(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>
X f πxf
-1 2 -2
3 1 3
-1 -2 2
0 -3 0
total =3
mean (π)=πxf ÷n
= 3÷4
= 0.75 these is not answer I thank so
Step-by-step explanation:
3y + 2x - 10 = 0
in standard form
2x + 3y -10=0
||
as (ax + by - c = 0)
m = -a/b
= -2/3
or
3y + 2x - 10 = 0
make y subject
y = -2/3x + 10/3
9514 1404 393
Answer:
38.2°
Step-by-step explanation:
The law of sines tells you ...
sin(x)/15 = sin(27°)/11
sin(x) = (15/11)sin(27°) . . . . . multiply by 15
x = arcsin((15/11)sin(27°)) ≈ arcsin(0.619078) ≈ 38.2488°
x ≈ 38.2°
_____
<em>Additional comment</em>
In "law of sines" problems, you need to identify a side and opposite angle that you know both values of. Then, you need to identify whether you're looking for an angle or a side, and whether its opposite side or angle is known. If two angles are known, you can always figure the third from the sum of angles in a triangle.
Here, we have angle 27° opposite side 11. We are looking for an angle, and we know its opposite side. This lets us use the ratio formula directly. Since the angle is the unknown, it is useful to write the equation with sines on top and sides on the bottom.
The given angle is opposite the shorter of the given sides, so this triangle has two solutions. We assume that we want the solution that is an acute angle (141.8° is the other solution). That assumption is based on the drawing. Usually, you're cautioned not to take the drawings at face value.