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 certain bacterium measures 2. 7 × 10–2 mm. A colony contains 5. 3 × 103 of the bacteria. What is the total length of this colony if it forms a straight line?
The length of the colony is the product of 5. 3 × 10^3 and the length of the bacteria
The total length of the colony is 143.1 mm
How to determine the length of the colony?The given parameters are:
Bacteria = 2.7 × 10^–2 mm.
Colony = 5. 3 × 10^3 of the bacteria
So, the length (L) of the colony is:
[tex]L = 5.3 * 10^3 * 2.7 * 10^{-2[/tex]
Rewrite as:
[tex]L = 5.3 * 2.7* 10^3 * 10^{-2[/tex]
Evaluate the products
[tex]L = 14.31* 10[/tex]
Evaluate the product
[tex]L = 143.1[/tex]
Hence, the total length of the colony is 143.1 mm
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Simon does some shopping on the internet. He buys 4 CDs at $8.63 each. How much do the CDs cost altogether?
Answer:
34.52
Step-by-step explanation:
Multiplication plus may i have branlies t
Answer:
the total would be 34.52
Step-by-step explanation:
If we have 4 Cd's that cost 8.63 a piece, all we would need to do is multiply 8.63 by 4, or just add 8.63 4 times.
hope this helps, please rate and mark as brainlest.
On May 1, Anna purchased a new condo. She pays a monthly maintenance fee of $230. Her monthly property taxes equal 13.5% of the monthly fee. How much will Anna pay in property taxes for this calendar year?
Answer:
$31.05
Step-by-step explanation:
You can get this answer by changing percent (13.5%) to just 13.5, or in other words, a decimal. you also change 230. to a decimal by by moving the decimal point two times to the left to get 2.30. You can then get your answer by multiplying the values together (2.30 x 13.5)
Can you guys please help!!!??
ur mom
Step-by-step explanation:
Please a quick question
Enter an expression equivalent to a^5 in the form of a^x/a^y.
Answer:
a^7/a^2Step-by-step explanation:
The exponents subtract. really easy 7-2=5
There are infinite possiblities to this.
SonicIsCoool, im at your service if you need more help :)
Thank you.
Answer:
[tex]\frac{a^{8} }{a^{3} }[/tex]
Step-by-step explanation:
using the rule of exponents
[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{(m-n)}[/tex] , then
[tex]\frac{a^{8} }{a^{3} }[/tex] = [tex]a^{(8-3)}[/tex] = [tex]a^{5}[/tex]
The group is trying to determine what the price difference would be per passenger if 10 of them go on the trip versus if 16 of them go on the trip. what is the difference in price per passenger for a group of 16 versus a group of 10? $46.25 $36.25 $56.25 $26.25
The difference in price per passenger for a group of 16 versus a group of 10 for this condition is given by: Option D: $26.25
What does a graph of a function represents?A graph contains data of which input maps to which output.
For Cartesian plane, this includes inputs x-axis, and corresponding output on y axis and the highlighted point (x,y) shows that the x value is related to the specific y value.
For the considered case, the missing image is attached below.
From the image, we see that corresponding to the value of number of people 10, the corresponding point on the graph is connected with vertical axis at $1300
For number of people 16, it is $2500
The price per passenger for 10 people is: 1300/10 = $130 The price per passenger for 16 people is: 2500/16 = $156.25The difference in these prices is 156.25 - 130 = 26.25 (in dollars)
Thus, the difference in price per passenger for a group of 16 versus a group of 10 for this condition is given by: Option D: $26.25
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Answer:
D. $26.25
Step-by-step explanation:
edg
A figure is made up of two triangles and a square. The triangles and the square have the same base length of 5 feet. The triangles have a height of 4 feet. What is the total area of the figure?
Answer:
45 ft^2.
Step-by-step explanation:
Area = area of the square + 2 * area of one triangle
= 5^2 + 2 * 1/2 * 5 * 4
= 25 + 20
= 45 fT^2.
Julio makes a scale drawing of the kitchen floor to determine how
many square feet of flooring he needs to buy. the scale of his drawing
is 1 inch:4 feet.
what is the area of julio's actual kitchen floor?
27
step 1 is to convert 3. to
step 2 is to convert 4. to
step 3 is to multiply each improper fraction by 4
step 4 is to multiply your answers to step 3 together to find the
answer
The scale drawing of Julio's kitchen would change the kitchen size
The actual area is 243 square feet
How to determine the actual area of Julio's kitchen?The parameters are given as:
Length = 4.5 inchesWidth = 3.375 inchesStart by converting the dimensions to feet using the scale ratio
Actual length = 4.5 inches/ (1 inch/ 4 feet) = 18 feetActual width = 3.375 inches/ (1 inch/ 4 feet) = 13.5 feetThe area is then calculated as:
Actual Area = Actual length * Actual Width
This gives
Actual Area =18 feet * 13.5 feet
Evaluate the product
Actual Area = 243 square feet
Hence, the actual area is 243 square feet
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find the value of x when y=14. y= -6x+5
Answer:
x = -3/2
Step-by-step explanation:
To find the unknown value, substitute all known values and solve for the one remaining. After substitution, this becomes a 2-step linear equation, so is solved by the procedure for such equations.
y = -6x +5 . . . . . given
14 = -6x +5 . . . . substitute known value
9 = -6x . . . . . . . subtract 5 (step 1)
9/-6 = x = -3/2 . . . . divide by the coefficient of x (step 2);
Hello!
In order to find the value of x, we should take the value of y and plug it in and then simplify.
[tex]\bold{y=-6x+5}[/tex]
Plug in:
[tex]\bold{14=-6x+5}[/tex]
Switch places:
[tex]\bold{-6x+5=14}[/tex]
Now, subtract 5 from both sides:
[tex]\bold{-6x=14-5}[/tex]
[tex]\bold{-6x=9}[/tex]
Divide both sides by -6 in order to isolate x:
[tex]\bold{x=-\displaystyle\frac{9}{6}}[/tex]
Can this fraction be reduced? Sure, we can divide the numerator (9) and the denominator (6) by 3:
[tex]\bold{-\displaystyle\frac{3}{2}}[/tex]
As a Mixed Fraction:
[tex]\bold{1\displaystyle\frac{1}{2}}[/tex]
Hence, the value of x is:
[tex]\huge\boxed{\boxed{\mathfrak{\star{Answer:{\boxed{-\frac{3}{2} }}}}}}[/tex]
Hope everything is clear.
Let me know if you have any questions!
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#NeverGiveUp
[tex]\rm{A~teen~who~never~gives~up}[/tex]
which fraction is between 2/3 and 6/7
Answer:
For example, 16/21
Step-by-step explanation:
Are there choices?
There is an infinite number of numbers between any two numbers.
2/3 = 14/21
6/7 = 18/21
One example of a fraction between 2/3 and 6/7 is 16/21
16/21 is between 2/3 and 6/7.
2(x-3)+3y when x=5 and y=3
Step-by-step explanation:
2 ( 5 - 3 ) + 3 ( 3 )
2 × 2 + 9 = 4 + 9 = 13
Greg works mowing lawns and babysitting.he earns $8.90 and hour for mowing and 7.90 and hour for babysitting how much will he earn for 6 hours of mowing and 5 hours of babysitting ?
Answer:
92.9
Step-by-step explanation:
8.90 times 6 equals 53.40
7.90 times 5 equals 39.50
39.50 plus 53.40 equals 92.9
5. A box contains 4 white balls and 6 yellow balls. A ball is drawn at random from the box and is not replaced. What is the probability that both balls are white?
8/45
3/25
4/25
2/15
Answer:
2/15
Step-by-step explanation:
Given:
A box contains 4 white balls and 6 yellow balls. A ball is drawn at random from the box and is not replaced. What is the probability that both balls are white?
8/45
3/25
4/25
2/15
Solve:
Knowing that total = 10 { 4 white balls and 6 yellow balls}
P(first white)=4/10=2/5 { 4 out of 10 balls are white}
P(second white)=3/9=1/3 { 3 out of 9 balls are white; Since no replaced}
P(both white)=2/5 × 1/3=2/15
Hence, Answer = 2/15
Lenvy~
Please help and explain WILL MARK BRAINLIEST!!!!
Answer:
x is 19.5 degress
Step-by-step explanation:
hmmm so here oh i see now okay:
since a line is 180 degress lets write
2x + 82.5 + 3x = 180
now we umm add the ones with the same variable and power
5x + 82.5 = 180
5x = 180 - 82.5
5x = 97.5
x = 19.5
This is an angle on a straight line and It is equal to 180°
2x° + 3x° + 82.5° = 180°
5x° = 180° - 82.5°
5x = 97.5°
x = 19.5°
To indicate the angle
2x => 2(19.5°) => 39°
3x => 3(19.5°) => 58.5°
The angle are (39°, 82.5°, 58.5°
if f(x)=4x^2-3 and g9x)=x+1, find (f-g)(x)
Step-by-step explanation:
(f-g)(x) = f(x) - g(x)
the same applies to all other basic operations (like addition, multiplication, ...).
so,
(f-g)(x) = 4x² - 3 - (x + 1) = 4x² - 3 - x - 1 = 4x² - x - 4
i need help with this problem
Answer:
the pizza one is 4/8
Step-by-step explanation:
skating one 6.75 miles
What is 60% markup on $18.25?
Compute the total cost of an item you purchased for $18.25, but you now want to resell it for 60% more than what you've paid for it. What is the new cost?
Answer:29.2
Step-by-step explanation:The equation used to add a markup percent to a product is the cost plus the markup percentage multiplied by the cost.
Answer:
$29.20
Step-by-step explanation:
The original price of an item is 100%, so a 60% mark up means that the price will now be 160% of the original price.
160% = 160/100 = 1.6
⇒ 160% of $18.25 = 1.6 × 18.25 = $29.20
Find the surface area of the prism. Write your answer as a decimal.
Answer:
49.2 square yards
Step-by-step explanation:
The surface area of a rectangular prism can be found using the formula.
A = 2(LW +H(L +W)) . . . . where L, W, H are length, width, height
A = 2(3×5 +1.2(3 +5)) = 2(15 +9.6) = 49.2 . . . . square yards
Which expression is equivalent to the expression -3(4x - 2) - 2x
A) -8x
B) -16x
C) -14x - 2
D) -14x + 6
Answer:
-14x + 6 (option D)
Step-by-step explanation:
To solve the given equation, you first need to distribute the negative 3.
So, you need to multiply
(4x)(-3) ; (-2)(-3)
(4x)(-3)= -12x
(-2)(-3)= 6
So, your new, distributed, equation would be:
-12x + 6 - 2x
If we combine like terms (-12x - 2x), our new equation will be:
-14x + 6
solve quadratic function
3(x-5)^2-17=-5
Answer:
x = 3 , x = 7
Step-by-step explanation:
3(x - 5)² - 17 = - 5 ( add 17 to both sides )
3(x - 5)² = 12 ( divide both sides by 3 )
(x - 5)² = 4 ( take square root of both sides )
x - 5 = ± [tex]\sqrt{4}[/tex] = ± 2 ( add 5 to both sides )
x = 5 ± 2
then
x = 5 - 2 = 3
x = 5 + 2 = 7
1+2=
3+4
4=3
)+0
you dont have to answer just put a random letter or something
Answer:
3
7
last one doesn't even make sense
Solve this question. Explain or show your reasoning. 1/2x-7=1/3(x-12)
The figure below consists of a square and a right triangle. Find the missing length x.
Answer:
12
Step-by-step explanation:
pythagorean theorem
x - 3y = 4
2x - 5y = 8
solve by substitution
Answer:
y = 0
x = 4
Explanation:
x - 3y = 42x - 5y = 8make x the subject,
x - 3y = 4
x = 4 + 3y __ equation 1
2x - 5y = 8
x = (8+5y)/2 __ equation 2
using substitution method:
(8+5y)/2 = 4 + 3y
8 + 5y = 8 + 6y
6y - 5y = 8 - 8
y = 0
Find x,
x = 4 + 3y
x = 4 + 3(0)
x = 4
Answer:
x = 4
y = 0
Step-by-step explanation:
Step 1. Pick one equation and rewrite in the form of x= OR y=x - 3y = 4 (original)
x = 4 + 3y (rewritten)
Step 2. Substitute for x in the other equation2x -5y = 8 (second equation)
2(4 + 3y) - 5y = 8 (substitute 4 + 3y for x)
Step 3. Solve for the unknown variable, y2(4 + 3y) - 5y = 8 (distribute)
8 + 6y - 5y = 8 (combine like terms)
y = 0 (first variable)
Step 4. Find x by plugging y into an equationx - 3y = 4 (original)
x - 3(0) = 4 (substitute 0 for y)
x = 4 (second variable)
FINAL SOLUTION: x = 4, y = 0You can double check this by plugging these numbers back into each equation; x = 4 and y = 0 is true for both.
I hope this helps!
Please help me
What is the difference between 14n +7 and 8n + 3/4
A research firm has determined that 80% of telephone
respondents will agree to answer an opinion poll. If 20
people are contacted, what is the probability that exactly 14
people agree to be polled?
The probability that out of 20, 14 agree to answer is:
P(14) = 0.109
How to find the probability?
We know that the 80% of the respondents will agree to answer the opinion poll (and 20% don't).
Then the probability that a random respondent agrees to answer the poll is 0.8
Now, the probability that out of 20, 14 agree to answer, is:
[tex]P(14) = C(20, 14)*(0.8)^{14}*(0.2)^6[/tex]
Where C(20, 14) is the number of different combinations of 14 elements that we can make out of the 20 elements (the number of permutations).
[tex]C(20, 14) = \frac{20!}{(20 - 14)!*14!} = \frac{20*19*18*17*16*15}{6*5*4*3*2} = 38,760[/tex]
Replacing that in the probability, we get:
[tex]P(14) = 38,760*(0.8)^{14}*(0.2)^6 = 0.109[/tex]
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A hole-punch machine is set to punch a hole 1. 84 centimeters in diameter in a strip of sheet metal in a manufacturing process. The strip of metal is then creased and sent on to the next phase of production, where a metal rod is slipped through the hole. It is important that the hole be punched to the specified diameter of 1. 84 cm. To test punching accuracy, technicians have randomly sampled 12 punched holes and measured the diameters. The data (in centimeters) follow. Use an alpha of. 10 to determine whether the holes are being punched an average of 1. 84 centimeters. Assume the punched holes are normally distributed in the population. 1. 81 1. 89 1. 86 1. 83 1. 85 1. 82 1. 87 1. 85 1. 84 1. 86 1. 88 1. 85
Using the t-distribution, as we have the standard deviation for the sample, it is found that it can be concluded that the holes are being punched an average of 1. 84 cm.
What are the hypotheses tested?At the null hypotheses, it is tested if the mean is of 1.84 cm, that is:
[tex]H_0: \mu = 1.84[/tex]
At the alternative hypothesis, it is tested if the mean is different of 1.84 cm, that is:
[tex]H_1: \mu \neq 1.84[/tex]
What is the test statistic?The test statistic is given by:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
The parameters are:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.s is the standard deviation of the sample.n is the sample size.Considering the hypothesis and the given sample, it is found that the parameters are as follows:
[tex]\overline{x} = 1.85, \mu = 1.84, s = 0.0235, n = 12[/tex].
Hence, the test statistic is given by:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{1.85 - 1.84}{\frac{0.0235}{\sqrt{12}}}[/tex]
[tex]t = 1.47[/tex]
What is the decision?Considering a two-tailed test, as we are testing if the mean is different of a value, with a significance level of 0.1 and 12 - 1 = 11 df, the critical value is of [tex]|t^{\ast}| = 1.7959[/tex]
Since the absolute value of the test statistic is less than the critical value, we do not reject the null hypothesis and it can be concluded that the holes are being punched an average of 1. 84 cm.
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find the value of x in the triangle shown below.
x=[]
Answer:
x=[80]
Step-by-step explanation:
angle 1+angle 2+angle x=180
50 +50+x=180
100+x=180
100-100+x=180-100
x=80
Answer:
80
Step-by-step explanation:
The triangle on the image is an isosceles triangle so both of the bottom angles' measure = 50
The sum of interior angles in a triangle is equal to 180
if two angles has 50 degrees then x:
50 + 50 + x = 180
100 + x = 180 subtract 100 from both sides
x = 80
How many 1/6 pound servings are there in 4/5 of a pound of chicken?
Answer: [tex]4\frac{4}{5}[/tex]
Step-by-step explanation:
To see how many [tex]\frac{1}{6}[/tex] pound servings are in [tex]\frac{4}{5}[/tex] of a pound of chicken we must divide [tex]\frac{4}{5}[/tex] by [tex]\frac{1}{6}[/tex]
[tex]\frac{4}{5}[/tex]÷[tex]\frac{1}{6}[/tex]
When dividing by a fraction you can take the reciprocal (flip the numerator and denominator) and you can multiply instead of dividing
[tex]\frac{4}{5}[/tex]×[tex]\frac{6}{1}[/tex]=[tex]\frac{24}{5}[/tex]=[tex]4 \frac{4}{5}[/tex]
Answer:
24/5, or 4.8, servings
Step-by-step explanation:
Let s represent the number of servings. We have:
[tex] \frac{1}{6} s = \frac{4}{5} [/tex]
[tex]s = \frac{24}{5} = 4.8[/tex]
At one farmer’s market, bananas cost $0. 80 per pound. At another farmer’s market, bananas are sold in 5-pound bags for $4. 50 per bag. Which explains how to find the better buy? Divide 4. 50 by 5 to find the unit rate for the 5-pound bag, and compare that number to $0. 80 per pound. Divide 0. 80 by 5 to find the unit rate for the 5-pound bag, and compare that number to $0. 80 per pound. Multiply 4. 50 by 5 to find the cost for 5 pounds, and compare to $4. 50 per bag. Multiply 4. 50 by 0. 80 to find the cost for 5 pounds, and compare to $4. 50 per bag.
To find the better buy divide 4.50 by 5 to find the unit rate for the 5-pound bag, and compare that number to $0. 80 per pound.
The cost price per pound is the amount of money required to buy one pound of a brand or goods.
To find the cost price per pound, divide the total amount of cost of the goods to the total number of goods.
At one farmer’s market, bananas cost $0.80 per pound.
At another farmer’s market, bananas are sold in 5-pound bags for $4. 50 per bag. To compare it with first market price, divide the 5 pound bags with $4.50.
The cost of one bag in this market is,
[tex]C=\dfrac{4.50}{5}\\C=0.5625[/tex]
As this cost is less, thus, the cost of this market for one banana is less than the first market and so this is the better buy.
Hence, to find the better buy divide 4.50 by 5 to find the unit rate for the 5-pound bag, and compare that number to $0. 80 per pound.
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