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
which of the following best describes the graph below?
plssss help!!
Answers
rate 5 starts
pls help :) not understanding this thank you!!!
Answers
Answer: equals Z
Step-by-step explanation:
simple you do y divided by mass energy
If point S ( 3, 4 ) is reflected across the line y=1, what are the coordinates of its reflections image?
Answers
Answer: C
Step-by-step explanation: If point P(3,10) is reflected across the line y=1, the coordinates of it's reflection image is (3,-8)
If a slingshot is used to shoot a marble straight up into the air from 2 meters above the
ground with an initial velocity of 30 meters per second, for what values of time t will the
marble be over 35 meters above the ground? (Refer to Exercise 25 in Section 2.3 for assistance
if needed.) Round your answers to two decimal places
Answers
Answer:
use this equation: GPE=mgh
Step-by-step explanation:
GPE = gravitational potential energy = J
m = mass = Kg
g = gravitational field = N/kg = world's gravitational field is 9.8N/kg
h = height = m
PLZ HELP ASAP IS FOR IMPORTANT ASSIGNMENT Find the function that represents the relationship shown in the
table below and explain how you determined the equation by
showing your solution and adding statements to explain your
steps.
X
0
1
2
3
4
ON
у
-5
9
16
23
N
Edit
View
Insert
Format
Tools
Table
Answers
Answer:
Step-by-step explanation:
Which expressions have a value of 54 when v= 6? Choose all the correct answers.
A 2(v2 – 9)
B V3 = 18 + 3
C (2v)2 – 90
-
D 13 = 3 – 18
E 2(v2 – 90)
F (v + 2)2 – 10
Answers
A boy dressed in a robot costume weighs a total of 50 7/8 lb. If the costume itself weighs 3 1/2 lb, how much does the boy weigh?
Answers
The weight of the boy in the robot costume is 351/8 lb or 43 7/8 lb.
To find the weight of the boy, we need to subtract the weight of the costume from the total weight of the boy in the costume.
Total weight of boy and costume = 50 7/8 lb
Weight of costume = 3 1/2 lb
To find the weight of the boy, we can subtract the weight of the costume from the total weight:
Weight of boy = Total weight - Weight of costume
Convert both the total weight and the weight of the costume to improper fractions:
Total weight = 50 + 7/8 = 400/8 + 7/8 = 407/8 lb
Weight of costume = 3 + 1/2 = 6/2 + 1/2 = 7/2 lb
Now, subtract:
Weight of boy = (407/8) lb - (7/2) lb
To perform subtraction, we need to have a common denominator, which is 8 in this case:
Weight of boy = (407/8) lb - (56/8) lb
Now, subtract the fractions:
Weight of boy = (407 - 56)/8 lb
Weight of boy = 351/8 lb
To learn more about fraction click on,
https://brainly.com/question/15898930
#SPJ2
How is the product of 2 and -5 shown on a number line?
-10-98235
-3 -2 -1 0 1 2 3 4 5 6 7 8 10
-10 - -
-3
-2 -1 0 1 2 3 4 5 6 7 8
10
-10 -4 -8 -7 -3
4 -3 -2 -1 0
1
2
3
4
5
6
7
9
10
-10-9-4-7-3
-4-1 -2 -1 0 1 2
3
5
6
7
10
Answers
Answer:
d
Step-by-step explanation
Step-by-step explanation:It starts at 0 and goes in the negative
The result of a division problem is the a ) divisor . b ) quotient . c ) factor . d ) remainder .
Answers
Answer:
b) quotient
Step-by-step explanation:
divisor is the number/value you are dividing with.
A remainder is a number that remains after you divide.
A factor is a number that can divide into a number or numbers without leaving a remainder
There are 25 students in a class, 7 of them will be chosen to go on a field trip. How many ways can these students be chosen.
Answers
Answer:
Step-by-step explanation:
order is not important so
25 ways to fill the first spot
24 ways to fill the second
23 ways to fill the third
...
19 ways to fill the 7th
25•24•23•22•21•20•19 = 2,422,728,000
which also equals 25! / (25 - 7)!
Does (7,5) make the inequality 16x + 16y 2 12 true?
Answers
Someone pls help me with these worksheets >.<
(Please answer properly, if u don't know, just ignore so someone who knows can answer)
Answers
Answer:
gsdddddddddddddddddddddddddddd
Step-by-step explanation:
Given: y || 2
Prove: m5+ m2+ m6 = 180°
L
A
M
1 1
23
y
4
5
6 7 z
С
B
Answers
The relationships between angles formed by two parallel lines having a common a transversal include, alternate interior, vertically opposite, corresponding, alternate exterior, same side, interior and exterior
The correct option for the missing reason in step 3. is as follows;
Alternate interior angles are congruent
The reason the above option is correct is as follows:
The given parameters are;
Line y is parallel to line z
The figure ABC forms a triangle
The two column proof is presented as follows:
Statement Reason
1. ABC is a triangle 1. Given
2. lines y and z are parallel 2. Given
3. ∠1 is congruent to ∠5; ∠3 ≅ ∠6 3. Statement reason required
∠3 is congruent to ∠6
4. m∠1 = m∠5; m∠3 = m∠6 4. By definition of congruency
5. m∠1 + m∠2 + m∠3 = m∠LAM 5. By angle addition Postulate
6. m∠1 + m∠2 + m∠3 = 180° 6. Angles on a straight line
7. m∠5 + m∠2 + m∠6 = 180° 7. Substitution (property)
Required:
The reason for the statement ∠1 ≅ ∠5; ∠3 ≅ ∠6
Solution:
From the attached diagram for the question, we have that angle ∠1 and angle ∠5 on line AC and ∠3 and ∠6 on line AB are alternate interior on two parallel lines, and they are therefore, congruent.
Therefore
∠1 ≅ ∠5, and ∠3 ≅ ∠6 by alternate interior angles theorem which states that alternate interior angles, which are the pair angles formed in the inside face of two parallel lines crossed by a common and the common transversal but on either of the transversal, are congruent
Therefore, the missing reason in Step 3 is; Alternate interior angles are congruent
8m – 5 for m = 9 answer please
Answers
Answer:
= 67
Step-by-step explanation:
8m – 5 for m = 9
~Substitute
8(9) - 5
~Simplify
72 - 5
~Subtract
67
Best of Luck!
A driver driving a business trip of 240 miles would have reached his destination if he'd been able to drive 12 mph faster than he made the trip. Find the average speed of his trip.
Answers
The average speed of his trip is = 12 mile/ hour
The total distance covered by the driver = 240 miles
The rate at which he traveled = 12 miles per hour
Therefore, the time he used to cover his distance
= 240/12
= 20 hrs
But average speed = distance/ time
= 240/ 20
= 12 miles/ hour
Therefore, the average speed of his trip is = 12 mile/ hour
Learn more here:
https://brainly.com/question/11753352
Michelle bought 4 packs of
soda for $10. How much did
each pack cost?
Answers
Answer: 2.50$
Step-by-step explanation:
4 x ( 2 + 5 )^2 - 5^2
Answers
=4*49-25
=196-25
=171
HOW DO I FIND QR
PLEASE HELP
Answers
Solution: For finding QR we need to apply Pythagoras Theorem
What is Pythagoras Theorem ?
ans : Pythagoras Theorem is the sum of square of two sides which is equal to the third side or the hypotenuse. This formula is valid oy incase of Right-Angled Traingle because one of three angles here is 90°
According to this law let's apply it in the diagram shown here.
(Hypotenuse)² = (Adjacent)² + (Opposite)²(PR)² = (QR)² + (PQ)² (5x - 2)² = (QR)² + (3x - 1)² (QR)² = (5x - 2)² - (3x - 1)²After factorising both of them we get
(QR)² = 25x² - 20x + 4 - (9x² - 6x + 1)(QR)² = 25x² - 20x + 4 - 9x² + 6x - 1(QR)² = 16x² - 14x + 3QR = √(16x² - 14x + 3)So, QR is √(16x² - 14x + 3)
Going through (-2,2) and (2,-2) Write the equation of lines with the following through
Answers
Answer:
Step-by-step explanation:
Seems like your question might be missing some parts.
If Not, Then
a line through the given points would have the form
y = mx + b
where m is the slope and b the y intercept
m = Δy/Δx = (-2 - 2) / (2 - (-2)) = -1
y = (-1)x + b
y = -x + b
now plugging in either point to find b
2 = -(-2) + b
b = 0
y = -x + 0
y = -x
Answer:
Step-by-step explanation:
(-2 - 2)/(2 + 2) = -4/4= -1
y - 2 = -(x + 2)
y - 2 = -x - 2
y = -x
Which number should come next at the end of this series: 1/2, 4, 1/8, 16, _?
Answers
Answer:
1/32
Step-by-step explanation:
sam's age is 125% of mary's age. mary's age is p% of sam's age. what is the value of p?
Answers
S(S+8) = 105
S^2+8S-105 = 0
(S+15)(S-7) = 0
Sam’s sister is 7 years and Sam is 15 years old.
What are the coordinates of the x-intercept of the line -3x-5y=12?
Answers
well, x-intercept means for a graphed funciton where the x-axis gets touched/intercepted, Check the picture below, when that occurs, y = 0, so if we want to know what "x" is at that point we can simply set y = 0 and solve for "x".
[tex]-3x-5y=12\implies \stackrel{\textit{setting y = 0}}{-3x-5(0) =12}\implies -3x-0=12 \\\\\\ -3x=12\implies x=\cfrac{12}{-3}\implies x = -4 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \stackrel{\textit{coordinates}}{(-4~~,~~0)}~\hfill[/tex]
do atoms have potential and kinetic energy
Answers
Answer: Kinetic and potential energy of atoms result from the motion of electrons. ... The further the orbital is from the nucleus, the higher the potential energy of an electron at that energy level. When the electron returns to a low energy state, it releases the potential energy in the form of kinetic energy.
(i searched it and found this. If it helped, pls mark me brainliest! tysm)
PLEASE NO LINKS DONT WASTE YOUR TIME IM NOT GONNA CLICK. What are the zeros of this function?
Answers
Answer: C. x = 4 and x = 6
Step-by-step explanation:
Zeros of a function would be the value of x when f(x) is 0.
Based on the given graph, the parabola has 2 locations where the y-value is 0 and the graph hits the x-axis.
The graph hits the x-axis at 4 and at 6.
Answer:
I dont but want to.
Hope this helps! :) ;-;
Step-by-step explanation:
geomtry plzz help 15 points
Answers
Answer:
False.
Step-by-step explanation:
The sides of a triangle rule asserts that the sum of the lengths of any two sides of a triangle has to be greater than the length of the third side. However, 8+6=14 is less than 15. Hence, the triangle cannot be formed.
PLEASE HELP! Economics
Answers
100 francs = 50 dollars
Exchange rate = 50/100
= 1/2
= 0.50 dollars per franc (C)
Note :-
It's dollars per franc because here the dollar has more value.
______
RainbowSalt2222 ☔
Answer:
Im pretty sure it is c
Step-by-step explanation:
Evaluate 51x3 - 21 + 7 when x = -2.
DONE
Answers
Answer:
-320 i guess
Step-by-step explanation:
51*-2*3-21+7=-320
Jacob followed a recipe that requires 2 cups of water for ever 3 cups of flour. If he used 8 cups of flour, how many cups of water did he use?
options
2 2/3
4
5 1/3
12
Answers
Answer:12
Step-by-step explanation:
3 divided by 2 = 1.5
1.5x8=12
He used 12 cups of water
Have A Good Day
The price of a video game is $32.99 before tax. Andre bought the video game for 20% off. He then paid 8% sales tax on the discounted price. Part A: How much did Andre pay in sales tax? Show all work and steps in your solution. (5 points) Part B: What is the total amount that Andre paid for the video game? Show all work and steps in your solution. (5 points)
Answers
Answer:
the answer is 24.23 $ thats what i got
Answer:
A. 2.11 and B. 26.39+2.11=28.50
Step-by-step eplanation:
Frank is going to buy some ties
at $7.50 per tie and some shirts
at $18.50 per shirt. If he buys
twice as many ties as shirts and
spends no more than $205, what is the greatest number of shirts he
can buy? [All prices include tax.]
Answers
Answer:
6 shirts
Step-by-step explanation:
The cost of a shirt and 2 ties is ...
$18.50 +2(7.50) = $33.50
For $205, Frank can buy $205/$33.50 = 6.12 sets of shirt and ties.
Frank can buy 6 shirts (and 12 ties) for an amount less than $205.
_____
Additional comment
Frank's cost will be $201 for that purchase.
