanation:
Check the picture below.
make sure your calculator is in Degree mode.
Answer:
Step-by-step explanation:
Answer:
Option B is correct
The average rate of change of d(t) between 2 second and 4 second is; 90 ft/s
and it represents the average speed of the object between 2 seconds and 4 seconds.
Step-by-step explanation:
Average rate of change of function is defined as the ratio of the difference in the function f(x) as it changes from a to b to the difference between a and b. Then, the average rate of change is denoted as A(x).
As per the given statement, the distance d(t) is in feet and t is the time in second.
To find the average rate of change of d(t) between 2 seconds and 4 seconds.
From the table we have;
at t = 2 , d(2) = 60
and
at t =4 , d(4) = 240.
Then, by the definition of average rate of change ;
=
Simplify:
therefore, the average rate of change of d(t) between 2 second and 4 second is; 90 ft/s and it represents the average speed of the object between 2 seconds and 4 seconds.
From your previous questions, you know
(3<em>w</em> + <em>w</em>⁴)' = 3 + 4<em>w</em>³
(2<em>w</em>² + 1)' = 4<em>w</em>
So by the quotient rule,
<em>R'(w)</em> = [ (2<em>w</em>² + 1)•(3<em>w</em> + <em>w</em>⁴)' - (3<em>w</em> + <em>w</em>⁴)•(2<em>w</em>² + 1)' ] / (2<em>w</em>² + 1)²
That is, the quotient rule gives
<em>R'(w)</em> = [ (denominator)•(derivative of numerator) - (numerator)•(derivative of denominator) ] / (denominator)²
I'm not entirely sure what is meant by "unsimplified". Technically, you could stop here. But since you already know the component derivatives, might as well put them to use:
<em>R'(w)</em> = [ (2<em>w</em>² + 1)•(3 + 4<em>w</em>³) - (3<em>w</em> + <em>w</em>⁴)•(4<em>w</em>) ] / (2<em>w</em>² + 1)²
