The general value of theta which satisfies the equation (cosФ+isinФ)(cos2Ф+isin2Ф)..............(cosnФ+isinnФ) is one is 4π/(n+1)
Real and imaginary numbers:
A real number can be a natural number, a whole number, an integer, a rational number, or an irrational number. But an imaginary number is the product of a real number and "i" where i = √(-1). For example, √(-9) = √(-1) . √9 = i (3) = 3i
cosФ+isinФ = [tex]e^{i0}[/tex]
cos2Ф+isin2Ф = [tex]e^{2i0}[/tex]
............................
cosnФ+isinnФ= [tex]e^{in0}[/tex]
Now,
[tex]e^{i0}[/tex]×[tex]e^{2i0}[/tex]×.......[tex]e^{in0}[/tex] =1
[tex]e^{i0(1+2+....n)}[/tex] = 1
[tex]e^{i0(n*(n+1)/2)}[/tex] =1
So
cos(n*(n+1)/2)Ф+isin(n*(n+1)/2)Ф =1
Now comparing the real and the imaginary part we get that
cos(n*(n+1)/2)Ф = 1
n*(n+1)/2Ф = 2nπ
Ф = 4π/(n+1)
Therefore, the general value of theta which satisfies the equation (cosФ+isinФ)(cos2Ф+isin2Ф)..............(cosnФ+isinnФ) is one is 4π/(n+1).
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The correct question should be:
find the general value of theta which satisfies the equation (cosФ+isinФ)(cos2Ф+isin2Ф)..............(cosnФ+isinnФ) equals to one.
A store increases the price of a shirt by 10%, then reduces the cost by $10. The
price is then 90% of the original price. Find the original price.
Answer:
111
Step-by-step explanation:
NP = (S x 1.10) - 10
OP = NP / .9
When filled, a balloon in the shape of a sphere has a diameter of 14 inches. What is the approximate volume of air, in cubic inches, needed to fill this balloon?
1,078
1,437
8,621
11,494
Answer:
1,437
Step-by-step explanation:
Answer:
a I'm not as smart so trust me
Step-by-step explanation:
Tell whether the angles are adjacent or vertical. Then find the value of x.
Answer:
vertical? (not sure
75=4x-25
100=4x
x=25
Please put the explanation!
Answer:
60
Step-by-step explanation:
In order to get this answer, we must know that a triangle's angles add up to exactly 180. Also, Angles that intersect will have congruent, opposite sides. The last thing is that a line is = 180 degrees. So, the triangle with the 94 and the 142, you can use that. the angle next to the 142 is going to be 180-142 which is 38 and since the other angle is opposite 94, as well. when you add those up u get 132 and 180-132= 48 which is the missing angle for the far right triangle. then, you get the opposite of that angle, put that in the other triangle, do the same with the 72, and add those up to get 120 and since a triagle adds up to 180, 180-120 = 60. So, 60 is your missing angle. Cheers
find the value of x
please help me do this
Answer: reminder u are loved. <3
Step-by-step explanation:
8. In a mock school election 5/7 of the students voted. There are 1095 ballots. Write and solve a equation to find the number of students in the school.
Alright, this is a fairly simple equation if you consider the overall question. As the question states, every 5 of out 7 students voted in the election. This means that five sevenths of all students in the school casted a vote.
Now, what can we do with this information? Well, we know that there were 1095 votes in total. This means that five sevenths of the school who voted represents 1095 students.
Can you see the equation you need to write now? Let's use a simple equation with the variable 's' to represent the total number of students:
[tex]\frac{5}{7}[/tex] * s = 1095
As I elaborated earlier, this equation essentially means "5/7 of the entire student population is 1095 students." Now, we just need to isolate the variable 's' to get our final answer.
To get rid of the denominator, let's multiply both sides by 7:
[tex]\frac{5s}{7}[/tex] * 7 = 1095 * 7
5s = 7665
Finish it off by dividing both sides by 5 to get rid of s's coefficient:
[tex]\frac{5s}{5}[/tex] = [tex]\frac{7665}{5}[/tex]
s = 1533
There are 1533 total students in the school
And that's it! If you have any questions about how I solved it, feel free to ask!
- breezyツ
T (1,3) translations on a coordinate plane
Answer:
Look at the image.
Step-by-step explanation:
easy points... round 12717. to the nearest hundredth
Plz Help I neeed to know
What is 2+2?
Answer:
4
Step-by-step explanation:
Answer:
You see the theoretical answer would be 4 but have you ever considered it to be a watermelon????
Step-by-step explanation:
With the 2 numbers added up its 2 fingers plus 2 fingers. Which is 4. BUT
Its 4 not a watermelon
can someone help me plz
Answer:
289
Step-by-step explanation:
6 sides to a cube, so the surface area would be the sum of all the sides. 1734/6 = 289
Answer:
17
Step-by-step explanation:
Subtract the following polynomials in this equation
She has written 90 page essay so far she needs 150 pages. What percent of pages has she completed.
Answer:
75%
Step-by-step explanation:
i am not going to say it right but i think it is but my teacher have us doing this now
The manager of The Counter noticed that the birthday club members all brought along a family member who spent an average of $22.00 in the restaurant. The tax on their bill was 9 percent. How much did the family member pay in total? (Hint: bill total + tax)
Answer:
Total amount pay by family member = $23.98
Step-by-step explanation:
Given:
Average amount spent on food = $22
Tax rate on restaurant food = 9%
Find:
Total amount pay by family member
Computation:
Amount of tax pay by family member = Average amount spent on food x Tax rate on restaurant food
Amount of tax pay by family member = 22 x 9%
Amount of tax pay by family member = 22 x 0.09
Amount of tax pay by family member = $1.98
Total amount pay by family member = Average amount spent on food + Amount of tax pay by family member
Total amount pay by family member = 22 + 1.98
Total amount pay by family member = $23.98
three times than five times a number
Answer:
15
Step-by-step explanation:
what is this i HATE math Oh MY GOD
I need help pls! A group of hikers park their car at a trail head and hike into the forest to a campsite. The next morning, they head out on a hike from their campsite walking at a steady rate. The graph shows their distance in miles, d, from the car on the day of their hike after h hours. How far is the campsite from their car? Write an equation that describes the relationship between d and h. After how many hours will the hikers be 16 miles from their car?
Answer:
Look down below ;)
Step-by-step explanation:
How far is the campsite from their car?
4 miles
(0,4)
Write an equation that describes the relationship between d and h.
d = 3h + 4
After how many hours will the hikers be 16 miles from their car?
16 = 3h + 4
12 = 3h
4 = h
After 4 hours
amelia machine changes one red token into three white tokens and one white token into two red tokens. amelia has three red tokens and one white token. she uses the machine three times what is the smallest number of tokens she can end up with?
WHOEVER ANSWERS FIRST GETS BRAINLIEST BUT IT MUST BE CORRECT'
George washington Who was as a president
Answer:
George Washington was the first president of the United States of America.
Answer: George washington
Step-by-step explanation:
Gal Gadot borrows $125,000 at a yearly simple interest rate of 4.5%. How much would she pay, in total, if she paid off the loan in 15 years?
Answer:
$241,910.31
Step-by-step explanation:
Compound interest
125,000(1.045)^15
Also, Gal Gadot is the best!
solve 0=-x^2+4x-2
a. -4
b. 8
c. 12
d. 24
Answer:
Question is not clear, and the options are none of the above
Step-by-step explanation:
Mhanifa can you please help me? This is due ASAP! Look at the picture attached. I will mark brainliest
Answer:
1.
y=40
x=14
2.
a=10
b=37
3.
u=62
v=59
4.
s=9
t=14
hope this helps.
Answer:
Properties of a parallelogram
Opposite sides and opposite angles are congruentAdjacent angles are supplementary (sum to 180°)Diagonals bisect each other#1
17 = x + 3 ⇒ x = 17 - 3 ⇒ x = 14y - 2 = 38 ⇒ y = 38 + 2 ⇒ y = 40#2
a + 5 = 15 ⇒ a = 15 - 5 ⇒ a = 103b = 111° ⇒ b = 111°/3 ⇒ b = 37°#3
2u = 124° ⇒ u = 124°/2 ⇒ u = 62°124° + v - 3 = 180° ⇒ v + 121° = 180 ⇒ v = 180° - 121° ⇒ v = 59°#4
t + 5 = 19 ⇒ t = 19 - 5 ⇒ t = 143s = 27 ⇒ s = 27/3 ⇒ s = 9PLEASE HELP?? Online school is kicking my butt
Answer:
60/360*22/7*3*3
=4.714cm^2
Answer:
I HA TE ONLINE SCHOOL
Step-by-step explanation:
Need to find JL Please awnser
Answer:
is that paper omg your in school lucky
what expression is equivalent to -5(x)+(-4)(-3)
Answer:-25+-12
Step-by-step explanation:so I made x value as 5 so I multiplied -5x5 and it's -25 then I multiplied -4x-7 and that's -12 so the equivalent expression for my way is -25+-12
Rosa and her friends are eating out for dinner.
The bill was $45.80. They want to leave a 20% tip.
How much should they leave for a tip (gratuity)?
Answer:$9.16
Step-by-step explanation:
What I did was 20% of $45.80! If you have a tip or a percent problem you can think of it as that percent of the certain number. In math "of" means mupltiply.
Punch in your calculator .2 which is 20% times 45.8 and you get your answer $9.16.
Hope this helps bwo
LAST ONE OK BUT HELP PLZ
Answer:
561 Inches
Step-by-step explanation:
8.5 * 5.5 * 12 = 561
Formula for Volume:
Length x Width x Hight
What is (-7, -3) reflected over the y-axis
Answer:
(7, 3)
Explanation:
(-7, -3) are reflected to positives over the y-axis
Answer:
(-7, -3) reflected over the y-axis = (7, -3)
Step-by-step explanation:
[y]
|
______|_____[x]
(-7, -3) |
|
_________
[y]
|
______|_____[x]
(-7, -3) →|
|
__________
[y]
(-x,+y) | (+x,+y)
______|_____[x]
(-7, -3) → |
(-x, -y) | (+x,-y)
____________
[y]
(-x,+y) | (+x,+y)
______|_____[x]
(-7, -3) → | (7, -3)
(-x, -y) | (+x,-y)
A frog is jumping onto a lily pad. Its height, h (in feet), is recorded at various seconds, t, in the
table below. Write an equation for the curve of best fit, then estimate the height of the frog after 6
seconds.
1
0
2
1
4.5
6
2
3
6.5
4
6
The curve of best fit is an illustration of a quadratic regression
The equation of the curve of best fit is [tex]y = -\frac{17}{18}x^2 + \frac{17}3x + 2[/tex], and the height of the frog after 6 seconds is 2 feet
How to determine the equation of the curve of best fit?To determine the equation of the curve of best fit, we make use of a graphing calculator
Using the graphing calculator, we have the following calculation summary
a = -17/18b = 17/3c = 2The equation of the curve of best fit is represented as:
[tex]y = ax^2 + bx + c[/tex]
Substitute the values for a, b and c.
So, we have:
[tex]y = -\frac{17}{18}x^2 + \frac{17}3x + 2[/tex]
After 6 seconds, the value of x is 6.
So, we have:
[tex]y = -\frac{17}{18} * 6^2 + \frac{17}3 * 6 + 2[/tex]
Evaluate
[tex]y = 2[/tex]
Hence, the height of the frog after 6 seconds is 2 feet
Read more about curve of best fit at:
https://brainly.com/question/25226042
An average batter hits a ball with a force of 380 N. If the bat contacts the ball for a distance of 50 m, how much work is done?
Answer:
...
Step-by-step explanation:
Please show full Solutions. I will mark brainliest for the best answer. Thank you and god bless.
9514 1404 393
Answer:
(2x +y)(2x -y +6)
Step-by-step explanation:
The shaded area is the difference of the areas of the outer square and the inner square. In turn, those areas are the square of the edge dimension of the square. So, the shaded area is the difference of squares:
area = (2x +3)² -(y -3)²
The difference of squares is a "special product" in that it has a factored form that is worth remembering.
a² -b² = (a -b)(a +b)
Using this form for our area, we have ...
area = ((2x +3) -(y -3))((2x +3) +(y -3))
area = (2x -y +6)(2x +y)