Answer:
-16 sqrt(3) +16i
Step-by-step explanation:
z = 2 cis (pi/6)
z^5 = 2^5 cis (5*pi/6)
z^5 = 32 cis (5pi/6)
z^5 = 32 cos (5pi/6) + 32 i sin (5pi/6)
= 32 * (-sqrt(3)/2) + 32i (1/2)
= -16 sqrt(3) +16i
It is asking for the intercept.
y = x + 3 becomes y - x = 3
multiply it by two, so it becomes -2x + 2y = 6. Then add it to the other equation, and solve for y.
2x + 4y = 60
(2x + 4y) + (-2x + 2y) = 60 +6
6y = 66
y = 11
Plug in the known y into the the easiest equation.
11 = x +3
x = 8
Intercept: (8, 11)
Answer:
1,100 is your area
Step-by-step explanation:
First we cut the shape into three, two triangles and a square, the formula to find the area of a square is A=a^2 (a is the side)
A=25^2
A=625
now to find the triangles the formula to find the are we use the right angled triangle formula twice which is A=a*b/2
A=25*19/2
A=475/2
A=237.5
now add them all up
625+237.5+237.5=
1,100
Take one sector that includes the shaded segment:-
There are 6 sectors altogether and the angle at center = 369 / 6 = 60 degrees.
The sides of the triangles ar equal to radius of the circle = 9 units.
Area of this sector = pi r^2 * 60 /360
= pi * 9^2 / 6 = 42.412 units^2
Area of the triangle = 1/2 * 9^2 * sin 60 = 35.074 units^2
So the area of the shaded segment = 42.412 - 35.074 = 7.338 unIt^2
AS there are 4 shaded segments the answer is 4 *7.338 = 29.3 units^2