Answer:
x = 2* pi* n
Step-by-step explanation:
cos(2x) cos(x) + sin(2x) sin x =1
We know cos(s) cos(t) + sin(s) sin(t) = cos(s - t)
Using s =2x and t = x
cos (2x-x) =1
cos (x) =1
We know this occurs at 0, 2pi, 4 pi etc
x = 2* pi* n where n is an integer
<h3>
Answer: 2072.4 square cm</h3>
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Explanation:
If you used scissors to cut a vertical slice down the lampshade, then it can be unrolled to form a rectangle.
The horizontal portion of this rectangle is the distance around the circle, which is the perimeter of the circle, or the circumference. That's C = 2pi*r. Check out the diagram below to see what I mean.
The diagram shows that the diameter is 20 cm, so the radius is half that at 20/2 = 10 cm.
The circumference is C = 2*pi*r = 2*pi*10 = 20pi cm exactly
The height of the rectangle is the height of the cylinder, which is h = 30 as shown in the diagram.
The area of the rectangle is length*height = (20pi)*(30) = 600pi square cm exactly.
If we were to use something like pi = 3.14, then its approximate area is 600*pi = 600*3.14 = 1884 square cm
Let's bump this up by 10%. To do so, we'll multiply by 1.10
1.10*1884 = 2072.4
Answer:
40w^3
Step-by-step explanation:
I'm assuming you meant w^3 (w to the third power). In that case, you would just add 34 + 13 + 11 - 18 because they are all like terms (coefficients of w^3).