Multiply both numerator and denominator of 
by the complex conjugate of the denominator, -2+9i.
Multiplication can be transformed into difference of squares using the rule: 
.
By definition, i² is -1. Calculate the denominator.
Multiply complex numbers 5-3i and -2+9i in the same way as you multiply binomials.
Do the multiplications in 
.
Combine the real and imaginary parts in -10+45i+6i+27.
Do the additions in 
.
Divide 17+51i by 85 to get 
.
The real part of 
is 
.
Answer:
( 6, pi/6)
Step-by-step explanation:
( 3 sqrt(3), 3)
To get r we use x^2 + y ^2 = r^2
( 3 sqrt(3) )^2 + 3^2 = r^2
9 *3 +9 = r^2
27+9 = r^2
36 = r^2
Taking the square root of each side
sqrt(36) = sqrt(r^2)
6 =r
Now we need to find theta
tan theta = y/x
tan theta = 3 / 3 sqrt(3)
tan theta = 1/ sqrt(3)
Taking the inverse tan of each side
tan ^-1 ( tan theta) = tan ^ -1 ( 1/ sqrt(3))
theta = pi /6
The total revenue for the event would the total amount earned from the tickets sold. So if x people attended the event, then there would be $(161x). We must keep in mind though the the maximum seating is 76 876. That means that the maximum revenue that can be earned must not exceed $(161)(76 867) = .
Hence we have f(x) = 161x where 0 ≤ x ≤ 76867.
From this, we can see that the domain is [0, 76867] while range is [0, 12375587]<span>.</span>
You'll have to c<span>ompass tip on A and draw a small ark with pencil approximately in the middle above AB line, now compass tip to point B and cross the ark you made previously.
Do the same on the opposite side without making any change to the compass
Join the lines where crosses of arks on the both side meet and then ,it's done.</span>
Combinatorial Enumeration. That whole class was a rollercoaster ride of mind-blowing generating functions to prove crazy things. The exam had ridiculous questions like 'count the number of cactus trees with n vertices such that etc etc etc' and you'd do three pages of terrible terrible sums and algebra. Then your final answer would be something beautiful like n/2 and you'd breath a sigh of relief and thank the math gods.
