Determine the area of the composite figure.​

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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Answer:

1

Step-by-step explanation:

All factors of 33 : 1, 3, 11, 33

All factors of 49 : 1, 7, 49

So the Greatest Common Factor for 33 and 49 is 1

The interest that Zollicoffer will receive in one year is $52.50.

The formula that is used for calculating the interest will be:

Interest = principal × rate × time

In this case, Mrs. Zollicoffer’s bank pays 5 1/4% interest. She has $1,000 in the bank. The interest that she would receive in one year will be:

Interest = Principal × Rate × Time

Interest = 1000 × 5.25% × 1

Interest = $52.5

The interest is $52.50.

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Answer: -5/3

Down -5

right 3

Step-by-step explanation: count the distance between the 2 dots looking from the y axis (up and down)and from the x axis (left to right)

By using trigonometry, it can be calculated that The measure of the angle is 53.13° First option is correct.

What is Trigonometry?

Trigonometry is a branch of mathematics that studies relationships between the sides and angles of triangles. It is used to calculate lengths, angles, and other geometric figures. Trigonometry has applications in many fields, including engineering, astronomy, and navigation. The most common trigonometric functions are sine, cosine, and tangent. These functions are used to solve problems related to triangles, circles, and other geometric figures. Trigonometric identities are also used to solve algebraic equations. Trigonometry is an important tool for studying the physical world, as it allows us to calculate the position and motion of objects in space.

There are six trigonometrical functions. They are

[tex]sin\theta, cos\theta, tan\theta, cot\theta, sec\theta, cosec\theta[/tex]

[tex]sin\theta = \frac{perpendicular}{hypotenuse}\\cos\theta = \frac{baser}{hypotenuse}\\tan\theta = \frac{perpendicular}{base}\\cot\theta = \frac{base}{perpendicular}\\sec\theta = \frac{hypotenuse}{base}\\cosec\theta = \frac{hypotenuse}{perpendicular}\\[/tex]

Trigonometry is a very important tool in mathematics.

Here, the trigonometric function given is

[tex]cos\theta = \frac{3}{5}[/tex]

[tex]\theta = cos^{-1}(\frac{3}{5})[/tex]

[tex]\theta = 53.13^{\circ}[/tex]

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Answer:

x = 3.66

Step-by-step explanation:

Area of a rectangle = length * width

In this case:

(x+10)x = 50

x*x + x*10 = 50

x² + 10x - 50 = 0

x = {-10±√((10²) -(4*1*-50))} / (2*1)

x = {-10±√(10² + 200)} / 2

x = {-10±√(100+200)} / 2

x = {-10±√300} / 2

x = {-10±17.321} /2        aprox,

It is a geometric figure so only the positive value is taken.

x = {-10+17.321} / 2

x = 7.321/2

x = 3.66

Check:

3.66(3.66+10) = 50

3.66*13.66 = 50

The volume expression for the box is 1.728lwh and it means that the volume increases by 72.8%

The complete question is added at the end of this solution

From the question, we have the following parameters that can be used in our computation:

Length = l

Width = w

Height = h

The volume of a box can be calculated using

Volume = lwh

Rewrite the volume equation as

v = lwh

When the dimensions of the box are increased by 20%, we have the following expressions

Length = 1.2l

Width = 1.2w

Height = 1.2h

So, the new volume is

V = 1.2l * 1.2w * 1.2h

Evaluate

V = 1.728lwh

Hence, the expression is 1.728lwh

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A food company sells its corn flakes in boxes of two different sizes: the regular box and the family value box. For the family value box, the length, width, and height of the box have all been increased by 20%.

Determine the expression for the new volume

36% of the animals in the shelter are hamsters.

[tex]\frac{27}{75}= 0.36[/tex]

0.36 = 36%.

36% of the animals in the shelter are hamsters.

Answer:

93 minutes

Step-by-step explanation

23/68 x/275= 93 min

Answer: $13.50

Step-by-step explanation:

It will cost Miguel $13.50 to send 6 small packages and 1 large package. To find the total cost, we can first calculate the cost of sending the small packages by multiplying the cost per small package by the number of small packages: 2.20 * 6 = $<<2.20*6=13.20>>13.20

We can then add the cost of the large package to find the total cost: 13.20 + 3.90 = $<<13.20+3.90=17.10>>17.10.

Therefore, it will cost Miguel $17.10 to send 6 small packages and 1 large package.

Answer:

$1916.73

Step-by-step explanation:

[tex]I=Prt=P(0.0401)(13/12) \\ \\ \implies P+P(0.0401)(13/12)=2000 \\ \\ P=\frac{2000}{1+(0.0401)(13/12)} \approx \$1916.73[/tex]

Answer:

22.2x²

Step-by-step explanation:

3.7x = 3.7 × x

6x = 6 × x

Multiplication of 3.7x and 6x

= 3.7 × 6 × x × x

= 22.2 × x²

= 22.2x²

Answer:

C. 22.2x^2

Step-by-step explanation:

There are a total of 2^10 = 1024 possible outcomes for a coin flipped 10 times. Out of these, there are only 10 outcomes that have exactly 4 tails and start and end with different faces.

To count the number of outcomes with 4 tails, we can use the binomial coefficient formula: n choose k = n!/(k! * (n-k)!), where n is the total number of flips (10 in this case) and k is the number of tails (4 in this case). This gives us 10 choose 4 = 10!/ (4! * 6!) = 210 outcomes with 4 tails.

To count the number of outcomes that start and end with different faces, we can consider the first and last flips separately. The first flip can be either heads or tails and the last flip can also be either heads or tails, for a total of 2 * 2 = 4 possibilities.

Thus, there are a total of 210 * 4 = 840 outcomes that have exactly 4 tails and start and end with different faces. However, there are two outcomes (THTHTHTHTHT and TTHTHTHTHTH) that are counted twice in this total, so we need to subtract these from the total to get the correct number of outcomes. This gives us 840 - 2 = 838 outcomes.

Finally, we need to subtract the two outcomes that start and end with the same face (HHHHHHHHTH and THHHHHHHHH). This gives us a total of 838 - 2 = 836 outcomes.

Therefore, there are a total of 836 outcomes that have exactly 4 tails and start and end with different faces out of a total of 1024 possible outcomes.

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Answer:

A, B, C.

Step-by-step explanation:

Answer: 3/5

Step-by-step explanation:

Let x be the required solution:

so, x= 3- (12/5)

⇒ 5x = 15-12 (Multiplying both sides 5 so that the denominator is the same)

⇒ 5x = 3

∴ x = 3/5

Answer:

684.

Step-by-step explanation:

Answer:

Z

Step-by-step explanation:

Angle V is congruent to angle z because they have the same placement in the letter order.

To calculate how much money David will have in this account after 5 years, we first need to find out how much interest the account earns each year. To do this, we need to multiply the interest rate by the amount of money in the account. In this case, the interest earned each year would be $800 * 0.023 = $18.40.

Next, we need to calculate how much interest the account earns over the 5-year period. Since the interest is compounded semiannually, this means that the interest is earned twice per year. Therefore, the total amount of interest earned over 5 years would be $18.40 * 2 * 5 = $184.

Finally, we need to add the interest to the original amount of money in the account to find out how much money David will have after 5 years. In this case, the total amount of money David will have after 5 years is $800 + $184 = $984.

Therefore, if David keeps the money in this account for 5 years, he will have $984.

Answer:

$897

Step-by-step explanation:

We know:

P = 800

n = 2

r = 2.3

t = 5

Write Equation:

[tex]F = 800(1+\frac{\frac{2.3}{100} }{2} )^{2(5)}[/tex]

Evaluate:

896.9

Thus the answer is $897

Answer:

R = (3, 14 )

Step-by-step explanation:

given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint M is

( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] ) ← midpoint formula

calculate the midpoint of PR using this formula and equate x and y coordinates to the coordinates of the given midpoint

let coordinates of R be (x, y ) and P = (- 15, 4 ) , then

[tex]\frac{x-15}{2}[/tex] = - 6 ( multiply both sides by 2 )

x - 15 = - 12 ( add 15 to both sides )

x = 3

and

[tex]\frac{y+4}{2}[/tex] = 9 ( multiply both sides by 2 )

y + 4 = 18 ( subtract 4 from both sides )

y = 14

the coordinates R = (3, 14 )

Answer:

CHECKING

let W = 10

C = W/2

C = 10/2

C = 5

C = 5     W = 10

Step-by-step explanation:

Because Pisaster is a keystone species, the proportion of living mussels was comparable to the control after Nucella removal.

Sea otters and sea gulls hunt for and eat Pisaster ochraceous. Its function as a keystone species has been well researched. When it was gone from Washington's intertidal regions, the area's species diversity declined.

Sea otters and sea gulls hunt for and eat Pisaster ochraceous. Its function as a keystone species has been well researched. When it was gone from Washington's intertidal regions, the area's species diversity declined.

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The magnitude of the acceleration of the particle is zero when the velocity of the particle is zero.

What is Acceleration ?

Acceleration is the rate of change of velocity. Usually, acceleration means the speed is changing, but not always. When an object moves in a circular path at a constant speed, it is still accelerating, because the direction of its velocity is changing.

Given,

Velocity  v= x² − 5x + 4

now, the acceleration

a = dv/dt

​a = 2x (dx/dt) - 5x(dx/dt)

​

given that, v= dx/dt =0

so, a = 2x*0−5*0

a=0 m/sec²

so, the acceleration is zero ,when the velocity is zero.

Hence ,The magnitude of the acceleration of the particle is zero when the velocity of the particle is zero.

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Answer:

7/12

Step-by-step explanation:

I set up the equation, but I first had to find the common denominator which is 12 so I multiplied 3/4 by 3 (top and bottom) and I multiplied 1/6 by 2   (also top and bottom) So I got 9/12-2/12 and when I subtracted I got 7/12

(hope you understood how I got my answer..)

The equations that are equivalent are (b) 8k ÷ 4 = 20 ÷ 4, (c) 8k × 3 = 20 × 3 and (d) 8k + 10 = 20 + 10

From the question, we have the following parameters that can be used in our computation:

8k = 20.

Divide both sides of the equation by 4

So, we have the following representation

8k ÷ 4 = 20 ÷ 4

Multiply both sides of the equation by 3

So, we have the following representation

8k × 3 = 20 × 3

Add 10 to both sides of the equation

So, we have the following representation

8k + 10 = 20 + 10

Hence, the equivalent equation is 8k + 10 = 20 + 10

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The like terms to make a simpler expression is   19 x^2-6 x+9 n-6

Group like terms

What is simpler expression?

Solving a math problem is the same thing as simplifying an expression. You basically strive to write an expression as simply as you can when you simplify it. At the conclusion, there shouldn't be any more multiplication, dividing, adding, or subtracting to be done.

[tex]=12 x^2+7 x^2+7 x-3 x-11 x+3 n+6 n-7+1+5-5[/tex]

Add similar elements[tex]: $12 x^2+7 x^2=19 x^2$[/tex]

[tex]=19 x^2+7 x-3 x-11 x+3 n+6 n-7+1+5-5[/tex]

Add similar elements: [tex]$7 x-3 x-11 x=-7 x$[/tex]

[tex]=19 x^2-7 x+3 n+6 n-7+1+5-5[/tex]

Add similar elements: [tex]$3 n+6 n=9 n$[/tex]

[tex]=19 x^2-7 x+9 n-7+1+5-5[/tex]

Add the numbers: [tex]$-7+1+5-5=-6$[/tex]

[tex]=19 x^2-7 x+9 n-6[/tex]

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The average of the provided numbers is calculated by dividing the total number of values by the sum of all the values that different socioeconomic classes are affected differently by religion membership.

The middle number, which is determined by dividing the sum of all the numbers by the total number of numbers, is the average value in mathematics. When determining the average for a collection of data, we add up all the values and divide this sum by the total number of values. a single number (such as a mean, mode, or median) that encapsulates or depicts the overall importance of a collection of disparate data. unkind sense 1b.: a calculation that approximates the arithmetic mean. an intellectual level that is characteristic of a group, class, or series. superior than average.

[tex]65, 85, 70, 90, 105.[/tex]

Average =

[tex](65+85+70+90+105)/5\\= 415/5\\= 83\\[/tex]

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Answer:

For the first one x= 60 degrees

Second one x= 125 degrees

Step-by-step explanation:

a) To figure out this we can see that the total of angles in a 5- angled shape is 540 degrees.

So (2x X 4) + x = 540 degrees

= 9x= 540

= x = 60

b) To figure out this we can see that the total of angles in a 7- angled shape is 900 degrees.

So 60+2x+x+x+x+x+90= 900

= 150 +6x= 900

= 6x= 750

= x= 125