Review the proof of de Moivre’s theorem.
Proof of de Moivre's Theorem
[cos(θ) + i sin(θ)]k + 1
A = [cos(θ) + i sin(θ)]k ∙ [cos(θ) + i sin(θ)]1
B = [cos(kθ) + i sin(kθ)] ∙ [cos(θ) + i sin(θ)]
C = cos(kθ)cos(θ) − sin(kθ)sin(θ) + i [sin(kθ)cos(θ) + cos(kθ)sin(θ)]
D = ?
E = cos[(k + 1)θ] + i sin[(k + 1)θ]
Which expression will complete the proof?
Answers
Answer:
D
Step-by-step explanation:
Just took it.
Answer: D. cos(kθ + θ) + i sin(kθ + θ)
Step-by-step explanation:
The screenshot pretty much speaks for itself, but you can see that the proof ends with cos[(k + 1)θ] + i sin[(k + 1)θ]. That means that addition is happening in Step D, and that the expressions in the cosine and sine parts are the same. So, the correct option is D. Hope that helps!
![Review The Proof Of De Moivres Theorem.Proof Of De Moivre's Theorem [cos() + I Sin()]k + 1A = [cos()](https://brainimage.s3.us-east-005.backblazeb2.com/answers/attachments/QGxE7rBv2erLEy1TzWTTZEx3BgElN9ta.png)
Related Questions
Melanie invested $63,000 in an account paying an interest rate of 7 1/8% compounded
quarterly. Lillian invested $63,000 in an account paying an interest rate of 7 3/8%
compounded continuously. After 15 years, how much more money would Lillian have
in her account than Melanie, to the nearest dollar?
Answers
Answer: $8727- thsi should be the correct answer
100 POINTS 100 POINTS 100 POINTS 100 POINTS IF YOU ANSWER THIS PROBLEM
Which expression represents the area of the figure?
Answers
Answer:
Option A
The Area of the given figure is 5x²/2 + 3x/2 - 4
Step-by-step explanation:
For a given Trapezoid
side a = x + 7
side b = 4x + 1
height (h) = x - 1
Now, Area of Trapezoid
Formula:A = ½ (a + b) × h
A = ½ (x + 7 + 4x + 1) × (x - 1)
A = ½ (5x + 8) × (x - 1)
A = ½ (5x² - 5x + 8x - 8)
A = ½ (5x² + 3x - 8)
A = 5x²/2 + 3x/2 - 8/2
A = 5x²/2 + 3x/2 - 4
Thus, The Area of the given figure is
5x²/2 + 3x/2 - 4
-TheUnknownScientist
Answer: the answer is a: 5/2x squared + 3/2x -4
Need help on this assignment
Answers
Answer:
(-1)^2+5= 1+5=6
(0)^2+5= 0+5= 5
(1)^2+5= 1+5= 6
6+5+6= 17
x-1 + x0 + x1 = (-1)^2 + 5 + (0)^2 + 5 + (1)^2 + 5 = 6 + 5 + 6 = 17
Angad was thinking of a number. Angad doubles it, then adds 8 to get an answer of 68.4. What was the original number?
Answers
Answer:
The answer is 30.2
Step-by-step explanation:
subtract 8. Then divide by 2
Answer: 30.2
Step-by-step explanation: so 68.4 - 8 because Angad added 8 so we have to subtract that. So 60.4 divided by 2 because Angad doubled the number, gets us 30.2.
Hope I could help!
The sum of − , − − is
Answers
In the diagram, QR=ST=480, CU=5x, and CV=9x-56. Find the radius of circle C
Answers
Answer:
your answer will be option C. 250
Step-by-step explanation:
hope it helps you
have a great day
Find two integers whose sum is -14 and product is 33
Answers
Answer:
Step-by-step explanation:
a+b=-14
a=-14-b
ab=33, using a from above makes this become
(-14-b)b=33
-14b-b^2=33
b^2+14b+33=0
(b+11)(b+3)=0
So the numbers are -3 and -11
Does this triangle have a hypotenuse about 39 feet long?
Answers
Answer:
yes it is exactly 39 ft long
Step-by-step explanation:
Answer:
yes
Step-by-step explanation:
using the Pythagorean theorem:
36² + 15² = c²
1296 + 225 = c²
1521 = c²
c = 39 ft
Find the slope of the line write your answer in simplest form
Answers
Answer:
-3/5
Step-by-step explanation:
(y2-y1)/(x2-x1)=Slope ((1)-(-2))/((-4)-(1)) or 3/-5
The length of Rebecca’s rectangular garden was two times the width “w”. She increased the length and width of the garden so that the area of the new garden is (2w2+7w+6)square yards. By how much did Rebecca increase the length and width of the garden. Show your complete working.
Answers
Answer:
rebecca increased the length by 3 and the width by 2
Step-by-step explanation:
First we need to find the length and width by factorizing the expressio ofr the area;
A = 2w^2+7w+6
A = 2w^2+4w+3w+6
A = 2w(w+2)+3(w+2)
A = (2w+3)(w+2)
Since l = 2w
Length = 2w+3
width = w+2
This shows that rebecca increased the length by 3 and the width by 2
Shellys square garden has an area of 81f ft^2 what is the length of the side PLS HELPPPP
Answers
Answer:
9 ft
Step-by-step explanation:
Hope this helps!
Have a great day!
Expand and simplify
(x+4)(2x-1)
Answers
Answer:
2x^2+7x−4
Step-by-step explanation:
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Evaluate the expression (13 − 3)2 ÷ 50.
The value of the expression is
Answers
Answer:
0.24
Step-by-step explanation:
(13 - 3) 2 / 50
10 + 2 / 50
12 / 50
=0.24
Hope this helped! Have a nice day! Plz mark as brainliest!!!
-XxDeathshotxX
Answer:
Exact form: 2/5
Decimal: 0.4
Step-by-step explanation:
#7: Find the surface area of the square pyramid shown below. * 10 IN. 6 IN. 6 IN. SURFACE AREA = IN2
Answers
360 IN.2?
Step-by-step explanation:
i don't know if correct
nakalimutan kuna yan kung pano gawin sorry
The projected population of Tennessee in 2030 is
about 5x5.9^8. Predict the average number of people
per square mile in Tennessee in 2030. Land area: about 5.9^6
Answers
Answer:
Population
Population estimates, July 1, 2019, (V2019) 6,829,174
Population estimates base, April 1, 2010, (V2019) 6,346,276
Population, percent change - April 1, 2010 (estimates base) to July 1, 2019, (V2019) 7.6%
Population, Census, April 1, 2010 6,346,105
Age and Sex
Persons under 5 years, percent 6.0%
Persons under 18 years, percent 22.1%
Persons 65 years and over, percent 16.7%
Female persons, percent 51.2%
Race and Hispanic Origin
White alone, percent 78.4%
Black or African American alone, percent(a) 17.1%
American Indian and Alaska Native alone, percent(a) 0.5%
Asian alone, percent(a) 2.0%
Native Hawaiian and Other Pacific Islander alone, percent(a) 0.1%
Two or More Races, percent 2.0%
Hispanic or Latino, percent(b) 5.7%
White alone, not Hispanic or Latino, percent 73.5%
Population Characteristics
Veterans, 2015-2019 431,274
Foreign born persons, percent, 2015-2019 5.1%
Housing
Housing units, July 1, 2019, (V2019) 3,028,213
Owner-occupied housing unit rate, 2015-2019 66.3%
Median value of owner-occupied housing units, 2015-2019 $167,200
Median selected monthly owner costs -with a mortgage, 2015-2019 $1,244
Median selected monthly owner costs -without a mortgage, 2015-2019 $388
Median gross rent, 2015-2019 $869
Building permits, 2019 41,361
Families & Living Arrangements
Households, 2015-2019 2,597,292
Persons per household, 2015-2019 2.52
Living in same house 1 year ago, percent of persons age 1 year+, 2015-2019 85.5%
Language other than English spoken at home, percent of persons age 5 years+, 2015-2019 7.2%
Computer and Internet Use
Households with a computer, percent, 2015-2019 87.1%
Households with a broadband Internet subscription, percent, 2015-2019 78.4%
Education
High school graduate or higher, percent of persons age 25 years+, 2015-2019 87.5%
Bachelor's degree or higher, percent of persons age 25 years+, 2015-2019 27.3%
Health
With a disability, under age 65 years, percent, 2015-2019 11.0%
Persons without health insurance, under age 65 years, percent 12.1%
Economy
In civilian labor force, total, percent of population age 16 years+, 2015-2019 61.0%
In civilian labor force, female, percent of population age 16 years+, 2015-2019 56.6%
Total accommodation and food services sales, 2012 ($1,000)(c) 12,499,013
Total health care and social assistance receipts/revenue, 2012 ($1,000)(c) 42,383,683
Total manufacturers shipments, 2012 ($1,000)(c) 139,960,482
Total merchant wholesaler sales, 2012 ($1,000)(c) 111,718,421
Total retail sales, 2012 ($1,000)(c) 91,641,605
Total retail sales per capita, 2012(c) $14,194
Transportation
Mean travel time to work (minutes), workers age 16 years+, 2015-2019 25.2
Income & Poverty
Median household income (in 2019 dollars), 2015-2019 $53,320
Per capita income in past 12 months (in 2019 dollars), 2015-2019 $29,859
Persons in poverty, percent 13.9%
BUSINESSES
Businesses
Total employer establishments, 2018 138,269
Total employment, 2018 2,683,214
Total annual payroll, 2018 ($1,000) 125,736,019
Total employment, percent change, 2017-2018 1.3%
Total nonemployer establishments, 2018 539,987
All firms, 2012 550,453
Men-owned firms, 2012 302,249
Women-owned firms, 2012 195,694
Minority-owned firms, 2012 105,234
Nonminority-owned firms, 2012 434,025
Veteran-owned firms, 2012 59,379
Nonveteran-owned firms, 2012 469,392
GEOGRAPHY
Geography
Population per square mile, 2010 153.9
Land area in square miles, 2010 41,234.90
FIPS Code
Step-by-step explanation:
6 more than the product of 22
Answers
Solve for the value of y.
Answers
Explanation is in the photo
Solved for the value of y and found that y = 5.
What is the Pythagorean theorem?In the Pythagorean theorem, the sum of the squares of the sides of a right-angled triangle is equal to the square of the longest side i.e, the hypotenuse of the triangle.
z² = x² + y²
The given triangle is a right-angled triangle. This means that we can use the Pythagorean theorem.
∴ y² + 12² = 13²
⇒ y² + 144 = 169
⇒ y² = 169-144
⇒ y² = 25
⇒ y = 5
Therefore, we have solved for the value of y and found that y = 5. The correct answer is option C.
Learn more about the Pythagorean theorem here-https://brainly.com/question/343682
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Xavier needs to bike a minimum of 80 miles this week for his training if he is already biked 14 miles this week and how many miles should he bike on each of the six remaining days this week?
Answers
Answer:
if he wants to bike the same amount of miles each day he should bike 11 miles each day .
Step-by-step explanation:
subtract 14 - 80 = 66. 66 in 6 days is 11 each day
please help fast!! Find the total surface area of the following cylinder:
Answers
explanation:total=addition
area=base x height plus the width (area the amount beneath the surface).
equation:3cm both sides 3cm
answer: 3+3= 6cm .
Answer: 36
Step-by-step explanation:
Formula: 2 pi rh + 2 pi r2
2 pi 3 • 3 + 2 pi 9
Leave answers in terms of pi
18 pi + 18 pi = 36 pi
Answer = 36
State if the triangles in each pair are similar. If so, complete the similarity statement.
Answers
Answer:
B
Step-by-step explanation:
Set up a proportion and see if it is true:
[tex]\frac{12}{8} =\frac{27}{18} \\\frac{3}{2} =\frac{3}{2}[/tex]
True, so they are similar.
The similarity statement would be QRS ~ QED
So B is the answer
7. Calculate the unit cost.
a) $1.85 for 4 kg of peaches
b) $16.99 for a 454 g package of cooked
shrimp
c) $2.99 for a 1.89 L bottle of juice
d) $283.28 for 22.5 m2 of flooring tiles
Answers
Answer:
Step-by-step explanation:
It cost $0.46 for 1 kg of peaches $.46/kg
It cost $12.6 for 1 m² of flooring tiles $12.6/1 m² of flooring tiles
It cost $1.6 for 1 L bottle of juice $1.6/L
dont know shrimp
The unit costs are:
(a) $1.85 for 4 kg peaches= $0.4625 per Kg
(b) $16.99 for a 454 g package cooked shrimp= $37.423 per Kg
(c) $2.99 for a 1.89 L bottle juice= $1.58 per L
(d) $283.28 for 22.5 m2 flooring tiles= $12.6 per m²
How to calculate unit value?In order to find the unit value of a quantity then divide the total cost by the quantity to get the unit price.
Unit price = total cost/ total number of quantity
here given
(a) $1.85 for 4 kg peaches
unit cost = total cost/ total number of quantity
= $1.85/4 Kg
=$0.4625 per Kg
(b) $16.99 for a 454 g package cooked shrimp
unit cost = total cost/ total number of quantity
= $16.99/454g
=$0.037 per gram
=$37.423 per Kg
(c) $2.99 for a 1.89 L bottle juice
unit cost = total cost/ total number of quantity
= $2.99/1.89L
=$1.58 per L
(d) $283.28 for 22.5 m2 flooring tiles
unit cost = total cost/ total number of quantity
=$283.28/22.5m²
=$12.6 per m²
Therefore the final unit costs are:
(a) $1.85 for 4 kg peaches= $0.4625 per Kg
(b) $16.99 for a 454 g package cooked shrimp= $37.423 per Kg
(c) $2.99 for a 1.89 L bottle juice= $1.58 per L
(d) $283.28 for 22.5 m2 flooring tiles= $12.6 per m²
Learn more about unit value
here: https://brainly.com/question/14125148
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Does this triangle have a hypotenuse about 39 feet long
Answers
Answer:
hypotenuse is about 33 ft long
Step-by-step explanation:
a^2+b^2=c^2
a= 30
b=14
30^2+14^2= 1096 =c^2
[tex]\sqrt{1096}[/tex]=c
33.1=c
hypotenuse is about 33 ft long
Answer:
No, the Hypotenuse is 33.11
Step-by-step explanation:
The formula for finding a hypotenuse is:
[tex]\sqrt{x^2+y^2}[/tex]
x=30 and y=14 here
[tex]x^2=900[/tex]
[tex]y^2=196[/tex]
[tex]x^2+y^2= 1,096[/tex]
[tex]\sqrt{1,096} = 33.11[/tex]
So it would be about 33, not 39
can somebody please help me
Answers
Answer:
Step-by-step explanation:
10
I need help ASAP , State whether set of ordered pairs represent a function
{(-13,4) , (7,-15), (-13,9) (6,-12) (-18,0)
Answers
Answer:
No, the given set of pairs does not represent a function
Step-by-step explanation:
For a set of values to be a function, each input must have one and only one output value
Now, for the given set, we can note that:
The input -13 has two output values; 4 and 9
Therefore, this set is not a function
Hope this helps :)
If P the incenter of triangle JKL, find MP.
Answers
9514 1404 393
Answer:
MP = 38
Step-by-step explanation:
Each of the lengths MP, NP, OP is the radius of the incircle, so they are all congruent.
3x +14 = 9x -34
48 = 6x . . . . . . . . . . . . . . add 34-3x to both sides
24 = 3x . . . . . . . . . . . . . . divide by 2 (we don't need x; we need 3x or 9x)
NP = 3x +14 = 24 +14 = 38
NP = OP = MP = 38
Hey guys I need help; will mark brainliest
The radius of a truck tire is 11 inches. Approximately how far will the truck have traveled after 3 rotations of these tires? Use 3.14 for . Round to the nearest tenth.
Answers
Answer:
207.2in
Step-by-step explanation:
Hey There!
So to solve this problem we need to find the circumference of the circle and multiply that by 3 because that is how many rotations the tire would have made
C=2πr
where r = radius
Now we plug in the values
C=2(3.14)11
3.14*2=6.28
6.28*11=69.08
So one full rotation would have traveled 69.08 inches
Now we have to multiply that by 3 becasue they want us to find the distance traveled after three rotations
3*69.08=207.24
Now we round to the nearest tenth
so after 3 rotations the truck will have traveled 207.2in
which one of the following is a factor of a²+bc+ab+ac?
Answers
a (a+b) + c (b + a)
(a+b) ( a+c)
Zayna has 4 boxes with 14 art books in each box. She has 3 bags with 12 math books in each bag. If she
gives 15 books away, how many art and math books does she have left?
Answers
Your answer is 11 art and math books left
Harold is on the diving team at school. The platform he uses is about 5 yards above the pool. On his best dive, he jumps an extra foot in the air before doing a flip. How many feet is he from the pool at the highest point of his jump?
Answers
Answer:
16 feet because 5 yards is equaled to 15 feet and then add the extra foot he uses to jump
Step-by-step explanation:
I need help on this and the person who answer this correctly gets a BRANLIST(answer if you know)
Answers
Answer:
-28.84
Step-by-step explanation:
-6π - 10
-6(3.14) - 10
-18.84 - 10
-28.84
Answer:
− 28.85
Step-by-step explanation: