Given the complex number z_1=3\big(\cos \frac{14\pi}{15} +i\sin \frac{14\pi}{15}\big)z 1 =3(cos 15 14π +isin 15 14π ) and z_2=3\sqrt{3}\big(\cos \frac{11\pi}{15} +i\sin \frac{11\pi}{15}\big)z 2 =3 3 (cos 15 11π +isin 15 11π ), express the result of z_1z_2z 1 z 2 in rectangular form with fully simplified fractions and radicals.
The product of z₁ = 3 · (cos 14π/15 + i · sin 14π/15) and z₂ = 3 √3 · (cos 11π/15 + i · sin 11π/15) in rectangular form with fully simplified expressions is z₁ · z₂ = 7.794 - i · 13.5.
How to determine the product of two complex numbers
Let be two numbers of the form z = a + i · b, where i = √-1, the product of two of these numbers in rectangular form is described by the following formula:
z₁ · z₂ = (a + i · b) · (c + i · d) = (a · c - b · d) + i · (a · d + b · c) (1)
If we know that a = 3 · cos 14π/15, b = 3 · sin 14π/15, c = 3√3 · cos 11π/15, d = 3√3 · sin 11π/15, then the result in rectangular form is:
z₁ · z₂ = 7.794 - i · 13.5
The product of z₁ = 3 · (cos 14π/15 + i · sin 14π/15) and z₂ = 3 √3 · (cos 11π/15 + i · sin 11π/15) in rectangular form with fully simplified expressions is z₁ · z₂ = 7.794 - i · 13.5. [tex]\blacksquare[/tex]
Remark
The statement presents typing mistakes and is poorly formatted, the correct form is introduced below:
Given the complex number z₁ = 3 · (cos 14π/15 + i · sin 14π/15) and z₂ = 3 √3 · (cos 11π/15 + i · sin 11π/15), express the result of z₁ · z₂ in rectangular form with fully simplified fractions and radicals.
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PLEASE HELP 50 POINTS OLUS BRAINLY
Answer: 4n-7
Step-by-step explanation:
HELP PLSS I NEED TO TURN IN RIGHT NOW!!!!
Mr. Foster wants to put a new carpet on the floor of his rectangular playroom. The playroom is 27 ft long and 18 ft wide. He has found an inexpensive carpet that is priced $14 per sq yd. What would be a reasonable price for enough carpet to cover the floor of his playroom?
Answer: $756
Step-by-step explanation:
convert feet to yards
1 yard = 3 feet
27 ft = 9 yards
18 ft = 6 yards
carpet represents area
area = length x width
area = 9 x 6
area = 54 yards^2
$14 for 54 yards^2 = 14 x 54
14 x 54 = 756
$756
1. What is the area of the triangle? (Area of triangle = 1/2*b*h)
2. What is the area of the semicircle? Round your answer to the nearest tenth (Area of circle = 3.14 *r^2)
1. The area of the triangle = 40 m².
2. The area of the semicircle = 64.3 m²
What is the Area of a Triangle?Area = 1/2(base × height)
What is the Area of a Semicircle?Area = 1/2(πr²)
1. Area of the Triangle = 1/2(base × height) = 1/2(10 × 8)
Area of the triangle = 40 m².
2. Use Pythagorean Theorem to find the hypotenuse of the triangle which is the diameter of the semicircle.
Hypotenuse = √(10² + 8²) = 12.8 m
Radius of the semicircle = 12.8/2 = 6.4 m
Area of the semicircle = 1/2(3.14 × 6.4²) = 64.3 m²
Learn more about the area of triangle and semicircle on:
https://brainly.com/question/12229862
1/4*3/4=what is the answer
Answer:
3 over 8
3
8
=0.375
Step-by-step explanation:
PLEASE HELP!!!
Write an expression using fractions to show how to determine the amount that each person will pay?Then calculate each person's contributions showing all steps in long division.
my chart:
jazzy: 35.7$
emily:48.9$
sarah:48.9$
layla:19.3$
total amount: 327$
________________________________________________________
SolveTo solve this problem, we must add each price together for the total.
[tex]4.26 + 9.76 + 6.33 + 14 = 34.35\[/tex]
To calculate our total store profits while finding the four contributions, we could divide by percent. For this case, 6%, also equal to 0.06
[tex]\frac{(estimate)34}{6\%(0.06)} = 573(estimate)[/tex]
Now that we have 573 as our estimate, subtract 573 by 34
[tex]573 - 34 = 539[/tex]
Therefore, the store's total profits were 573 dollars, and the four contributions from Jane, John, Zoey, and Hailey contributed to 34 dollars of it.
________________________________________________________
SolvedWe made 573$ total! That is a lot.Note that using percent and division was actually to calculate the store's total profits followed by the four contributions listed earlier. If any of this confuses you, please feel free to ask a question.________________________________________________________
Questions?Ask in the comments box.
pls i need the answer rightnow pls pls pls im begging you pls
Answer:
20 -- 300 words
25 -- 600 words
30 -- 900 words
35 -- 1200 words
40 -- 1500 words
50 -- 2100 words
3) 600 words
4) 2100 words
5)No because the formula only accounds for ages between 20 and 50 months.
Brainliest would be appreciated
Step-by-step explanation:
How many solutions are there to the equation below?
x2 = 16
O A. 2
B. 16
C. 1
O D.O
E. 4
Answer:
A.2
Step-by-step explanation:
x² = 16
take the square root of both sides
x = ±4
there are 2 solutions to the equations, those 2 solutions being 4 and -4
just to double check
4² = 4 × 4 = 16
-4² = -4 × -4 = 16
Teresa is loading her car with boxes that each weigh 4 3/4 pounds. If Teresa loads 9 of theses boxes find the combined weight of each box
Total weight:-
9(19/4)171/442-3/4lbsmultiplication problem
Answer:
No, that is incorrect.
When doing a multiplication problem, you cannot simply take out a number from a number and expect the same result. This is under some circumstances. Let's solve the equations to see the results.[tex]21 * 34 = 714\\20 * 35 = 700[/tex]
As shown in the expressions, the results differ, proving our theory from earlier.__________________________________________________________
Questions?Ask me in the comments box, please.
For which inequality is x = 5 a solution
Answer:
4<x<6
Step-by-step explanation:
4 is smaller than x
and x is samller than 6
so its 5
Frank bought 20 pounds of sugar for $10. How many pounds of sugar did he get per dollar?
Answer:
$2
Step-by-step explanation:
20lb divided by $10.
20 divided by 10 is 2
PLEASE HELP ASAP
Reginald Wallace's gross weekly salary is $515. His weekly federal withholding is $55. The Social Security tax is 6.2% of the first $97,500 he earns. The Medicare tax is 1.45% of gross pay. The state tax is 1.5% of gross pay. Each week he pays $12.40 for medical insurance. How much is deducted from Reginald's weekly wages for state tax and Medicare tax?
Answer:
$15.20
Step-by-step explanation:
Had the same question last year and found the answer in some flashcards. You can browse the question too.
Plot the image of triangle AABC under a reflection across the y-axis.
Answer:
(6,4) (4,4) (2,3) or (2,2)
Step-by-step explanation:
hope it helps
¿Qué significa un punto en el diagrama de líneas?
un punto en un gráfico de líneas es un valor específico que normalmente es un valor de entrada y salida (x)
Circumference of the circle
Answer:
37 5/7
Step-by-step explanation:
use formular it will be 2pie -22/7 ×radius
since we have been given only radius it will be
2×22/7×6=37 5/7
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Let's find the circumference of given circle ~
Circumference :
[tex] \qquad \tt \dashrightarrow \: 2\pi{r}^{} [/tex]
where, r = radius
Now, let's calculate it ~
[tex] \qquad \tt \dashrightarrow \: c = 2×\pi{}^{}×6 [/tex]
[tex] \qquad \tt \dashrightarrow \: c = 12\pi\: \: m[/tex]
That's the answer I terms of π, but we can also plug in the approximate value of pi as 3.14
[tex] \qquad \tt \dashrightarrow \: c = 12 \times 3.14{}^{} [/tex]
[tex] \qquad \tt \dashrightarrow \: c = 37.68\: \: m[/tex]
[tex] \qquad \tt \dashrightarrow \: c \approx 37.7\: \: m[/tex]
Please help!!! I'm struggling
Step-by-step explanation:
please mark me as brainlest
Answer:
I hope it helped you
Step-by-step explanation:
Pls refer the given attachment
PLEASE HELP PLEASE PLEASE HELP
Answer:
[tex]\frac{1}{4}*\frac{25}{25} = 25/100[/tex]=25%
Step-by-step explanation:
I WILL MARK BRAINLIEST
Is an antacid polar or non-polar?
Answer:
Antacid tablets react with water but not oil so its polar
Identify the type of polynomial
3x2 + 2x +1
A recent survey found that 5% of the population of the United States is unemployed. If Charlotte, North Carolina, has 30,850 unemployed, what is the population of Charlotte?
The population of Charlotte, North Carolina is approximately_____?
Answer:
617000
Step-by-step explanation:
Division reverses multiplication.
If the total population of Charlotte which we'll call 'x' follows
x * 0.05 = 30850, then
30850 / 0.05 = x
x = 617000
I NEED HELP ASAP
Solve.
4x + 2(3x – 9) = x
A.
x = –2
B.
x = 1.8
C.
x = 2
D.
x = 18
Answer:
x=2
Step-by-step explanation:
[tex]4x+2(3x-9)=x\\\\\implies 4x +6x - 18 -x =0\\\\\implies 9x = 18\\\\\implies x = \dfrac{18}9 = 2[/tex]
Find the interest rate for a principal of $9442 and charged $30233 in interest for 18 years.
Evaluate
A)9
B)-9
c) 729
d) -729
The correct option is c) 729
Explanation :-
[tex] \frac{1}{ {3}^{ - 2} {x }^{ - 4} {y}^{2} } [/tex][tex] = \frac{ {3}^{2} {x}^{4} }{ {y}^{2} } [/tex]Now , we just need to substitute " x = 3 " and " y = -1 " in the equation above.
[tex] ⇢ \frac{ {3}^{2} {(3)}^{4}}{ {( - 1)}^{2} } [/tex][tex] = \frac{3 \times 3 \times 3 \times 3 \times 3 \times 3}{( -1) \times ( - 1)} [/tex][tex] = \frac{729}{1} [/tex][tex] = \underline { \boxed{ 729}}[/tex]
Which of the following is equivalent to (x + 1)^2 ?
x2 + 2x + 1
x2 + 1x + 1
x2 + 1
x2 + 1x
Answer:
x^2 +2x +1
Step-by-step explanation:
(x+1)^2
=(x+1)(x+1)
= x×x+x×1+1×x+1×1
=x^2+x+x+1
=x^2+2x+1
Find the measure of each angle.
x - 7
X
x + 10
Answer:
x - 7: 52
x: 59
x + 10: 69
Step-by-step explanation:
Since we have a straight line, we know that the angles must add up to 180. We can set up an equation to solve:
x - 7 + x + x + 10 = 180
Combine like terms:
3x + 3 = 180
Subtract 3 on both sides:
3x = 177
Divide by 3 on both sides:
x = 59
Now plug in 59 for each angle.
The "x - 7" angle should equal 52, the "x" angle should equal 59, and the "x + 10" angle should equal 69.
Answer:
52°, 59°, and 69°
Step-by-step explanation:
Each of these angles add up to make a straight line, or = 180°
(x - 7) + x + (x + 10) = 180
3x + 3 = 180
3x = 177
x = 59
Angle A = 52°
Angle B = 59°
Angle C = 69°
52 + 59 + 69 = 180!
(2ax -6by + 4cz )+ (4by-14ax)+(9cz-4ax-6by) add the following expression pls i will mark you a brainest
Answer:
=2ax -6by +4cz + 4by -14ax +9cz -4ax -6by
=2ax -14ax -4ax -6by +4by -6by +4cz +9cz
= -16ax -8by +13cz
A local farmer decides to sell his produce at the farmer's market. Every Sunday he uses his own fuel to drive
to the market which is 300km away. This costs him R650.00 per week. He sells 50 boxes of fruit for R250.00
and 100 boxes of fruit for R350.00.
What is the dependent variable in this scenario?
Answer:
The money
Step-by-step explanation:
The drive to the farmers market is a certain distance away, which costs him a specific amount of money. If the distance were to change, then so would the price it took to get there per week. Additionally, as the amount of boxes increases, so does the price.
A dependent variable is a variable that directly changes as the independent variable(s) change. In this scenario, the money, or cost is what's changing based on other factors.
hope this helps :)
which term describes the point where the three medians of a triangle intersect?
Answer: It is the centroid of a triangle or A. Centroid
Step-by-step explanation:The centroid of a triangle is the intersection of the three medians of the triangle (Where each median connecting a vertex with the midpoint of the opposite side)
The incenter of a triangle is the point where the angle bisectors of the all vertices of the triangle intersect.
The orthocenter of the triangle is the point where all three altitudes of the triangle intersect. where An altitude is a line which passes through a vertex of the triangle and is perpendicular to the opposite side.
The circumcenter of the triangle is the point where the perpendicular bisector of the sides of the triangle intersect.
Help me please !!!!!!
Answer; hi sisters daddy chill
Step-by-step explanation:
