Write the following complex number in rectangular form. 6(cos π/ 4+ isin π/ 4)
6(cos π/ 4 + i sin π/ 4) =
(Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression. Type your answer in the form a+bi. Rationalize all denominators.)
Answers
[tex]\stackrel{\textit{complex form}}{\stackrel{\stackrel{r}{\downarrow }}{6}\left[ \cos\left( \frac{\pi }{4} \right) +i\sin\stackrel{\stackrel{\theta }{\downarrow }}{\left( \frac{\pi }{4} \right)} \right]}\implies 6\left[ \frac{\sqrt{2}}{2}+i\frac{\sqrt{2}}{2} \right]\implies \cfrac{6\sqrt{2}}{2}+i\cfrac{6\sqrt{2}}{2} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \stackrel{\textit{rectangular form}}{\stackrel{\stackrel{a}{\downarrow }}{3\sqrt{2}}+\stackrel{\stackrel{b}{\downarrow }}{3\sqrt{2}}i}~\hfill[/tex]
Related Questions
if a triangle perimeter=150cm, side A=86cm, side B=50cm, then side C=__.
Answers
Answer:
150-86-50=14cm
Step-by-step explanation:
Answer:
C=14cm
150-86-50= 14
Step-by-step explanation:
Ms. McCullough bought a bunch of bananas. If she ate 2/8
the bananas and Mrs. Byrd ate 1/4, what fraction of bananas
remains?
Answers
Answer:
1/2
Step-by-step explanation:
that's the answer because 2/8-1/4 is 1/2
Lucas invests $2000 per year in his retirement account for 40 years in an investment with an average annual return of 10%. Approximately how much will he have after 40 years?
A.$88,000
B.$176,000
C.$312,000
D.$975,000
Answers
The amount Lucas would have in his account is $885,000.
The formula that would be used to determine the amount of money Lucas would be in 40 years is:
The formula for calculating future value = A x annuity factor
Annuity factor = {[(1+r)^n] - 1} / r
Where:
A = amount invested each year = $2000r = interest rate = 10%n = number of years = 40 years$2000 x [(1.1^40 - 1) / 0.1] = $885,000
To learn more about future value, please check: https://brainly.com/question/14640433
Two sides of a triangle measure 10 feet and 14 feet. Which
inequality shows the possible lengths for the third side, x?
Answers options:
10 ≤ x ≤ 14
4 ≤ x ≤ 24
10 < x < 14
4 < x < 24
Answers
[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
The third side of the Triangle should be greater than the difference of other two sides, so
[tex]x > 14 - 10[/tex][tex]x > 4[/tex]And, The third side should be less than the sum of other two sides that is ~
[tex]x < 14 + 10[/tex][tex]x < 24[/tex]Considering these two inequalities, we get ~
[tex]4 < x < 24[/tex]help me w differentiation
Answers
Answer:
4 better inbox
Step-by-step explanation:
Avery read 1.75 pages in to of an hour. At what rate, in pages per hour, did she read?
On the double number line below, fill in the given values, then use multiplication t
find the missing value. Enter your answers as fractions, whole numbers, or decimals.
pages
o
O
hours
Enter your final answer as a whole number or decimal.
Answers
Answer:
10.5? sorry if it doesnt work
Step-by-step explanation:
Help please!!!!!!!!!!!!!!
Answers
Answer:
Negative
Step-by-step explanation:
Slope is negative since as x increases, y decreases.
с
6
D
15
8
B
?
А
1) Find the missing side length.
es
A) 14
B) 16
18
D) 20
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its
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3
Answers
Answer:
The answer would be 19
Step-by-step explanation:
Using pythagoras theorem
15+6= 21
a^2+b^2= c^2
In this scenario,
c^2-a^2= b^2
Meaning it would be 21^2+8^2
= 377
Square root of 377 would be 19.416
?= 19.416
The missing side length of the right angle triangle is 20
How to solve missing sides using Pythagoras theoremPythagoras theorem States that the square of the longest side of a triangle is equal to the sum of the square of the opposite side and no square of the adjacent side.
The diagram is a right angle triangle with sides AB, BC and CA.The longest side is BCBC² = AB² + CA²
(15 + 6)² = x² + 8²
21² = x² + 8²
21² - 8² = x²
441 - 64 = x²
377 = x²
find the square root of both sidesx = √377
x = 19.41648783894759891856148511263886343
Approximately to the nearest whole number
= 20
Learn more about Pythagoras theorem:
https://brainly.com/question/654982
A parabola can be drawn given a focus of (1,-3) and a directrix of x=9, what can be said about the parabola?
Answers
Check the picture below.
well, we can say that since its directrix is a vertical line, the parabola opens horizontally, the focus point is at the left of the directrix thus it opens leftwards, ithas a vertex at (5,-3), recall that the vertex is half-way between the focus point and the directrix.
Miles is 33 year old and single in 2020 his only income consisted of $10500 in wages what is the maximum amount he can contribute to a traditional ira for 2020
Answers
Answer:
$6,000
Step-by-step explanation:
$6,000 Because miles younger than 50
You weigh a group of eight kittens for 6 days and get the following data (in lb.):
1.6, 1.4, 1.1, 1.8, 1.3, 1.8, 1.2, 1.4
Select the correct average weight. Round your answer to one decimal place.
1.8 lb.
1.8 lb.
1.1 lb.
1.1 lb.
1.5 lb.
1.5 lb.
1.4 lb.
Answers
Answer:
1.5
Step-by-step explanation:
Emilia waited 11 minutes for the bus today. That is 4 minutes less than she waited yesterday. How long did Emilia wait for the bus yesterday?
Answers
11 minutes + 4 minutes more yesterday = 15 total minutes
Answer: 15 minutes
Answer:
Emilia waited 11 minutes wich was 4 minutes earlier so 11+4 because it was 4 miutes earlier so 11 minutes + 4 minutes = 15 minutes so this means Emilia wait 15 minutes for the bus yesterday
Step-by-step explanation:
graph the solution of the inequality 2.25k≤−9
Answers
Answer:
Wouldn’t negative 9 be the inequality because its less than 2.25
Step-by-step explanation:
Hey budddy if i got this wrong im soooooo, sorry
In which quadrant does the point (13 , -6) lie?
A.
Quadrant III
B.
Quadrant I
C.
Quadrant IV
D.
Quadrant II
Answers
Answer:
C
Step-by-step explanation:
i hope you'll find these useful......
Answer:
C, quadrant IV
Step-by-step explanation:
The X (13) is positive meaning the point is on the right side of the graph, and Y (-6) is negative so it's below the x axis
When asked to factor the trinomial 8x^2-8x-16) a student gives the answer (X - 2)(x + 1). What is one thing wrong with this answer? - A. 8 is also a factor of this trinomial B. The minus sign should be a plus sign C. The factors are not simplified D. There is nothing wrong with the answer
Answers
Answer:
8 is also a factor of this trinomial
Step-by-step explanation:
What is the Nth term rule of the Quadratic sequence -5 -4 -1 4 11 20 31
Answers
Step-by-step explanation:
an = A×n² + B×n + C
a1 = -5 = A×1² + B×1 + C = A + B + C
a2 = -4 = A×2² + B×2 + C = 4A + 2B + C
a3 = -1 = A×3² + B×3 + C = 9A + 3B + C
a2 - a1 = -4 - -5 = 1 = 4A+2B+C-A-B-C = 3A + B
3A = 1 - B
A = (1 - B)/3
a3 - a2 = -1 - -4 = 3 = 9A+3B+C-4A-2B-C = 5A + B
3 = 5A + B = 5(1 - B)/3 + B
9 = 5(1 - B) + 3B = 5 - 5B + 3B = 5 - 2B
4 = -2B
B = -4/2 = -2
A = (1 - -2)/3 = (1 + 2)/3 = 3 / 3 = 1
-5 = A+B+C = 1 - 2 + C = -1 + C
-4 = C
so,
an = n² - 2n - 4
Need help with 17 pre college
Answers
Prepare a mixture of 100g of 8% cream into 200g of 3% cream. What is the resulting concentration?
Answers
Answer:
14=300X
X=14/300
X=.04667 OR 4.67%
Step-by-step explanation:
100*.08+200*.03=(100+200)X
8+6=300X
14=300X
X=14/300
X=.04667 OR 4.67% SOLUTION ANS.
If this process is wrong, let me know
Please help me I need to turn this in very soon
Answers
Answer:
1331/3375
Step-by-step explanation:
(11/15) ^3 = (11*11*11)/(15*15*15) =1331/3375
cho a,b,c là các số nguyên. Chứng minh rằng nếu a mũ 3 + b mũ 3 + c mũ 3 chia hết cho 9 thì một trong các số a , b ,c chia hết cho 3
Answers
Answer:
let a, b, c be integers. Prove that if a to the power 3 + b to the power 3 + c to the power 3 is divisible by 9, then one of the numbers a , b , c is divisible by 3
Step-by-step explanation:
Adult tickets to the fall play cost $8 and student tickets cost $4 . The drama class sold 30 more adult tickets than student tickets to the fall play. If the class collected $840 from ticket sales, how many adult tickets were sold?
The drama class sold blank adult tickets.
Answers
Answer:
60 adult tickets were bought.
Step-by-step explanation:
9514 1404 393
Answer:
80 tickets
Step-by-step explanation:
Let 'a' represent the number of adult tickets sold. Then a-30 is the number of student tickets sold. The total revenue is ...
8a +4(a -30) = 840
12a -120 = 840 . . . . . . eliminate parentheses
a -10 = 70 . . . . . . . . . divide by 12
a = 80 . . . . . . . . . . . add 10
The drama class sold 80 adult tickets.
__
Check
The number of student tickets was 30 less, so 50 student tickets. The total revenue was ...
50($4) +80($8) = $200 +640 = $840 . . . . as required
how do you do 4 3/16 + 1 1/10?
Answers
Answer:
5 23/80
Step-by-step explanation:
First, you need to find the least common multiple of 16 and 10 to add the fractions. The LCM of 16 and 10 is 80. You have to multiply 5 to 16 to get 80 and 8 to 10 to get 80, so you also multiply the numerator by those numbers. In the end you would get 4 15/80+1 8/80, which equals 5 23/80.
Select all the statements that show correct reasoning for finding 14/15÷7/5 Group of answer choices Multiplying 1415 by 5 and then by 17. Multiplying 1415 by 5 and then dividing by 7. Dividing 1415 by 5, and then multiplying by 17. Multiplying 1514 by 7 and then dividing by 5. Multiplying 14/15 by 7 and then multiplying by 15.
IF YOUR ANSWER IS INCORRECT OR BS I WILL GIVE YOU 0 STARS AND TAKE MY POINTS BACK!!!!!
Answers
Answer:
Option BStep-by-step explanation:
Correct way of dividing fractions:
14/15 ÷ 7/5 = 14/15 × 5/7Answer choices
A) Multiplying 14/15 by 5 and then by 17. FALSEB) Multiplying 14/15 by 5 and then dividing by 7, TRUEC) Dividing 14/15 by 5, and then multiplying by 17. FALSED) Multiplying 15/14 by 7 and then dividing by 5. FALSEE) Multiplying 14/15 by 7 and then multiplying by 15. FALSELet's see
[tex]\\ \sf\longmapsto \dfrac{14}{15}\div \dfrac{7}{5}[/tex]
[tex]\\ \sf\longmapsto \dfrac{14}{15}\times \dfrac{5}{7}[/tex]
[tex]\\ \sf\longmapsto \dfrac{70}{105}[/tex]
[tex]\\ \sf\longmapsto \dfrac{2}{3}[/tex]
A shirts costs $20, the cost of the shirt increases 30%, what is the price of the shirt now?
Answers
Answer: 10
Step-by-step explanation:
Pre college need help
Answers
Answer:
sorry I can't answer that because I need points very3× sorry
What is the simplified form of the fraction below?
30
*
O A.
OB.
C.
olo
D.
لا اعر
Answers
Answer:
A. 30÷6 = 5
24÷6=4
=4/5.
Step-by-step explanation:
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plz help with this!!!
Answers
Answer:50
Step-by-step explanation:
Consider 2 1/2 divided by 1/4 write a real world problem for the division.Create a model or write an equation for the division.Find the quotient for the real world problem.Find the quotient.
Answers
Answer:
Step-by-step explanation:
How many 1/4 kg bread loaves can be made from 2½ kg of dough?
2½ / 1/4 = (5/2)•(4/1) = 20 / 2 = 10
The number of puffs made by 2½ kg of dough will be 10.
What is an expression?The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.
The problem is given below:-
How many 1/4 kg puffs can be made from 2½ kg of dough?
The number of the puffs will be calculated as:-
2½ / 1/4 = (5/2) x (4/1) = 20 / 2 = 10
Therefore, the number of puffs made by 2½ kg of dough will be 10.
To know more about an expression follow
https://brainly.com/question/21446512
#SPJ5
Write in word form: 5,278.081
Answers
Answer:
.............................
In a recent year, 32.4% of all registered doctors were female. If there were 47,400 female registered doctor that year, what was the total number of registered doctors?
Answers
Answer:
come, seamen or even spherm
Step-by-step explanation:
basically when the male and female get involved in sexual activity it creates a child through sperm and egg interaction. the fastest sperm wins the race and 68.6% of them are male doctors