[tex]z1=\stackrel{a}{3}+\stackrel{b}{3}i~~ \begin{cases} r = \sqrt{a^2+b^2}\\ r = \sqrt{18}\\[-0.5em] \hrulefill\\ \theta =\tan^{-1}\left( \frac{b}{a} \right)\\ \theta =\frac{\pi }{4} \end{cases}~\hfill z1=\sqrt{18}\left[\cos\left( \frac{\pi }{4} \right) i\sin\left( \frac{\pi }{4} \right) \right] \\\\[-0.35em] ~\dotfill[/tex]
[tex]\cfrac{z1}{z2}\implies \cfrac{\sqrt{18}\left[\cos\left( \frac{\pi }{4} \right) i\sin\left( \frac{\pi }{4} \right) \right]} {7\left[\cos\left( \frac{5\pi }{9} \right) i\sin\left( \frac{5\pi }{9} \right) \right]} \\\\[-0.35em] ~\dotfill\\\\ \qquad \textit{division of two complex numbers} \\\\ \cfrac{r_1[\cos(\alpha)+i\sin(\alpha)]}{r_2[\cos(\beta)+i\sin(\beta)]}\implies \cfrac{r_1}{r_2}[\cos(\alpha - \beta)+i\sin(\alpha - \beta)] \\\\[-0.35em] ~\dotfill[/tex]
[tex]\cfrac{z1}{z2}\implies \cfrac{\sqrt{18}}{7}\left[\cos\left( \frac{\pi }{4}-\frac{5\pi }{9} \right)+i\sin\left( \frac{\pi }{4}-\frac{5\pi }{9} \right) \right] \\\\\\ \cfrac{\sqrt{18}}{7}\left[\cos\left( \frac{-11\pi }{36} \right) +i\sin\left( \frac{-11\pi }{36} \right) \right]\implies \cfrac{\sqrt{18}}{7}\left[\cos\left( \frac{83\pi }{36} \right) +i\sin\left( \frac{83\pi }{36} \right) \right] \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \cfrac{z1}{z2}\approx 0.348~~ + ~~0.496i~\hfill[/tex]
The value of z1/z2 is √18/ 7 (cos ( 11π/36 ) - isin ( 11π/36 )).
What is complex number?"A complex number is the sum of a real number and an imaginary number and it is of the form x + iy and is usually represented by z".
For the given situation,
z1= 3+3i and
z2= 7(cos(5π/9) + i sin (5π/9))
To divide the complex numbers, both should be in same form.
Convert z1 in polar form.
z is of the form x+iy, so, r=[tex]\sqrt{x^{2}+y^{2} }[/tex]
⇒[tex]r=\sqrt{3^{2}+3^{2} }[/tex]
⇒[tex]r=\sqrt{18}[/tex]
θ = [tex]tan^{-1}(\frac{b}{a} )[/tex]
⇒[tex]tan^{-1}(\frac{3}{3} )[/tex]
⇒[tex]tan^{-1}(1)[/tex]
⇒[tex]45[/tex]°
The polar form is of the form, z= r (cosθ + i sinθ),
⇒ z1 = [tex]\sqrt{18}[/tex] (cosπ/4 + isinπ/4)
The formula for dividing complex number is
z1/z2 = r1(cos θ1 + isin θ1) / r2(cos θ2 + isin θ2)
⇒ z1/z2 = r(cosθ + isinθ)
where, r = r1/r2 and θ = (θ1 - θ2)
z1/z2 = [tex]\sqrt{18}[/tex] (cos π/4 + isin π/4) / 7 (cos 5π/9 + isin 5π/9)
⇒ r = [tex]\sqrt{18}[/tex] / 7 and
θ = (π/4 - 5π/9 )
⇒ θ = (-11π/36)
cos(-θ) = cos θ
⇒cos( -11π/36 ) = cos ( 11π/36 )
sin(-θ) = -sin θ
⇒ sin ( -11π/36 ) = -sin ( 11π/36 )
Thus, z1/z2 = [tex]\sqrt{18}[/tex] / 7 (cos ( 11π/36 ) - isin ( 11π/36 ))
Hence we can conclude that the value of z1/z2 is
√18/ 7 (cos ( 11π/36 ) - isin ( 11π/36 )).
Learn more about complex number here
https://brainly.com/question/19612663
#SPJ2
what is the rate of change for these data?
Answer:
-2 gallons per minute
Step-by-step explanation:
As we can clearly see, the water is continuously decreasing every 15 minutes by 30 gallons.
So, the rate of change is -30 gallons per 15 minutes
However, we can simplify this ratio by dividing both sides by 15, so we get
-2 gallons per minute
I need a step by step explanation as well as work
Answer:
x = 2
m = 15/4
a = 5/4
Step-by-step explanation:
When the "base" lines are parallel, all of the triangles are similar. That means corresponding segments are proportional, including corresponding parts of segments.
We see that x corresponds to a partial segment marked 3. That same top-bottom correspondence has another pair of segments marked 2 and 3. That means x=2.
x/3 = 2/3 ⇒ x = 2
__
The segments marked 'm' and 'a' are "whole side" segments, so we need to put those in proportions with corresponding whole sides. If we use the bottom side, we find ...
a/3 = 5/(3+6+3) = 5/12 ⇒ a = 5/4 = 1 1/4 . . . . . multiply by 3
and
m/(6+3) = 5/12 ⇒ m = 15/4 = 3 3/4 . . . . . multiply by 9
__
x = 2
m = 15/4
a = 5/4
At TGI Fridankay's you order a drink for $2.99, an appetizer for $9.99, the cajun chicken pasta for $11.50, and a dessert for $7.99. You had amazing service and know that you are going to tip your waiter 20%! The waiter also gave you a 10% coupon to use. There is also a 7% sales tax on the bill. What is your total bill after the tip, discount, and tax?
The total bill after the tip, discount, and tax is $37.76.
The total cost of the order is reduced by the coupon and increased by the tax paid and tip.
Total cost of the items bought = cost of the drink + appetizer + Cajun + dessert
$2.99 + $9.99 + $11.50 + $7.99 = $32.47
Value of the tip = 20% x $32.47 = $6.49
Cost of the items after the coupon: (100% - 10%) x $32.47
90% x $32.47
0.9 x $32.47 = $29.22
Cost of the items after the tax: (1.07) x $29.22 = $31.27
Total cost of the items = $31.27 +$6.49 = $37.76
To learn more about taxes, please check: https://brainly.com/question/25311567
Mary Alice is making a curtain for her kitchen window. She bought 2 1/12 yards of fabric. Her total cost was $16.
What is the COST PER YARD?
Answer:
7.68$
Step-by-step explanation:
2+(1/12)=2.08
16/2.08=7.68
Answer:
6.4
Step-by-step explanation:
Food fryers manufactured by a company that supplies food trucks can fry a
mean of 132.4 pounds of food per hour with a standard deviation of 3.9
pounds per hour. In a given hour, how much food would 99.7% of these fryers
fry?
A. 124.6 pounds per hour to 140.2 pounds per hour
B. 128.5 pounds per hour to 136.3 pounds per hour
C. 120.7 pounds per hour to 144.1 pounds per hour
D. 116.8 pounds per hour to 148.0 pounds per hour
Answer:
Correct Answer is C. 120.7 pounds per hour to 144.1 pounds per hour.
Step-by-step explanation:
Just took the Quiz <3
Frederico's checking account balance is -$15, and Neela's checking account balance is -$285. How many times the balance of Frederico's checking account is Neela's checking account balance? A. -19 B. -270 C. 270 D. 19
Answer:
2
Step-by-step explanation:
the answer is 2 because I need points for my brainly so I can get a 100 on this assignment
1. The total amount of what you eam during the pay period before taxes and deductions are taken out is known as what?
Wage
Net pay
Salary
Gross pay
Answer:
net pay if im not mistaking
Step-by-step explanation:
Directions: Simplify the following expressions. 1. (3x-10)² 6. (-15y + 3)² 7. (q-2r) (q + 2r) 8. (m-6)³ 9. (u−5)(u+ 5) 10. (x + 2) ³ 2. (12az-11b)² 3. (3b² + 2v) ( (3b²-2v) 4. (2v + 3w)³ 5. (2t+4y) (41²-8ty + 16y2)
Answer:
1. 9x^2-60x+100
6. 225y^2-90y+9
7. q^2-4r^2
9. u^2-25
10. x^3+6x^2+12x+8
2. 144a^2z^2-264abz+121b^2
3. 9b^4-4v^2
4. 8v^3+36^2w+54vw^2+27w^3
5. -16t^2y+64y^3+3362t+6724y
Step-by-step explanation:
There you go
Question 1: Whose percentage increased more from 1984 to 2014, males or females? By how much more did it increase?
My Answer: Between 1984 to 2014 males diagnosed with diabetes increased more than females. The number of males diagnosed with diabetes increased more than .9% compared to females.
Help my teacher said it was wrong
The percentage increase are applied to the number of male and female
from the previous period.
From 1984 to 2014, the percentage of females increased more than males.Reasons:
Let F represent the initial number of females and let M represent the initial number of males before 1984.
We have;
In 1984
Number of females = F × 1.026 = 1.026·F
number of males = M × 1.031 = 1.031·M
In 1994
Number of females = 1.026·F × 1.032 = 1.058832·F
Number of males = 1.031·M × 1.032 = 1.063992·M
In 2004
Number of females = 1.058832·F × 1.056 = 1.118126592·F
Number of males = 1.063992·M × 1.049 = 1.116127608·M
In 2014
Number of females = 1.118126592·F × 1.066 = 1.191922947072·F
Number of males = 1.116127608·M × 1.059 = 1.181979136872·M
Therefore, between 1984 and 2014, we have;
The percentage increase of females = 1.191922947072 × 100 - 100 ≈ 19.2%
The percentage increase of males = 1.181979136872 × 100 - 100 ≈ 18.2%
Therefore;
The percentage increase of the females is more than the males by (1.191922947072 × 100 - 100) - (1.181979136872 × 100 - 100) ≈ 0.994%
Learn more about percentages and compounded percentages here:
https://brainly.com/question/3783619
https://brainly.com/question/1301322
Plz help me NOW I will mark u brainliest
[tex]m\% \: \: of \: \: p\% \: \: of \: \: n \\ = \frac{m}{100} \times \frac{p}{100} \times n \\ = \frac{m \times p \times n}{100 \times 100} \\ = \frac{mnp}{10000} [/tex]
Hope you could get an idea from here.
Doubt clarification - use comment section.
find the discriminant of -2x^2+8=x^2-28
Answer:
If I'm not wrong I think the answer should be (-28)
A table of values of a linear function is shown below. Find the output when the input is n.
Answer:
Step-by-step explanation:
output = y
input = x
y=-2x + 3
if you follow the pattern, the next input is 5 which will output -7
Which term of the AP 21, 42, 63, 84, ..... is 210 ?
Answer:
The 10th term
Step-by-step explanation:
As we see these are all incrementing by 21 (and divisible by 21), we can divide all the terms by 21 and get 1, 2, 3, ...., 10
Therefore 210 is the 10th term.
Answer:
The 10th term is 210
Step-by-step explanation:
Let's revise our tables of 21.
21 x 1 = 2121 x 2 = 4221 x 3 = 6321 x 4 = 8421 x 5 = 10521 x 6 = 12621 x 7 = 14721 x 8 = 16821 x 9 = 18921 x 10 = 210Therefore, the 10th term will give 210.
Hoped this helped.
Which values from the given replacement set make up the solution set of this inequality?
5m≤10; {0, 2, 4, 6}
{0, 4, 6}
{2}
{0, 2}
{2, 4, 6}
Answer:
the solution to the inequality is m[tex]\leq[/tex] 2, so the solution set can include 2 and 0 since it is less then 2. but the rest do not work. so the answer is {0,2}
Step-by-step explanation:
5m[tex]\leq[/tex]10
divide by 5 on both sides and you are left with
m[tex]\leq[/tex]2
only 2 and 0 are less than or equal to 2
Hope this helps!
Five and 1/3÷2 2/3 simplified
Answer:
5 1/3 ÷ 2 2/3
Write both mixed fractions (whole number in front of fully-reduced fraction) as improper fractions (numerator is larger than denominator).
5 1/3 = 16/3
2 2/3 = 8/3
16/3 ÷ 8/3
When dividing, switch the numerator and the denominator of the fraction after the division sign and change the division sign to a multiplication sign.
16/3 x 3/8
Multiply.
16/8
Divide by 8.
2
Hope this helps! :)
AYO y'all can someone help wit this question urgent?
the amount in Maddies back account can be written ad a function of time. What is the equation for maddies bank account?!?
Answer:
I think this is right lol
Step-by-step explanation:
f(x)=49+x
) The price of broccoli is $1.25 per pound. Let y be the total cost in dollars of buying a pounds
of broccoli
.) Which equation represents this situation?
y = 1.252
• Which graph represents the situation?
Broccoli Prices
Broccoli Prices
Broccoli Prices
(4,5)
.
(3.4.5)
15
15
(5.
(3.3.75
(2,3)
(3.75,3)
(2.2.5)
3
5 25
8 2
(2.5.2
1.5 (1.1.25)
(1.1.5)
(0.5, 0.75)
(1.25.1)
0.5
0.5
0 05 1 1.5 2 25 3 3.5 4 US 5
Amount of Broccoli (b)
0 0.5 1 1.5 2 2.5 3 3.5 4 155
Amount of Broccoli (b)
0 05 1 15 2 2.5 3 3.5 5 5
Amount of Broccoli (b)
DONE
Answer:
The graph that represents the situation is A
Step-by-step explanation:
What is the vertical shift for the absolute value function below f(x) =9 |x+1|+2
Answer:
Slide UP 2
Step-by-step explanation:
In the equation,
f(x) = 9|x+1| + 2
There are three transformations of the parent function f(x)=|x| (this is the simplest form of this function, it's a v-shaped graph)
The 9 in front will vertically stretch the graph and make it look like a "skinny" v-shaped graph.
The +1 in close to the x inside the absolute value bars |x+1| will shift (slide) the graph to the left (it's the opposite of what you might think-- 'plus' shifts the graph left and 'minus' shifts the graph right)
The +2 at the end is the transformation you're looking for. It slides the graph as you would expect UP 2 units. If it was a minus it would shift the graph down instead.
The total length of 3 pipes is 24 inches. The middle-sized pipe is 6 inches longer than the smallest. The largest is twice as long as the smallest. How long is the middle-sized pipe?
Answer:
18
Step-by-step explanation:
let the be x
if the middle sized pipe is 6 inches longer than the smallest.
so 24 subtract from 6=18
A ant runs 45 inches in 15 seconds, a snail crawls 12 inches in 3 seconds. Who is faster? I need help please and thank you :)
Answer:
the snail
Step-by-step explanation:
in order to find who is faster you have to find how many inches each one does in one sec
Ant= 45/15 which is 3 inches per sec.
snail=12/3 which is 4 inches per sec.
so from the above calculations we can see that according to the question given a snail crawls faster than an ant runs
I hope this helps
round the following number to the nearest ten 7377.38?
Answer:
7377.4
Step-by-step explanation:
152 feet in 16 seconds
Answer:
I'm not sure what you're asking but that is 9.5 feet per second.
Step-by-step explanation:
152÷16=9.5
Answer:
if you are asking about the unit rate it is 9.5 feet per second
Step-by-step explanation:
You just have to do 152/16
hope this helps
A box contains 7 green marbles, 10 blue marbles, and 5 red marbles. Three marbles are selected at random from the box, one at a time, without replacement. Find the probability that two of the marbles selected are green and the other marble is red.
Answer:
5/253
Step-by-step explanation:
The first green is 7/23, the second is 6/22 and the red is 5/21. Multiply them together for 5/253.
what the area of a triangle whose base is 23 inches and whose height is 28. write your answer in decimal
Answer:
322
Step-by-step explanation:
Triangle area = base*height)2Here, area = 23*28/2=322
Answer:
322 [tex]in^{2}[/tex]
Step-by-step explanation:
Hope this helped!
Line f is parallel to line g.which statements about line f and g is true
Answer:
Step-by-step explanation:
They have different y intercepts.
They have the same slope.
Here are 2 examples
y = 3x + 5
y = 3x + 19
The slopes are both three. The y intercepts are 5 for the top equation and 19 for the bottom equation.
They are both lines. That means their domain is -infinity <x < + infinity
Their range is - infinity <y < + infinity.
We are excluding examples like x = 3 and x = 5 and y = 1 and y = 3.
It is true that they both are parallel in both cases, but the discussion for each pair is a little different.
What is correct answer For this problem
The table shows how the length of a fish changes over time.
Which equation represents the relationship between x, the time in years, and y, the length in centimeters?
Question options:
x = 4.5y
x = 9y
y = 4.5x
y = 9x
Answer:
C. y=4.5x
Step-by-step explanation:
divide y by x
5x + 3y = 18 solve for y
[tex]5x+3y = 18\\\\\implies 3y = 18 -5x\\\\\implies y = \dfrac 13(18-5x) = 6 - \dfrac 53 x[/tex]
Answer:
y=18-5x/3
Step-by-step explanation:
Hope this helps~
Have a great day
Zero
A hardware store mixed 7 gallons of red paint with every 11 gallons of blue paint to make purple paint. Which ratio of gallons of red paint to gallons of blue paint will make the same shade of purple paint?
Answer:
2 b + 6 r = 2 * 24
5 b + 3 r = 2 * 21 ... 10 b + 6 r = 84
subtracting equations (to eliminate r) ... 8 b = 36
solve for b , then substitute back to find r
HELP ME PLEASEEEEEEE I WILL GIVE POINTS AND BRAINLIEST
please HELPPP!!!!!!!!!!!!!!!!
Answer:
40,44,48,52
Step-by-step explanation:
These are multiples of 4 because 4 can be multiplied into all of them like
4x11=44
4x10=40
4x12=48
4x13=52