Answer:
C
Step-by-step explanation:
I substituted the x value with the different options. I kept doing that until the equation made sense.
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➷ Angle XBC = 55 degrees because corresponding angles are equal
b) We already know angle XBC
Angle XCB = Angle XBC because isosceles base angles are equal
Therefore, angle XCB = 55 degrees
Angles in a triangle equal 180 degrees
180 - (55 + 55) = 70
Angle BXC = 70 degrees
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De Moivre's theorem uses this general formula z = r(cos α + i<span> sin α) that is where we can have the form a + bi. If the given is raised to a certain number, then the r is raised to the same number while the angles are being multiplied by that number.
For 1) </span>[3cos(27))+isin(27)]^5 we first apply the concept I mentioned above where it becomes
[3^5cos(27*5))+isin(27*5)] and then after simplifying we get, [243 (cos (135) + isin (135))]
it is then further simplified to 243 (-1/ √2) + 243i (1/√2) = -243/√2 + 243/<span>√2 i
and that is the answer.
For 2) </span>[2(cos(40))+isin(40)]^6, we apply the same steps in 1)
[2^6(cos(40*6))+isin(40*6)],
[64(cos(240))+isin(240)] = 64 (-1/2) + 64i (-√3 /2)
And the answer is -32 -32 √3 i
Summary:
1) -243/√2 + 243/√2 i
2)-32 -32 √3 i
Answer: 11.4
Step-by-step explanation:
area of rect. = 24
area of circle (half circle+half circle = full circle) = pi*r^2 = pi*(2*2) = pi*4 = about 12.57
2 = radius since 4 = diameter
24-12.57 = 11.43
round = 11.4
