Express √3 + i in polar form:
|√3 + i| = √((√3)² + 1²) = √4 = 2
arg(√3 + i) = arctan(1/√3) = π/6
Then
√3 + i = 2 (cos(π/6) + i sin(π/6))
By DeMoivre's theorem,
(√3 + i)³ = (2 (cos(π/6) + i sin(π/6)))³
… = 2³ (cos(3 • π/6) + i sin(3 • π/6))
… = 8 (cos(π/2) + i sin(π/2))
… = 8i
Answer:
Step-by-step explanation:
Well, a series in math is simply the sum of the various numbers, or elements of a sequence. For example, to make a series from the sequence of the first five positive integers 1, 2, 3, 4, 5, just add them up. So, 1 + 2 + 3 + 4 + 5 = 15 is a series.
that all what i know i am really sorry bro but that is what i understand !
Answer:
468.4 meters
Step-by-step explanation:
Find the width of the rectangle.
The area of a rectangle is A=length*width. Substitute the values of length and area and solve for width.
A=length*width
8,400=140*width
60= width
Use the width of the rectangle to find the circumference of the semicircles. Since each semicircle is half of a circle, the perimeter of the two semicircles is equal to the circumference of one circle.
The circumference of a circle is equal to pid, where d is the diameter. The diameter of the semicircle is the same as the width of the rectangle.
So, the diameter is 60 meters. Substitute the diameter into the formula for the circumference and simplify using 3.14 for pi.
≈188.4
(2 times 140)+ 188.4
So, the perimeter of the track is 468.4 meters.
Answer:
176.625 sq.ft, 4.8 sq.ft
Step-by-step explanation:
Area of circle=πr^2 or πd^2/4
11. Given,
d=15 ft
Now,
Area=πd^2/4
3.14*15^2/4
176.625 ft^2
Therefore, the area approximation is 176.6 sq.ft
12.
Given,
d=3.5 ft
Now,
Area= πd^2/8
3.14*3.5^2/8
4.8 sq.ft
I got the answer by dividing the area of circle by 2 as semicircle is half of circle.
Answer:
x = 18°
y = 6
Step-by-step explanation:
in a parallelogram:
Any two opposite sides are congruent
and any two opposites angles are congruent:
then
y + 4 = 10
and 3x = 54
then
y = 6
and x = 54/3 = 18
