(a) The "average value" of a function over an interval [a,b] is defined to be
(1/(b-a)) times the integral of f from the limits x= a to x = b.
Now S = 200(5 - 9/(2+t))
The average value of S during the first year (from t = 0 months to t = 12 months) is then:
(1/12) times the integral of 200(5 - 9/(2+t)) from t = 0 to t = 12
or 200/12 times the integral of (5 - 9/(2+t)) from t= 0 to t = 12
This equals 200/12 * (5t -9ln(2+t))
Evaluating this with the limits t= 0 to t = 12 gives:
708.113 units., which is the average value of S(t) during the first year.
(b). We need to find S'(t), and then equate this with the average value.
Now S'(t) = 1800/(t+2)^2
So you're left with solving 1800/(t+2)^2 = 708.113
<span>I'll leave that to you</span>
The slope is 6.cuse the slope also means sometimes 6
Answer:
-3x-15
Step-by-step explanation:
you use the distributive property. So it would be 3 times -x and 3 times -5 so you get -3x-15.
Using the table, we will see that the function is:
t(l) = 3*l
<h3>
How to write the function?</h3>
Here we only have a table to work with, so we need to use that.
In the table, we can see the pairs:
- t(1) = 3
- t(2) = 6
- t(3) = 9
- t(4) = 12
So, in each new level, we just add 3 more toothpicks. Even more, we can see that the number of toothpicks is 3 times the value of l (the level) for all the cases in the table. So this is a linear function.
From that we can conclude that the function will be:
t(l) = 3*l
If you want to learn more about linear functions, you can read:
brainly.com/question/4025726
