The period of the given function is T = 2π
What is the period of the function?The period T of a function f(x) is such that:
f(x + T) = f(x).
In this case, our function is:
f(θ) = e^{iθ}
Remember that this can be written as:
f(θ) = cos(θ) + i*sin(θ)
So yes, this is in did a periodic function.
Then the period of the function f(θ) is the same as the period of the cosine and sine functions, which we know is T = 2π.
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The period of the considered function f(θ) = e^{iθ} is found to be P = 2π (assuming 'i' refers to 'iota' and 'e' refers to the base of the natural logarithm)
What is euler's formula?For any real value θ, we have:
[tex]e^{i\theta} = \cos(\theta) + i\sin(\theta)[/tex]
where 'e' is the base of the natural logarithm, and 'i' is iota, the imaginary unit.
What are periodic functions?Functions which repeats their values after a fixed interval, are called periodic function.
For a function [tex]y = f(x)[/tex], it is called periodic with period 'T' if we have:
[tex]y = f(x) = f(x + T) \: \forall x \in D(f)[/tex]
where D(F) is the domain of the function f.
Suppose that, the period of the function [tex]f(\theta) = e^{i \theta}[/tex] be P, then we get:
[tex]f(\theta + P) = f(\theta)\\\\e^{i(\theta)} = e^{i(\theta + P)}\\\\\cos(\theta) + i\sin(\theta) = \cos(\theta + P) + i\sin(\theta + P)[/tex]
When two complex numbers are equal, then their real parts are equal and their imaginary parts are equal.
That means,
[tex]\cos(\theta) + i\sin(\theta) = \cos(\theta + P) + i\sin(\theta + P)[/tex] implies that:
[tex]\cos(\theta) = \cos(\theta + P)\\\sin(\theta) = \sin(\theta + P)[/tex]
Also, we know that the period of sine and cosine function is [tex]2\pi[/tex]
Thus, we get:
[tex]P = 2\pi[/tex]
Thus, the period of the function [tex]f(\theta) = e^{i \theta}[/tex] is P = 2π
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A cylinder has a height of 9 millimeters and a radius of 11 millimeters. What is its volume? Use ≈ 3.14 and round your answer to the nearest hundredth.
Answer:
3419.46 mm3
Step-by-step explanation:
volume of cylinder = area of circle x heoight
A of circle = pie r sqy = 3.14 x 11 x 11 = 379.94
379.94 x 9 = 3419.46
Part A
Which angles are congruent to ∠5 ? Select all that apply.
A. ∠1
B. ∠2
C. ∠3
D. ∠4
E. ∠6
F. ∠7
Answer:
A, F, C
Step-by-step explanation:
(I think)
∠A and ∠B are supplementary. The measure of ∠A is 34°.
What is the measure of ∠B?
Enter your answer in the box.
Please help!
Answer:
146
Step-by-step explanation:
Given;
∠A and ∠B are supplementary. The measure of ∠A is 34°.
To Find;
What is the measure of ∠B?
Note:
Supplementary = 180 degree
Solve:
Since supplementary = 180 degree
34 + x = 180
Subtract 34 from both sides
x + 34 - 23 = 180 - 34
Simplify
x = 146
Hence, the measure of ∠B is 146
~Learn with Lenvy~
328 rattle snakes in 2008. How many will there be in 2024?
402853
21498508
32800
20992
Answer:
[tex]{ \tt{12 \: months = 328}} \\ { \tt{(12 \times 15) = \frac{(15 \times 328)}{1} }} \\ \\ = { \tt{4920}}[/tex]
Answer:
2008=328
2024=?
Step-by-step explanation:
12×13 = 16×328/1
find the area of the triangle if the length is 22 and the height is 15
Answer:
low 0.5 *the length of the base * the height
Step-by-step explanation:
0.5*22*15=165
Is (3, -5) a solution to this system of equations?
y = -1/3x - 4
y = -2x + 1
Yes or No
Answer: Yes
Step-by-step explanation:
Solve the system of equations by setting the two substituting the first y equation in for the second and getting: -1/3x - 4 = -2x + 1.
Now, add 2x to the left side to cancel it from the right and add 4 to the right side to cancel if from the left to get: (5/3)x = 5
Solve for x to get 3.
Plug x into the second equation (could be either equation though) and get: y = -2(3) = 1 = -5.
Thus, (3,-5) is a solution :)
Use any method to solve the system:
y = 3x - 10 and y=2x-5
Answer:
x=5
y=5
y = 3x - 10 -----------(1)
y=2x-5------------(2)
Step-by-step explanation:
put the value of y in 2nd equation
y=2x-5
=3x - 10=2x-5
=3x-2x=-5+10
= x=5,
now put the value of x in 1st equation.
y = 3x - 10
=y=3×5-10
=y=15-10
= y=5.
check
put the value of x and y in 1st equation.
y = 3x - 10
x=5,,y=5
=5=3×5-10
= 5=5
hope it's help you
:-befrank
The table shows the masses of eight polar bears.
An outlier is a number that is way smaller or way larger than that of other numbers in a data set. The outlier is 62. As a result, the median and the mean would be smaller. The mode would not be affected by the outlier.
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Please help me with complement or supplement of an angles.
Answer: 101 degrees
Step-by-step explanation:
Drag each tile to the correct box.
The given steps for constructing a line tangent to circle O that is tangent to the circle at point P on the circle are listed out of order. Arrange the steps in the correct sequence.
A. Without changing the compass width, place the compass on R and make another arc, intersecting the first, and label the intersection S.
B. Draw a line through P and S.
C. With the compass on P, draw an arc on each side of P. Label the intersections Q and R.
D. Draw a straight line from the center, O, through P and extending past P.
E. With the compass on Q, set its width to a setting greater than. Make an arc outside the circle
Answer:
D, C, E, A, B
Step-by-step explanation:
This is essentially the construction of a perpendicular bisector.
D. Draw a straight line from the center, O, through P and extending past P
C. With the compass on P, draw an arc on each side of P. Label the intersections Q and R.
E. With the compass on Q, set its width to a setting greater than. Make an arc outside the circle
A. Without changing the compass width, place the compass on R and make another arc, intersecting the first, and label the intersection S
B. Draw a line through P and S.
How to find arc in math?Arc length is the distance between 2 points in the arc of a circle. The arc of the circle could be calculated by using the following formula: Arc: Length = Θ x r
What does arc mean?
In general, the arc is a portion of the curve. In mathematics, unless otherwise begain, then arc usually refers to the portion of the circle. Types of arcs. A chord, or the central angle and an inscribed angle may divide the circle into 2 arcs.
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Please help I will give brainliest.
To answer these questions, we need to graph the equation as well as turn this into slope-intercept form, this is y = mx + b. The m is our slope and the b is the y-intercept.
-> See attached for graph
1.5x + 4.5y = 18
4.5y = -1.5x + 18
y = -[tex]\frac{1}{3}[/tex]x + 4
The slope is -[tex]\frac{1}{3}[/tex]
y = -1/3x + 4
The y-intercept is (0, 4)
The x-intercept is (12, 0)
Rotate shape A 90° anti-clockwise with centre of rotation (0,0).
What are the coordinates of the vertices of the image?
Answer:
(-6, 1) (-6, 3) (-5, 3) (-5, 2) (-3 2) -3, 1
Step-by-step explanation:
By rotating 90 degrees x become y and y becomes negative x
Help please I need helps please
Answer:
I belive the answer is 96 ft.
Step-by-step explanation:
Hope that helps!
Write f(x) = 2x2 – 44x 185 in vertex form. To write f(x) = 2x2 – 44x 185, factor out from the first two terms. Next, form a perfect square trinomial keeping the value of the function equivalent: f(x) = 2(x2 – 22x 121) 185 – 242 The function written in vertex form is f(x) = (x – )2.
The quadratic function f(x) = 2x² – 44x + 185 is written in vertex form is f(x) = 2(x – 11)² – 57.
What is a quadratic equation?It is a polynomial that is equal to zero. Polynomial of variable power 2, 1, and 0 terms are there. Any equation having one term in which the power of the variable is a maximum of 2 then it is called a quadratic equation.
The quadrattic equation is f(x) = 2x² – 44x + 185.
Take common 2 from the equation, we have
[tex]f(x) = 2(x^2 - 22x )+ 185[/tex]
Add and subtract 121, we have
[tex]f(x) = 2(x^2 - 22x +121 - 121 )+ 185\\\\f(x) = 2[(x^2 - 11)^2-121]+ 185\\\\f(x) = 2(x-11)^2 - 242 + 185\\\\f (x ) = 2(x-11)^2 -57[/tex]
And we know that the standard equation
f(x) = a(x - h)² + k
On comparing, we have
The vertex (h, k) is (11, -57).
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Answer:
1. 2
2. 2
3. 11
4. -57
Step-by-step explanation: actual answers
A circle is to be drawn with radius 3.5 inches. the radius is measured as 3.6 instead, what error does this cause in the area of the circle?(leave your answer in terms of pi )
Answer:
[tex]0.71\pi\: in^2[/tex]
Step-by-step explanation:
[tex]r_1= 3.5\: in[/tex]
[tex]r_2= 3.6\: in[/tex]
[tex]A_1=\pi r_1^2=\pi(3.5)^2= 12.25\pi \:in^2[/tex]
[tex]A_2=\pi r_2^2=\pi(3.6)^2= 12.96\pi \:in^2[/tex]
[tex]Difference\: in \:area =A_2-A_1=0.71\pi\:in^2[/tex]
[tex]\implies Error \:in\: the \:area \:of\: the \:circle = 0.71\pi\: in^2[/tex]
2. What is the measure of angley?
(2 pts.)
52°
to
Answer: the answer is 55 degrees
Step-by-step explanation:
6
It costs 35p per minute to hire a powerful computer. How much will it cost to hire the
computer from 07:40 to 08:15?
Answer:
1225p
Step-by-step explanation:
1 minute = 35p
07:40 to 08:15 : 35 minute
=> 35 minute *35p=1225p
Simplifying into an equivalent expression, fill in the missing pieces:
Write the following expression using an exponent.
1x7x7x7x7x7
Answer:
7^5
Step-by-step explanation:
Hopefully this helps :)
A median drawn to a side of a triangle is
Select one:
O a. a ray
O b. a segment
O c. a line
The length of one leg of an isosceles right triangle is 3 ft. What is the perimeter of the triangle? 3 3 StartRoot 2 EndRoot ft 3 3 StartRoot 3 EndRoot ft 6 3 StartRoot 2 EndRoot ft 6 3 StartRoot 3 EndRoot ft.
The perimeter of the isosceles right triangle comes to be 6+3√2.
Given that the length of one leg of an isosceles right triangle = 3 ft
What is an isosceles right triangle?A right-angle triangle having sides other than hypotenuse equal to each other is called an isosceles right triangle.
So, The length of the other leg of an isosceles right triangle = 3 ft
From Pythagoras theorem
Hypotenuse²=Perpendicular²+Base²
So, in the given isosceles right triangle
Hypotenuse²=Leg 1²+Leg2²
Leg 1=Leg2 = 3 feet
Hypotenuse² = 3²+3²
Hypotenuse = 3√2 ft.
So, the perimeter of the triangle = 3+3+ 3√2
The perimeter of the triangle =6+3√2
Therefore, The perimeter of the isosceles right triangle comes to be 6+3√2.
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Answer:
6 + 3 StartRoot 2 EndRoot ft
Step-by-step explanation:
Edge2022
Question 1
1 pts
Use the GSS file to investigate whether or not Americans use the Internet at least 7
hours per week (estimating an hour per day). Perform the One Sample T Test
procedure (as presented in SPSS Demonstration 1) to do this test with the variable
WWWHR. Do the test at the .01 significance level. What is the T [1]?
Put 40 in the
The computation of the significance level shows that the p-value is less than 0.01 and the conclusion is that Americans use the internet more than 7 hours weekly.
What is a significance level?It should be noted that the significance level simply means the probability that an event occured by chance.
From the complete question, it can be noted that at 0.01 significance level, the t statistic is 17.873 and the degree of freedom is 539.
The p-value for the right tailed test is 0. Therefore, since the p value is less than 0.01, we will reject the null hypothesis. The conclusion is that Americans use the internet more than 7 hours weekly.
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Unit 10: circles homework 6: arc & angle measures
**please explain how you get your answer**
Circles are perfectly round figures that have only one central angle
The measure of JML is 233 degrees
How to determine the measures of angle JML?The question is incomplete, so I will give a general explanation using the following parameter:
JL = 127 degrees.
Angles at a point add up to 360 degrees
So, we have:
JML + 127 = 360
Make JML the subject
JML = 360 - 127
JML = 233
Hence, the measure of JML is 233 degrees
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Can y’all please solve this
Find the 7th term of the geometric sequence whose common ratio is 2/3 and whose first term is 6.
! PLEASE HELP!
A signal can be sent from one location to another by running different colored flags up a flagpole, one above the other. There are 15 different colored flags to choose from but only 4 flags will be flown. Find the number of different signals consisting of 4, if the first flag must be orange.
If the first flag is orange then the number of different signals consisting of 4 flags is ____
Using the combination formula, it is found that if the first flag is orange then the number of different signals consisting of 4 flags is 364.
The order in which the flags are chosen is not important, hence, the combination formula is used to solve this question.
What is the combination formula?[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this problem, considering that the first flag is orange, 3 flags will be chosen from a set of the remaining 14, hence the number of signals is given by:
[tex]C_{14,3} = \frac{14!}{3!11!} = 364[/tex]
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What does Mean median and mode mean?
Answer:
mean-average of a data set
mode-most common number in a set
median-middle number of the set
Step-by-step explanation:
you can ask me a question for more info
Answer:
Step-by-step explanation:
Mean - Is the average taken for a set of numbers
Median - The middle value in a data set of numbers
Mode - The number that occurs the most in a given list of numbers.
If x = 2and y = - 2 , find the value of 4x ^ 2 * y ^ - 2
=========================================================
Plug in the values of the variables & simplify:-
[tex]\longrightarrow\pmb{4x^2y^2}[/tex]
The values of the variables are:-
[tex]\bigstar{\boxed{x=2~and~y=-2}[/tex]
Simplify:-
[tex]\longrightarrow\pmb{4(2)^2(-2)^2}[/tex]
[tex]\longrightarrow\pmb{4*4-4}[/tex]
[tex]\longrightarrow\pmb{16-4}[/tex]
[tex]\longrightarrow\pmb{12}[/tex]
==========================================================
note:-Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I'll comment and/or edit my answer :)
Answer:
the answer for this is 4.
Find the sum of the following polynomials
(3x^3+ 8x^2– 3) + (7x^3- 4x + 4)
Answer:
10x^3+8x^2-4x+1 is answer
(will mark brainlist)
How would we name the polyonomi ?
PLS SOMEONE HELP ME FIND THE ANSWER AND EXPLAIN #1 to me. and maybe steps. Also if you can help with any other questions that be nice! ILL MARK BRAINLIST
Answer:
I don't necessarily understand your question but usually the answer to a polynomial question is a binomial answer