The product $c_1 c_2$ in rectangular frame is [tex]\$10 e^{i(2\theta \pm \frac{pi}{3})}\$.[/tex]
How to find the product $c_1 c_2$ in rectangular formLet $c_1$ and $c_2$ be the two complex numbers that frame an even triangle with $3+2i$ and $6+i$.
The dispose of between two complex numbers $a$ and $b$ is given by $|b-a|$. Since the triangle is even, the wipe out someplace in the scope of $3+2i$ and $6+i$ ought to be equivalent to the underlying venture with to the kill among $3+2i$ and $c$, conjointly make back the underlying speculation with to the take out among $6+i$ and $c$.
So, we have the following conditions:
$|6 + i - (3 + 2i)| = |c - (3 + 2i)|$
$|6 + i - (3 + 2i)| = |c - (6 + i)|$
Tackling these conditions, we get:
$|3 - i| = |c - (3 + 2i)|$
$|3 - i| = |c - 6 - i|$
Presently, let's discover the esteem of $c$:
$|c - (3 + 2i)| = |3 - i|$
[tex]\$|c - (3 + 2i)| = \sqrt{(3-0)^{2} + (-1-0)^{2} = \sqrt{10}\$[/tex]
So, [tex]\$c - (3 + 2i) = \pm \sqrt{10} e^{i\theta}\$[/tex], where [tex]\$\theta\$[/tex] is the point between the positive genuine hub and the line interfacing $3+2i$ and $c$?
Presently, let's discover the esteem of $c$ utilizing the moment condition:
$|c - (6 + i)| = |3 - i|$
[tex]\$|c - (6 + i)| = \sqrt{(3-0)^{2} + (-1-0)^{2} = \sqrt{10}\$[/tex]
So, [tex]\$c - (6 + i) = \pm \sqrt{10} e^{i\theta'}\$[/tex], where [tex]\$\theta'\$[/tex] is the point between the positive genuine hub and the line interfacing $6+i$ and $c$?
Since the triangle is equilateral, $theta$ [tex]\$\theta'\$[/tex] must vary by [tex]\$\pm[/tex] [tex]\frac{\pi}{3}\$.[/tex]
Presently, let's discover the item $c_1 c_2$:
$c_1 c_2 = (c - (3 + 2i))(c - (6 + i))$
$c_1 c_2 =[tex](\pm \sqrt{10} e^{i\theta})(\pm \sqrt{10} e^{i(\theta \pm \frac{\pi}{3})})\$[/tex]
$c_1 c_2 = [tex]10 e^{i\theta} e^{i(\theta \pm \frac{\pi}{3})}\$[/tex]
$c_1 c_2 = [tex]10 e^{i(2\theta \pm \frac{\pi}{3})}\$[/tex]
So, the item $c_1 c_2$ in rectangular frame is [tex]\$10 e^{i(2\theta \pm \frac{\pi}{3})}\$.[/tex]
Learn more about rectangular form here:
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find the volume of the cone
Answer:
A≈249.02cm
Step-by-step explanation:
Find the circumference of this circle
using 3 for T.
C [?]
34
C = id
HELPPPP
Step-by-step explanation:
C = 3 × 34
C = 102
Usually it's
C = 3.14 × 34
C = 106.76
This is a more accurate answer but with your question specifically, the answer above is more correct.
What is the value of x? Show your work.
Please help
Answer:
b=5√3
Step-by-step explanation:
Find the last side of the triangle using the Pythagorean theorem.
[tex]a^{2} +b^{2} =c^{2} \\5^{2} +b^{2} =10^{2} \\b^{2} =10^{2}-5^{2}\\\\b=5\sqrt{3}[/tex]
como serian las dimensiones de un tanque australiano (redondo) que tiene que almacenar 5300 litros de agua?
Step-by-step explanation:
a thing or situation that is annoying because it is complicated or involves a lot of effort
-14+u=50 I need help
How much should you invest at 4.8% compounded continuously to have $5000 in 2 years?
Answer:
The total compound interest is $502.74 i think
Step-by-step explanation:
24/5
[tex] \frac{24 \times 5000 }{5 \times100 } = \frac{240 \times 5000}{100} = 240 \times 50 = 12000 =12000 + 240 = 12240 [/tex]
PLEASE HELP I NEED THE ANSWER ASAP ILL GUVE BRAINLIST
Hope this helps. please mark me brainliest if it did
Answer:B $225
Step-by-step explanation:
$2,700.00 divided by 12 = $225
12 = 1 year
what is the area if this triangle? enter your answer as a decimal in the box. round only your final answer to the nearest tenth.
The answer to your question is 38.6
what’s the answer for this I need help
Answer:
18 ft^2
Step-by-step explanation:
4 x 4 = 16
4 x 1 = 4
4 / 2 = 2
16 + 2 = 18 ft.^2
Answer:
18 ft²
Step-by-step explanation:
Area of the triangle: [tex]\frac{1}{2}[/tex] (1 × 4) = 2 ft
Area of the square: 4 × 4 = 16 ft
Add up the areas
You get 18 ft²
The table below shows the values of f(x) and g(x) for different values of x. One of the functions is a quadratic function, and the other is an exponential function. Which function is most likely increasing exponentially?
Answer:
G(x) or at least in the question i hae seen but i do not see your table so just gonoff of what i say below becase it might be f(x)
Step-by-step explanation:
Exponetial funtions are when you have a power of, for example g(x)=1+6x^2
It increases at a rather fast pace because of the power of 2 in this equaion when if it did not have thepower of 2 it would increase at a slower pace
Quantitative reasoning l week 2 discussion What is an example of a situation from your professional or personal life that requires you to compare, understand, and make decisions based on quantitative comparison? Be sure to describe the types of quantitative comparisons you had to make, what decisions you made, and why.
Answer:b
Step-by-step explanation:
hey! i’ll give brainliest please help
Answer:
conjunction
Step-by-step explanation:
Answer:
Conjunction is correct answer. (I think)
Which of the following is a subset of the set E which contains all even integers?
A) {4, 10, 22)
B) {2,4,5,8,10}
C) {1,2,3,4}
D) n(E) = 6
Answer:
A
Step-by-step explanation:
the numbers available in the set is {4,10,22} all are even numbers only.
In the past, the mean running time for a certain type of flashlight has been 9.2 hours. The manufacturer has introduced a change in the production method and wants to perform a hypothesis test to determine whether the mean running time has increased as a result. They hypotheses are as follows. Explain a type 2 error.
Answer:
what are the hypotheses?
Step-by-step explanation:
you said the hypotheses are as folows its not there
PLEASE HURRY!!!! Which Graph shows a set of ordered pairs that represent a function?
A blockbuster movie makes about $247,000,000 in the United States during opening weekend. That same weekend another movie opens but only makes about $5,200,000. Question: write each dollar amount in scientific notation PLEASE HELP.
Answer:
$247,000,000 = 2.47 * 10⁸$5,200,000 = 5.2 * 10⁶Step-by-step explanation:
Scientific notation allows us to write large numbers in smaller quantity by reducing the number to a figure less than 10 but more than one and then multiplying it by a power of 10 to show its actual size. For instance, 65,000,000 will be written as 6.5 * 10⁷ to represent the total number of digits that it has after the decimal.
$247,000,000:
This would be 2.47 * 10⁸
$5,200,000:
This is 5.2 * 10⁶.
pls help me! i’m really confuse on how to tackle this problem (no links)
Answer:
Step-by-step explanation:
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Hi guys I need help this is exterior angles of a triangle so plz do me a favor 3x+20x+120
Answer:3x+140
Step-by-step explanation:
Answer:
23x+120
Step-by-step explanation:
3x+20x+120
Combine Like Terms:
=3x+20x+120
=(3x+20x)+(120)
=23x+120
You flip a coin three times in a row. What is the probability you will get three tails?
Answer:
50/50
Step-by-step explanation:
Answer:
1/8 because {(T , T , T), (T , T , H),(T , H , T), (T , H , H),(H , H , H),(H , H , T),(H , T , H),(H , T , T)} which has 8 combinations in total so that means 1/8... 8 is denominator because 8 combinations 1 is for each one.
A race horse runs one lap around a lake in 10 minutes.
How long will it take for the horse to run 6 laps around the lake at the same pace?
gaving brainliest out
Answer:
60 minutes
Step-by-step explanation:
HELP ME WITH THIS PLEASE!! #∆# ~∆~
Find the RATIO and the EXACT VALUE of the given Cot B.
Answer:
Step-by-step explanation:
take angle B as reference angle
using cot rule
cot B=adjacent/opposite
cot B=5/12
cot B=0.41
B=cot 67.5
B=67.5 degree
for ratio,
cot B=5/12
Please Help! WIll Give 25 Points And Brainliest!
Please solve the picture below
Answer: n × n× 6
length time width both = n and hight is 6 so n × n × 6
Step-by-step explanation:
To get to his parents' house, Mateo would have to drive due north 2.1 miles. To get to his grandparents' house, he would have to drive due east 9.6 miles. What is the straight-line distance between the parents' and grandparents' houses? If necessary, round to the nearest tenth.
Answer:
The straight-line distance between the parents' and grandparents' houses = 9.83 miles.
Step-by-step explanation:
Given - To get to his parents' house, Mateo would have to drive due north 2.1 miles. To get to his grandparents' house, he would have to drive due east 9.6 miles.
To find - What is the straight-line distance between the parents' and grandparents' houses? If necessary, round to the nearest tenth.
Solution -
By the given information, the figure becomes -
From the Graph, we can see that,
The side MP = 2.1
The side MG = 9.6
And By using Pythagoreas Theorem, we get
(PG)² = (MG)² + (MP)²
⇒(PG)² = (9.6)² + (2.1)²
⇒(PG)² = 92.16 + 4.41
⇒(PG)² = 96.57
⇒PG = √96.57
⇒PG = 9.827
∴ we get
The straight-line distance between the parents' and grandparents' houses = 9.83 miles.
Pls help me with #10 I need a answer and a explanation
Answer:
C y/9 = 3
Step-by-step explanation:
An equation needs an equals sign
A rectangular is 11 inches long and 8 inches wide. Find its area
Answer:
The area is 88 square inches.
Step-by-step explanation:
To get the area of a rectangle, you multiply the length and the width.
The length of this rectangle is 11 inches and the width is 8 inches.
11x8=88
Tip: You can multiply by 11s easily if you replace the ones with the number you are multiplying. This only works for numbers up to 9 though.
Example:
11x5=55
11x2=22
No files!!!
Will give brainliest and please don’t guess
Answer:
i think its 54. i might be incorrect.
Step-by-step explanation:
Answer:
54º
Step-by-step explanation:
This really cannot be determined because the combined angle is not marked as 90º
let's assume it is 90º
(7x + 12) +(2x + 24) = 90
Combine like terms
9x + 36 = 90
Subtract 36 from both sides
9x = 54
Divide both sides by 9
x = 6
-----------------------
7(6) + 12 = 54º
2(6) + 24 = 36º
54º is the larger angle
Part A
This year, water usage has increased by 20% for both regular days and special events.
LAST YEAR'S WATER USAGE:
All regular days - 13,505 gallons
Per special event - 18.5 gallons
Total for the year - 13,616 gallons
Write an equation for the total water usage, U, at the park this year in terms of x, the number of special events the park has hosted.
Answer:
The total water usage at the park this year, in gallons, U = 16,206 + 22.2·x
Step-by-step explanation:
The given parameters are;
The increase in water usage for both regular days and special event for the current year = 20%
The water usage for last year regular days = 13,505 gallons
The water usage per special event = 18.5 gallons
The total water usage = 13,616 gallons
Therefore, we have;
The water usage for regular days on the current year = 13,505 gallons + (20/100)×13,505 gallons = 16,206 gallons
The water usage per special event for the current year, x = 18.5 gallons + (20/100) × 18.5 gallons = 22.2 gallons
The total water usage, U, at the park this year in terms of 'x', the number of special events the park hosted is given by the sum of the amount of water used on regular days and the product of 'x', and the amount of water used per special event this year as follows;
U = 16,206 gallons + x × 22.2 gallons
∴ The total water usage at the park this year, U = 16,206 + 22.2·x
Answer:
U=16,206+22.2 ^. x
Step-by-step explanation:
what 3 1/2 times 2 3/4
Answer: 9/4 or 2.25
Step-by-step explanation:?????
127/4 + 62/3 × 24/6 solve this fraction by BODMAS
Answer:
The correct solution is "114.39".
Step-by-step explanation:
The given expression is:
⇒ [tex]\frac{127}{4} +\frac{62}{3}\times \frac{24}{6}[/tex]
On solving the above expression with the help of BODMAS rule, we get
Firstly we will have to apply division, we get
= [tex]31.75+20.66\times 4[/tex]
Now we will have to apply multiplication, we get
= [tex]31.75+82.64[/tex]
On adding, we get
= [tex]114.39[/tex]
If the m∠1=123° m ∠ 1 = 123 ° and m∠2= (2x+7)° m ∠ 2 = ( 2 x + 7 ) ° , determine the value of x that supports l∥m l ∥ m . Show your work to support your answer.
Answer:
25
Step-by-step explanation:
Let us assume that m<1 nad m<2 are supplementary. Since the sum of supplementary angles is 180degrees, hence;
<1 + <2= 180
123+2x+7 = 180
130+2x = 180
2x = 180 - 130
2x = 50
x = 50/2
x = 25
Hence the value of x is 25