Rewrite The Complex Number 3 (Cos 3(Cos(5) + I Sin(5)). In A + Bi Form. Use Exact Values Only In A

Answer:

\( \sqrt{6} \)

Step-by-step explanation:

We first divide sqrt8 by to 2.

Next we multiply that by sqrt3

\( \sqrt{8} \ \div 2 \times \sqrt{3} \)

Answer:

3 fl. oz.

Step-by-step explanation:

75% of 12 is the same as multiplying 3 by 4 to get 12. So, you have 3 fl. oz.

Hope it helps!!!!! :))

As per the volume of a rectangular prism, it is found that 34.76% of the container is empty.

Volume of a rectangular prism

The volume of the rectangle prism is calculated by multiplying the length, breadth and height of the prism.

The formula for the volume of rectangle prism is

V = l x w x h

where

l represents the length

w represents the width

h represents the height

Given,

A shipping container is in the form of a right rectangular prism, with dimensions of 30 ft by 8 ft by 7 ft 3 in.

Here we need to find if the container holds 1096 cubic feet of shipped goods, what percent is empty

According to the given question,

Let us consider the length is 30ft, Width is 8ft and Height is 7ft.

Here the value 3ft refers the depth.

That one is also multiplied with the volume.

Therefore, the volume of the container is

=> 8 x 7 x 30

=> 1680

Therefore, the volume of the container is 1680 cubic feet.

So, here we have to percentage of the empty space for that we have to find the difference of them and convert it into percentage,

=> 1680 - 1096

=> 584

The percent of empty space is,

=> x% of 1680 = 584

=> x% = 584/1680

=> x% = 0.3476

=> x = 34.76

Therefore, 34.76% of rectangular prism container is empty.

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Answer: 4th option

Step-by-step explanation: divide it by 27x12 and the result should be close to 3 and because the 4th option is also close to 3, then that should be the correct answer.

Answer:

Step-by-step explanation:

Correct choice is B

Answer:

the second option is the one for you :D

ps. (side note: hope u  dont fail)

Answer:

10 minutes

Step-by-step explanation:

t × s = d

if they catch up distance is equal and time is except for 5 minute difference

therefore s × t = s × t

convert minutes to hours

(a+5)/60 and a/60

60 × (a+5)/60 = 90 ×a/60

times both sides by 60

60a+300=90a

300=30a

a=10

$390 represent 100%. To find what percentage $7.80 represent, we can use the next proportion:

Solving for x,

The sales tax rate is 2%

Answer:

the 4th table and the last one

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

This is because the other ones were going to be spent on something else, but then they were spent on magazines or flowers.

Answer:

2

Step-by-step explanation:

The other are impulse purchases:

1. She does not buy the groceries because she wanted magazines.

3.She does not buy the groceries, instead she buys flowers.

Answer:

x = 8.4

y = -2

Step-by-step explanation:

Step 1: Sub y=-2 into y=5x + 40

-2 = 5x + 40

Step 2: Solve for 'x'

-2 = 5x +40

-42 = 5x

x = 42/5

x = 8.4

Step 3: Solve for 'y'

y is given in the question, y=-2

The equation of the sine function will be y = -3 sin [2(x + π)] + 2. Then the correct option is A.

It is a function that repeats itself in a particular time interval.

The equation is given as

y = A sin (ωx + Ф) + C

Where A is the amplitude, ω is the frequency, Ф is the phase difference, and C is the constant.

From the graph, we have

A = -3

ω = 2

Ф = 2π

C = 2

Then we have the equation will be

y = -3 sin [2(x + π)] + 2

Then the correct option is A.

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Answer:

Robie made an image but I'll give you points to plot in case you are confused.

Step-by-step explanation:

(0,-2)

(1,0)

(2,2)

etc.

(x goes up by 1, y goes up by 2 start from -2 y)

Answer:

The number that goes in the ( ) is 0.

Step-by-step explanation:

Answer:

x=26

Step-by-step explanation:

1/3(x-2)=1/5(x+4)+2

x-2=3/5x+42/5

5x-10=3x+42

5x-3x-10=42

5x-3=42+10

2x=42+10

2x=52

x=26

2a) potential number of boxes that would all give you profit from 0 to 1600 dollars.

b) equation of the line ≥ x

c) basically anything less than or equal to 420

d) yeah think so

Answer: 10x + 10

Step-by-step explanation: (3x +4) + (7x + 5)

= (3x) + (4) + (7x) + (5)

= (3x + 7x) + (4 + 5)

= 10x + 9.

Answer:

10x +9

Step-by-step explanation:

(3x +4) + (7x + 5)

= (3x) + (4) + (7x) + (5)

= (3x + 7x) + (4 + 5)

= 10x + 9.

Externality refers to the impact of a good or service on third parties who are not directly involved in the transaction. In the context of a market, an externality can be positive (beneficial) or negative (harmful).

To identify a market for a good or service that does NOT cause an externality, we can consider a basic example of a local grocery store selling apples. In this case, the transaction between the store and the buyer does not have any significant impact on third parties. The store sells the apples, and the buyer consumes them. There are no external effects on others in the market or the surrounding community.

This market for apples does not generate positive or negative externalities because the transaction is limited to the buyer and the seller. It does not create any spillover effects that affect others, such as increased pollution, traffic congestion, or health benefits to nearby individuals.

In summary, a market for apples in a local grocery store is an example of a market for a good or service that does NOT cause an externality.

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The integral of \(x^3/\sqrt(x^2+4)\) using trigonometric substitution is: \(8 * (1/3)tan^2\theta(1 + tan^2\theta)^(3/2) + C\), where θ is determined by x = 2tanθ, and C represents the constant of integration

What is integration?

Integration is a fundamental concept in calculus that involves finding the integral of a function.

To integrate the function \(\int(x^3/\sqrt(x^2+4))\) dx using a trigonometric substitution, we can use the substitution x = 2tanθ. Let's go through the steps:

Substitute x = 2tanθ. This implies \(dx = 2sec^2\theta d\theta.\)

Rewrite the integral in terms of θ:

\(\int((8tan^3\theta)/(\sqrt(4tan^2\theta+4))) * 2sec^2\theta d\theta.\)

Simplify the expression inside the square root:

\(\int((8tan^3\theta)/(2sec\theta)) * 2sec^2\theta d\theta.\\\\\int(8tan^3\theta) * sec\theta d\theta.\)

Simplify further:

\(16\int tan^3\theta sec\theta d\theta.\)

Apply the trigonometric identity: \(sec^2\theta = 1 + tan^2\theta\). Rearranging, we get: \(sec\theta = \sqrt(1 + tan^2\theta).\)

Substitute \(sec\theta = \sqrt(1 + tan^2\theta)\) in the integral:

\(16\int tan^3\theta * \sqrt(1 + tan^2\theta) d\theta.\)

Let u = tanθ, which implies \(du = sec^2\theta d\theta\). We can rewrite the integral in terms of u:

\(16\int u^3 * \sqrt(1 + u^2) du.\)

Now we have a rational power of u. We can use the substitution \(v = 1 + u^2\) to simplify it:

\(v = 1 + u^2\), which implies dv = 2u du.

Rewrite the integral using v:

\(16\int (u^3 * \sqrt v) * (1/2u) dv.\\\\8\int (u^2\sqrt v) dv.\)

Simplify and integrate:

\(8\int (u^2\sqrt v) dv = 8\int(u^2 * v^{(1/2)}) dv = 8\int u^2v^{(1/2)} dv.\)

Integrate \(u^2v^{(1/2)\) with respect to v:

\(8 * (1/3)u^2v^{(3/2)} + C.\)

Replace v with \(1 + u^2\):

\(8 * (1/3)u^2(1 + u^2)^{(3/2)} + C.\)

Substitute u = tanθ back into the expression:

\(8 * (1/3)tan^2\theta(1 + tan^2\theta)^{(3/2)} + C.\)

So, the integral of \(x^3/\sqrt(x^2+4)\) using trigonometric substitution is:

\(8 * (1/3)tan^2\theta(1 + tan^2\theta)^{(3/2)} + C,\)

where θ is determined by x = 2tanθ, and C represents the constant of integration

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Answer:

-5

12

36

60

Step-by-step explanation:

not really sure,. are you going to solve for the x only? or should you include the y?

Answer:

(+,-)

Step-by-step explanation:

quadrant 1 is (+,+)

quadrant 2 is (-,+)

quadrant 3 is (-,-)

quadrant 4 is (+.-)

(a) The boundary conditions for the wave equation on the elastic string are as follows: At x = 0: The displacement of the string is fixed, i.e., u(0, t) = 0. This means that the end point of the string at x = 0 does not move.

At x = x: The displacement of the string is fixed, i.e., u(x, t) = 0. This means that the end point of the string at x = x does not move.

(b) The initial conditions for the wave equation on the elastic string are given by the initial displacement f(x) sin(ωt), where f(x) is the initial displacement function and ω is the angular frequency.

To explain the initial conditions with a plot of the string, we can plot the shape of the string at t = 0. The plot will show the initial displacement of the string at each point x. The shape of the string will be determined by the function f(x).

(c) To solve the boundary value problem of the wave equation with the given boundary and initial conditions, we need to solve the one-dimensional wave equation with the appropriate boundary conditions.

The one-dimensional wave equation is given by:

∂²u/∂t² = c² ∂²u/∂x²

where u(x, t) represents the displacement of the string at position x and time t, and c is the wave speed.

Using the boundary conditions u(0, t) = 0 and u(x, t) = 0, and the initial condition f(x) sin(ωt), we can solve the wave equation to find the solution u(x, t) that satisfies the given conditions.

The specific method for solving the wave equation depends on the form of the initial displacement function f(x) and the properties of the string. Common methods include separation of variables, Fourier series, or using appropriate Green's functions.

The solution to the boundary value problem will provide the complete description of the displacement of the string at any point x and time t, satisfying the boundary and initial conditions.

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The boundary conditions for the wave equation on the elastic string are as follows: At x = 0: The displacement of the string is fixed, i.e., u(0, t) = 0. This means that the end point of the string at x = 0 does not move.

At x = x: The displacement of the string is fixed, i.e., u(x, t) = 0. This means that the end point of the string at x = x does not move.

(b) The initial conditions for the wave equation on the elastic string are given by the initial displacement f(x) sin(ωt), where f(x) is the initial displacement function and ω is the angular frequency.

To explain the initial conditions with a plot of the string, we can plot the shape of the string at t = 0. The plot will show the initial displacement of the string at each point x. The shape of the string will be determined by the function f(x).

(c) To solve the boundary value problem of the wave equation with the given boundary and initial conditions, we need to solve the one-dimensional wave equation with the appropriate boundary conditions.

The one-dimensional wave equation is given by:

∂²u/∂t² = c² ∂²u/∂x²

where u(x, t) represents the displacement of the string at position x and time t, and c is the wave speed.

Using the boundary conditions u(0, t) = 0 and u(x, t) = 0, and the initial condition f(x) sin(ωt), we can solve the wave equation to find the solution u(x, t) that satisfies the given conditions.

The specific method for solving the wave equation depends on the form of the initial displacement function f(x) and the properties of the string. Common methods include separation of variables, Fourier series, or using appropriate Green's functions.

The solution to the boundary value problem will provide the complete description of the displacement of the string at any point x and time t, satisfying the boundary and initial conditions.

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Answer:

60 m = 65.62, so 66 yds

95 m = 103.89, so 104 yds

The simplified expression of the expression \((x - y)^p(x^2 + y^2 + q - y)\)while done the simplification through binomial theorm.

\((x - y)^p(x^2 + y^2 + q - y)\)

Expanding the first term using the binomial theorem, we get:

\((x - y)^p = \sum_{k=0}^{p} {p \choose k} x^{p-k} (-y)^k\)

where [ p choose k ] is the binomial coefficient, given by p! / (k! × (p-k)!).

Substituting this expansion into the original expression, we get:

\(\sum_{k=0}^{p} {p \choose k} x^{p-k} (-y)^{k} (x^2 + y^2 + q + y)\)

Expanding the last term, we get:

\(\sum_{k=0}^{p} {p \choose k} x^{p-k} (-y)^{k} (x^2 + y^2) + \sum_{k=0}^{p} {p \choose k} x^{p-k} (-y)^{k} (q+y)\)

The first term can be simplified by distributing the x² and y² terms:

\(\begin{aligned} &\sum_{k=0}^{p} {p \choose k} x^{p-k} (-y)^{k} x^{2} + \sum_{k=0}^{p} {p \choose k} x^{p-k} (-y)^{k} y^{2} \\&= x^{2} \sum_{k=0}^{p} {p \choose k} x^{p-k} (-y)^{k} + y^{2} \sum_{k=0}^{p} {p \choose k} x^{p-k} (-y)^{k} \\&= x^{2}(x-y)^{p} + y^{2}(x-y)^{p} \\&= (x^{2}+y^{2})(x-y)^{p}\end{aligned}\)

The second term can be simplified by distributing the x and y terms:

\(\begin{aligned} &\sum_{k=0}^{p} {p \choose k} x^{p-k} (-y)^{k} q + \sum_{k=0}^{p} {p \choose k} x^{p-k} (-y)^{k} y \\&= q \sum_{k=0}^{p} {p \choose k} x^{p-k} (-y)^{k} - y \sum_{k=0}^{p} {p \choose k} x^{p-k} (-y)^{k} \\&= q (x-y)^{p} - y (x-y)^{p} \\&= (q-y) (x-y)^{p}\end{aligned}\)

Putting these simplified terms together, we get:

\(\begin{aligned}(x-y)^p \cdot (x^2 + y^2 + q - y) &= (x-y)^p \cdot [(x^2 + y^2) + (q - y)] \\&= (x-y)^p \cdot (x^2 + y^2) + (x-y)^p \cdot (q - y) \\&= (x^2 + y^2) \cdot (x-y)^p + (q - y) \cdot (x-y)^p \\&= (x^2 + y^2 + q - y) \cdot (x-y)^p\end{aligned}\)

Therefore, the simplified expression is \((x-y)^p \cdot (x^2 + y^2 + q - y)\)

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The value of the given expression [\(87^3+ 13^3/87^2 -87 * 13 + 13^2\)] by simplifying the numerator and denominator using suitable identities is 100.

We will first calculate the numerator:

As  (\(a^3\) + \(b^3\)) = (a + b)(\(a^2\) - ab + \(b^2\)) :

\(87^3\) + \(13^3\) = (87 + 13)(\(87^2\) - \(87 * 13\) + \(13^2\))

= 100(\(87^2\) - 87 * 13 + \(13^2\))

Now, calculate the denominator:

\(87^2 - 87 * 13 + 13^2\)

As,(\(a^2 -2ab +b^2\)) =\((a - b)^2\):

\(87^2 - 87 * 13 + 13^2 = (87 - 13)^2\)

\(= 74^2\)

So by solving the equation further:

\((87^3+13^3) / (87^2- 87 * 13+13^2) = 100*(87^2- 87 *13 + 13^2)/(87^2 - 87 * 13 + 13^2)\)

As we can see the numerator and denominator are the same expressions (\(87^2 - 87 * 13 + 13^2\)). so, they cancel each other:

\((87^3 + 13^3) / (87^2 - 87 * 13 + 13^2) = 100\)

So, the value of the given expression is 100.

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A line equation, in slope-intercept form, has the following format:

Where 'm' represents the slope and 'b' the y-intercept.

To match the lines with its respectives slopes and intercepts, we can just rewrite all the equation in slope-intercept form and compare them.

Let's start with those already in slope intercept form.

The second line is:

The slope is -6, and the y-intercept is (0, 5).

The third line is:

The slope is 5/6, and the y-intercept is (0, 1).

Now, the first line and the fourth, we need to rewrite them in slope intercept form. Let's start with

Rewriting in slope intercept form we have

The slope is 5/6, and the y-intercept is (0, -5).

For the last one, we can just match with the remaining slope and intercept.

For the last one, The slope is 5/6, and the y-intercept is (0, -1).

Given:-

\( \: \)

\( \: \)

To find:-

\( \: \)

By using formula:-

\( {\color{hotpink}\bigstar} {\boxed{\sf {\green{ slope : m = \: \frac{y_2 - y_1}{x_2 - x_1} }}}}\)

Solution:-

\( \sf \: m = \frac{y_2 - y_1}{x_2 - x_1} \)

\( \: \)

where ,

\( \: \)

\( \: \)

\( \sf \: m = \frac{( -2 ) - ( -3 ) }{1 - 2} \)

\( \: \)

\( \sf \: m = \frac{ - 2 + 3}{ \: 1 - 2} \)

\( \: \)

\( \sf \: m = \cancel \frac{1}{ - 1} \)

\( \: \)

\( \underline{\boxed{ \sf{ \blue{ \: m = -1 \: }}}}\)

\( \: \)

━━━━━━━━━━━━━━━━━━━━━━━

hope it helps:)

Answer:

0.22

Step-by-step explanation:

Answer:

0.22

Step-by-step explanation:

brainliest plsss

Answer:

Step-by-step explanation:

The calculated height of the kite is 10.61 feet

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

Length of the string = 15 feet

Angle with the ground = 45 degrees

Since the string is a straight line, we have

Height of the kite = Length of the string/√2

This is because the angle is 45 degrees

substitute the known values in the above equation, so, we have the following representation

Height of the kite = 15/√2

Evaluate

Height of the kite = 10.61

Hence, the height of the kite is 10.61 feet

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Answer:

x = 4

Step-by-step explanation:

When you have a coefficent in front of a logarithm function, you can take the argument to the power of that coefficient. For example, the 3 in front of the logarithm can be brought into the argument, and you can take 'x' to the third power. You get:

\( log_{4}( {x}^{3} ) = log_{4}(32) + log_{4}(2) \)

When you add logarithms, it is equivalent to multiplying their arguments:

\(log_{4}( {x}^{3} ) = log_{4}(32 \times 2) = log_{4}(64) \)

Since both sides are log base 4, the arguments must equal each other:

\( {x}^{3} = 64\)

\(x = \sqrt[3]{64} = 4\)

here it is, this is ur answer x=4