For the answer to the question above,
The mean value theorem states the if f is a continuous function on an interval [a,b], then there is a c in [a,b] such that:
<span>f ' (c) = [f(b) - f(a)] / (b - a) </span>
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So [f(a) - f(b)] ( b - a ) = [sin(3pi/4) - sin(pi/4)]/pi </span>
= [sqrt(2)/2 - sqrt(2)/2]/pi = 0
So for some c in [pi/2, 3pi/2] we must have f ' (c) = 0
In general f ' (x) = (1/2) cos (x/2)
We ask ourselves for what values x in [pi/2, 3pi/2] does the above equation equal 0.
0 = (1/2) cos (x/2)
0 = cos (x/2)
x/2 = ..., -5pi/2, -3pi/2, -pi/2, pi/2, 3pi/2, 5pi/2,...
x = ..., -5pi, -3pi, -pi, pi. 3pi, 5pi, ....
and x = pi is the only solution in our interval.
So c = pi is a solution that satisfies the conclusion of the MVT
Given:
The triangle ABC rotated 270 degrees clockwise.
The rule of rotation is
To find:
The coordinates of point B after the given rotation.
Solution:
From the given graph, it is clear that the coordinates of point B are (4,4).
The given rule of rotation is:
Using this rule, we get
The coordinates of point B after the given rotation are (-4,4).
Therefore, the correct option is C.
Answer:
factors of 36 are 1,2,3,4,6,9,12,18,and 36
Answer: $8.60
Step-by-step explanation:
1 pint = 0.5 quart
12 pint = 6
51.6/6 = 8.6
33 sweets in a 7x to 4x ratio
7x + 4x = 33
11x = 33
x = 3
33 sweets can be put in a 7(3) to 4(3) ratio
which is a 21 to 12 ratio
so 21 sweets are yellow, and 12 sweets are purple to get the ratio of 7 to 4
Note:
<span>a(b) = ab = a x b = a times b
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