(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>
Answer:
yes because every time x changes y changes the same amount
Step-by-step explanation:
Answer:
65kg
Step-by-step explanation:
Answer:
(-3, -8) I think
Step-by-step explanation
over the origin mean it would be going diagonally across (0,0). Not directly down (over the x-axis/ across the y-axis), nor to the side (over y-axis/ across the x-axis
Answer: w - 7
Step-by-step explanation:
The expression is simply less 7 less than w, or w - 7.
