Answer:
a) x changes by 6.5 units
b) y changes by 13 units
Step-by-step explanation:
a. Over this interval, how much does x change by?
Initially, we have that x = 2.
In the end, we have that x = 8.5.
So x changes by 8.5-2 = 6.5 units
b. Over this interval, how much does y change by?
Initially, when x = 2, we have that y = 2x + 11 = 2*2 + 11 = 15
In the end, when x = 8.5, we have that y = 2*8.5 + 11 = 28
So y changes by 28 - 15 = 13 units
(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 answer for angle b is: 25°
The arc angle AC is measured as 55 degrees.
<h3>How to find arc angle?</h3>
If two secant intersect in the exterior of a circle, then the measure of the angle formed is half the positive difference of the arcs intercepted.
Therefore, the secants intersect outside the circle at point E.
The arc angle AC can be found as follows:
Therefore,
m∠BED = 1 / 2 (arc angle AC - arc angle BD)
arc angle AC = x
arc angle BD = 23 degrees.
m∠BED = 16 degrees.
m∠BED = 1 / 2 (arc angle AC - arc angle BD)
16 = 1 / 2 (x - 23)
16 = 1 / 2x - 23 / 2
16 + 11.5 = 0.5x
27.5 = 0.5x
x = 27.5 / 0.5
x = 55 degrees.
Therefore,
arc angle AC = 55 degrees.
learn more on arc angle here: hhttps://brainly.com/question/23117081
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