a) The phasor form of E-field = xˆ 2cos(wt - kz) - yˆ 4cos(wt - kz) is 2√5 L(-63.43).
Polarization type is linearly polarised.
b) The phasor form of E-field = ?
E(z,t) = xˆ 2cos(wt + kz) - yˆ 4sin(wt + kz) is E(z,t) =2√5 L(-143.43). polarization type is elliptical.
We have given that
E⃗(z,t) =2xˆcos(wt - kz) - 4 yˆcos(wt - kz)
|r⃗ | = √((2cos(wt - kz))² + (- 4cos(wt - kz))²)
= √(4cos²(wt - kz) + 16cos²(wt - kz))
= √(20cos²(wt - kz))
= 2√5 cos(wt - kz)
φ = 4cos(wt - kz)/(2cos(wt - kz))
= tan⁻¹ 1(-2) = -63.43°
So, E(z,t) = 2√5 L(-63.43)
b) E(z,t) = xˆ 2cos(wt + kz) - yˆ 4sin(wt + kz)
= xˆ 2cos(wt + kz) - yˆ 4cos(wt + kz -π/2)
|r| = √((2cos(wt + kz))² + (- 4sin(wt -+kz))²)
= √20
phi = tan⁻¹(- 4cos(wt - kz)/(2cos(wt - kz)) - π/2
= tan⁻¹( -2) + π/2 = - 143.43
so, E(z,t) =2√5 L(-143.43)
E(z,t) = xˆ 2cos(wt - kz) - yˆ 4cos(wt - kz)
if wt = 0°
E(z,t) = xˆ 2cos(0 - kz) - yˆ 4cos(0- kz)
= 2xˆ - 4yˆ
wt = 30° , E(z,t) = xˆ 2cos( - kz) - yˆ 4cos(0- kz)
E(z,t) = √3/2(2) xˆ - √3/2(4) yˆ
= √3xˆ - 2√3yˆ
for wt = 45°
E(z,t) = √2 xˆ - 2√2 yˆ
for wt = 90° =>E(z,t) = 0
for wt = 60° , E(z,t) = xˆ - 2 yˆ as seen in above graph that is linear polarised
For part (b) ,
E(z,t) = 2 xˆcos(wt - kz) - 4yˆ sin(wt + kz)
From graph elliptical polarised,
for wt = 0 , E(0,t) = 2 xˆ
for wt = 90° , E(0,t) = -4yˆ
for wt =180° , E(0,t) = -2 xˆ
for wt = 270° , E(0,t) = -4yˆ
Hence, we get the answer of both parts.
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Find the area of the equilateral triangle to the nearest hundredth, given the radius.
9514 1404 393
Answer:
20.78 square units
Step-by-step explanation:
The area of a regular polygon of radius r and number of sides n is given by ...
A = (n/2)r²sin(360°/n)
For this regular 3-gon of radius 4, the area is ...
A = (3/2)(4²)sin(360°/3) = 24(√3/2) = 12√3 . . . square units
The area is about 20.78 square units.
HELP (for the first select answer its “yes” or “no”)
Answer:
No, the sample is too small compared to the size of the shipment.
Step-by-step explanation:
Find the exact value of cos (11pi/8)
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The exact value of [tex]cos(\frac{11\pi }{8} )[/tex] is [tex]-\sqrt{\frac{2+\sqrt{2} }{4} }[/tex].
What is the exact value of trigonometric function?The exact values of trigonometric functions are values of trigonometric functions of certain angles that can be expressed exactly using expressions containing real numbers and roots of real numbers. These values are also called analytic values of trigonometric functions or trigonometric values of special angles.
What is trigonometric function?The trigonometric functions are also called the angle functions, which relates the angles and the ratios of the sides of a right angle triangle.
According to the given question.
We have a trigonometric function
[tex]cos(\frac{11\pi }{8} )[/tex]
We have to find the exact value of the above trigonometric function.
since,
[tex]\frac{11\pi }{8}[/tex] can be written as [tex](\pi +\frac{3}{8\pi } )[/tex]
[tex]\implies cos(\frac{11\pi }{8} ) = cos(\pi +\frac{3}{8}\pi )[/tex]
And we know that,
Cos(π + θ) = -cosθ
Because, π + θ lies in third quadrant and in third quadrat cos gives negative values.
Also,
[tex]cos\frac{\alpha }{2} = \pm\sqrt{\frac{1+cos\alpha }{2} }[/tex] ....(i)
Therefore,
[tex]cos(\pi +\frac{3}{8} \pi )[/tex]
[tex]= -cos(\frac{3}{8} \pi )[/tex]
[tex]= -cos(\frac{3}{2(4)} \pi )[/tex]
[tex]= -\sqrt{\frac{1+cos\frac{\pi }{4} }{2} }[/tex]
[tex]= -\sqrt{\frac{1+\frac{1}{\sqrt{2} } }{2} }[/tex]
[tex]= -\sqrt{\frac{1+\frac{\sqrt{2} }{2} }{2} }[/tex]
[tex]= -\sqrt{\frac{2+\sqrt{2} }{4} }[/tex]
Hence, the exact value of [tex]cos(\frac{11\pi }{8} )[/tex] is [tex]-\sqrt{\frac{2+\sqrt{2} }{4} }[/tex].
Thus, option A is correct.
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what is the slope of the line shown?
The rabbit population at the city park increases by 14% per year. If there are intially 481 rabbits in the city park.
Write a model for the population (y) in terms of years (t).
y =
Find the population in 17 years.
Answer:
y = 0.14t + 481
Population in 17 years: 483.38
Step-by-step explanation:
y = (m) (x) + b
y = (slope) (x) + starting value
help with math!!
Find the volume of each right rectangular prism
Answer:
7: 7.75 8: 6.98
Step-by-step explanation:
What is the correct equation for this phrase?
Nine less than twice a number.
Answer:
[tex]2k - 9[/tex]
Step-by-step explanation:
jsjsjsjsjjsjsksksksksksksksksksjskkwjwjwjwkw
A walking path 78 mile long Colleen planted 14 bushes the same distance apart along the path how far power are the 1st 2 bushes along the path
Answer:
The bushes will be located 6 meters apart from each other.
Step-by-step explanation:
Given that at a walking path 78 mile long Colleen planted 14 bushes the same distance apart along the path, to determine how far away are the 1st 2 bushes along the path, the following calculation must be performed:
78/13 = X
6 = X
Thus, since the first bush is at meter 0, the remaining 13 bushes will be located 6 meters apart.
1. Write an integer that can
represent 200 years ago?
At a furniture store, the employees earn a 2.5% commission on every sale they make. If Ginny made $8850 in sales one week, how much did she earn in commission?
help please :( 100 points
Answer:
She earned 221.25 in commission
Step-by-step explanation:
2.5% of 8850 is 221.25
Which of the numbers given
are rational?
Select all that apply:
8.634092...
6.28232
7144
1.465359...
32.71481
Answer:
7144
Step-by-step explanation:
Determine if the triangle is a right triangle.
Answer:
Yes, this is a right triangle
Step-by-step explanation:
a² + b² = c²
65² + 72² = 97²
4225 + 5184 = 9409
9409 = 9409
Since the hypotenuse equals the 2 legs, it's a right triangle
What is the answer please help no links I will report
Answer:
6
Step-by-step explanation:
because its the middle number
Find the surface area of the prism. 3m, 4m, 8m,5m
Step-by-step explanation:
480 is the answer // provide picture for better answer
There are 400 thousand people living in Miami and 300 thousand people living in Anchorage. Which statement below shows which city has more people living in it? - 400 thousand people > 300 thousand people, so there are more people living in Miami. 400 thousand people < 300 thousand people, so there are more people living in Miami. 400 thousand people > 300 thousand people, so there are more people living in Anchorage. 400 thousand people < 300 thousand people, so there are more people living in Anchorage.
Answer:
Your answer is A <3
Step-by-step explanation:
Answer:
400 thousand people > 300 thousand people, so there are more people living in Miami.
what is solution to 8x=2/3
there should be a cross multiplication
3(8x)=2
expanding bracket
24x=2
multiple both sides by 24
x=1/12
Please help me i will give you 50 points if you do
Answer:
6(4X-1) = 24X -6 , (2 . 12X ) - (2 . 3) .
24X+6 = (6 . 4X) + (6 . 1) , 6( 4X + 1 ) .
(4 . 6X) - (4 . 2) = 24X + 8 , 4(6X + 2) .
Step-by-step explanation:
Hope it was helpful dear , good luck ^^
help please it needs to be don by 4:00
can someone pls help me
Answer:
arc EFC = 237°
Step-by-step explanation:
arc DEF = 140°
arc EF = 140° - 83° = 57°
arc DC = arc FG
arc DC = (360° - 140° - 140°)/2 = 40°
arc EFC = arc CG + arc FG = arc EF = 140° + 40° + 57° = 237°
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Answer:
Is this called
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Answer:
A tropism (from Greek τρόπος, tropos, "a turning") is a biological phenomenon, indicating growth or turning movement of a biological organism, usually a plant, in response to an environmental sti
Pricilla makes a profit of $24.50 on every scarf she sells the materials for each scarf cost
$8.39 how much does Priscilla sell each scarf for?
85% of x is 51. Write an equation that represents the situation.
Answer:
85/100*x=51
Step-by-step explanation:
85x=5100
Write 2.83 as a mixed number and as an improper fraction.
Do not try to simplify your answers.
Answer:
Mixed number: [tex]2\frac{83}{100}[/tex]
Improper Fraction: [tex]\frac{283}{100}[/tex]
Answer:
[tex]\frac{238}{100}\\\\2\frac{38}{100}[/tex]
Step-by-step explanation:
2.83/1
To make this a normal fraction, the top has to be a whole number, so we can multiply the top and bottom by 100 to slide the decimal point twice.
238/100
This can be shown as a mixed number by removing the 200 which is divisible by 100
[tex]2 \frac{38}{100}[/tex]
Note: The reason the question says not to simplify is because 283 is a prime and cannot be simplified
A class consists of 1/2 freshmen, 1/8 sophomores, and 1/8 juniors; the rest are seniors. What fraction of the class is seniors?
Answer:
2/8 are seniors
Step-by-step explanation:
one half = 4/8
4/8 + 1/8 + 1/8 = 6/8.
What's left is 2/8
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What is the volume of the cylinder below? write your answer in terms of pie.
Height= 11.5 cm
Radius= 6 cm
Answer:
414π
Step-by-step explanation:
Volume of a cylinder = area of circle/ cross-section x height
Area of cross-section = πr² = 6²π = 36π
36π x 11.5 = 414π
Answer:
1300.61936 cm
Step-by-step explanation:
:))
can someone help me pls?
15) Suzanne bought 3 quarts of orange juice, 4 quarts of apple juice, and 5 quarts of
water at the store. How many gallons of liquid did she buy?
Answer:
3 liquid gallons
Step-by-step explanation:
3 + 4 + 5 = 12
12 ÷ 4 = 3 liquid gallons
Select the most accurate statement regarding the normal distribution. Group of answer choices It is always the appropriate distribution in simulation modeling. It does not permit negative values. There is a 95% chance that values will be within ±2 standard deviations of the mean. The user must specify the maximum positive value allowed. It is obtained by the positive and negative square roots of a uniform random variable.
Answer:
There is a 95% chance that values will be within ±2 standard deviations of the mean.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
In this question:
According to the empirical rule, 95% of the measures are within 2 standard deviations of the mean. So the correct statement is:
There is a 95% chance that values will be within ±2 standard deviations of the mean.
Giving brainly to the correct answer!
Answer: A
Step-by-step explanation:
Well four weels in every car so it’s 4 times cars (a)
4 times A=W
Step-by-step explanation: im smart also if u do multiply it by a by 4 it equals W
This angle cuts out 1/4 of the circle. Find the measure of the angle.
Answer:
90 degrees
Step-by-step explanation: