Trigonometry need this done please

Trigonometry Need This Done Please

Answers

Answer 1

\(\tan 30^{\circ} = \dfrac{AB}{AC}\\\\\implies \dfrac 1{\sqrt 3} = \dfrac{AB}{6}\\\\\implies AB= \dfrac 6{\sqrt 3}=2\sqrt 3 \approx 3.47\)


Related Questions

Write the equation of the line which passes through (1, 2) and with slope of −1/3
in standard form.

Answers

Answer:

         x + 3y = 7            

Step-by-step explanation:

The equation of a line which passes through (x₁, y₁) and with slope of m in point-slope form:

                                y - y₁ = m(x - x₁)

m = -¹/₃

(1, 2)    ⇒   x₁ = 1,  y₁ = 2

Therefore,  the equation of the line which passes through (1, 2) and with slope of −1/3 in point-slope form:

y - 2 = -¹/₃(x - 1)

y - 2 = -¹/₃x + ¹/₃                     {add ¹/₃x to both sides}

¹/₃x + y - 2 = ¹/₃                     {add 2 to both sides}

¹/₃x + y = 2¹/₃                       {multiply both sides by 3}

x + 3y = 7            

QUESTION 11
Which classification best represents a triangle with side lengths 48 in., 56 in., and 83 in.?
O A. acute, because 832> 48² +56²
O B. acute, because 832 < 48² +56²
OC. obtuse, because 832> 48² +56²
O D. obtuse, because 832 < 482 +56²
h

Answers

The triangle with side lengths of  48 in., 56 in., and 83 in.  is obtuse, because 832> 48² +56²

What is triangle?

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.

here, we have,

The side lengths of the triangles are 48 in., 56 in., and 83 in

The smallest side lengths are: 48 in., 56 in

The sum of the squares of these side lengths is

48^2+ 56^2

For the triangle to be obtuse, then the following must be true

83^2> 48² +56²

Evaluate the exponents

6889> 5440

The above inequality is true.

Hence, the triangle is obtuse, because 83^2> 48² +56²

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Helppppppppppppp pleaseeeeeeee

Circle theorems. Please help me solve for x.

Brainliest, thanks, points and 5 stars for whoever gets this correct and has the right working out.

Please Do not reply if you don’t know the answer

Helppppppppppppp pleaseeeeeeeeCircle theorems. Please help me solve for x. Brainliest, thanks, points

Answers

Answer: x = 50°

Step-by-step explanation:

Helppppppppppppp pleaseeeeeeeeCircle theorems. Please help me solve for x. Brainliest, thanks, points

HURRY!!!:) Find the sum of the opposite of (-3b+5) and -3b. *

Answers

Answer:

Answer: -6b + 5 here you go have a great day:)

Answer:

6b + 5

Step-by-step explanation:

The opposite of (- 3b + 5) + (- 3b) is (3b + 5) + (3b).

3b + 5 + 3b

6b + 5

Miguel is posting photos on a school website . He has 48 photos , and he is allowed to use 12 pages . He wants to put the same number of photos, p. on each page

How many photos are in each page

Answers

4 because 12 x 4 is 48

p=91 [ Consider the plane curve defined by the parametric equations x = p +t sin(t).y = p< +t cos(t). Calculate the Arc length of the curve over the domain 0

Answers

The arc length of the curve over the given domain is π^3/24 + π/2.

To calculate the arc length of the curve defined by the parametric equations x = p + t sin(t) and y = p + t cos(t) over the domain 0 ≤ t ≤ π/2, we use the formula for arc length:

L = ∫√[dx/dt]^2 + [dy/dt]^2 dt

First, we need to find dx/dt and dy/dt:

dx/dt = cos(t) + t cos(t)

dy/dt = -sin(t) + t sin(t)

Next, we plug these into the arc length formula and integrate over the given domain:

L = ∫[cos(t) + t cos(t)]^2 + [-sin(t) + t sin(t)]^2 dt from 0 to π/2

L = ∫[cos^2(t) + 2t cos^2(t) + t^2 cos^2(t)] + [sin^2(t) - 2t sin(t) cos(t) + t^2 sin^2(t)] dt from 0 to π/2

L = ∫[1 + t^2] dt from 0 to π/2

L = [(π/2)^3/3 + (π/2)] - [(0)^3/3 + (0)]

L = π^3/24 + π/2

Therefore, the arc length of the curve over the given domain is π^3/24 + π/2.

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Suppose that cell H15 is an output cell in a spreadsheet for which we have run a simulation. How could you compute the probability of that cell's value exceeding 500

Answers

By using  1-PsiTarget(H15, 500) we compute the probability of cell H15's value exceeding 500 in a spreadsheet simulation.

PsiTarget is a function commonly used in spreadsheet simulation software to calculate probabilities.

The first argument (H15) specifies the cell you want to calculate the probability for.

The second argument (500) represents the target value you want to compare against.

The PsiTarget function returns the probability of the cell's value being less than or equal to the target value.

By subtracting this probability from 1, you get the probability of the cell's value exceeding the target value.

Therefore, the correct formula to compute the probability of cell H15's value exceeding 500 is 1-PsiTarget(H15, 500).

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the radis of circle A is three feet les than twice the diameter of Circle b. If the sum of the diameters of bothj circles is 49 feet, find the area and circumferance of circle A

Answers

The required area and circumference of circle A are 1,134.57feet² and 119.43 feet.

What is a circle?

All points in a plane that are at a specific distance from a specific point, the center, form a circle.

In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.

So, the area and circumference of circle A:

d = the circumference of circle B

r = radius of circle A

r = 2d - 3

Diameter of circle A = 2 x (2d - 3) = 4d - 6

By figuring out d, we may find the diameter of circle B.

4d - 6 + d = 49

5d = 55

d = 11

Diameter of circle A = 4(11) - 6 = 38

Radius of circle A = 38/2 = 19 feet

Area of a circle = πr²

22/7 x 19² = 1,134.57 feet²

Circumference of a circle = πD

22/7 X 38 = 119.43feet

Therefore, the required area and circumference of circle A are 1,134.57feet² and 119.43 feet.

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C=/5(F−32)
The equation above shows how a temperature F, measured in degrees Fahrenheit, relates to a temperature C, measured in degrees Celsius. Based on the equation, which of the following must be true?
I. A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of 95 degree Celsius.
II. A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit.
III. A temperature increase of 95 degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius
a. I only
b. II only
c. III only
d. Iand II only

Answers

At the lowest temperature he could get a water and salt solution to attain, Fahrenheit set zero.

What is meant by Fahrenheit ?

Fahrenheit is named for German scientist Daniel Gabriel Fahrenheit, who was born there in 1686 as part of the Polish-Lithuanian Commonwealth. He was the first to develop a constant, accurate method of measuring temperature. At the lowest temperature he could get a water and salt solution to attain, Fahrenheit set zero.

To assist us remember that we go from colder to hotter as we walk up the scale on our thermometer, let's label it. In other terms, a higher number of degrees Fahrenheit is hotter than a lower number.

\($$\begin{aligned}& \text { Given:- } \mathrm{C}=\frac{5}{9}(\mathrm{~F}-32) \\& \Rightarrow \mathrm{F}=\frac{9}{5} \mathrm{C}+32\end{aligned}$$\)

(I) If \($F^{\prime}=F+1$\)

\($$\begin{aligned}\mathrm{C}^{\prime} & =\frac{5}{9}\left(\mathrm{~F}^{\prime}-32\right) \\\mathrm{C}^{\prime} & =\frac{5}{9}(\mathrm{~F}+1-32) \\\mathrm{C}^{\prime} & =\frac{5}{9}(\mathrm{~F}-32)+\frac{5}{9} \times 1 \\\mathrm{C}^{\prime} & =\mathrm{C}+\frac{5}{9}\end{aligned}$$\)

Hence, a temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of \($\frac{5}{9}$\) degree Celsius.

Therefore, statement I exists true.

(II) If \($\mathrm{C}^{\prime}=\mathrm{C}+1$\)

\($$\begin{aligned}& \mathrm{F}^{\prime}=\frac{9}{5} \mathrm{C}^{\prime}+32 \\& \mathrm{~F}^{\prime}=\frac{9}{5}(\mathrm{C}+1)+32 \\& \mathrm{~F}^{\prime}=\left(\frac{9}{5} \mathrm{C}+32\right)+\frac{9}{5} \\& \mathrm{~F}^{\prime}=\mathrm{F}+\frac{9}{5} \\& \mathrm{~F}^{\prime}=\mathrm{F}+1.8\end{aligned}$$\)

Therefore, a temperature increase of 1 degree Celsius exists equivalent to a temperature increase of 1.8 degrees Fahrenheit.

Therefore, statement II exists true.

\($$\begin{aligned}& \text { (III) If } F^{\prime}=F+\frac{5}{9} \\& C^{\prime}=\frac{5}{9}\left(F^{\prime}-32\right) \\& C^{\prime}=\frac{5}{9}\left(F+\frac{5}{9}-32\right) \\& C^{\prime}=\frac{5}{9}(F-32)+\frac{5}{9} \times \frac{5}{9} \\& C^{\prime}=C+\frac{25}{81}\end{aligned}$$\)

Therefore, a temperature increase of \($\frac{5}{9}$\) degree Fahrenheit exists equivalent to a temperature increase of \($\frac{25}{81}$\) degree Celsius.

Therefore, statement III exists false.

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Find the area of rectangle ABCD.
Round to the nearest hundredth if necessary.
Show work.

Find the area of rectangle ABCD.Round to the nearest hundredth if necessary.Show work.

Answers

The area of the rectangle ABCD is 26 square units

Finding the area of rectangle ABCD.

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

The rectangle

The side lengths of the rectangles are calcualated as

Length 1 = √(3² + 2²) = √13

Length 2 = √(6² + 4²) = √52

The area of rectangle ABCD is then calculated as

Area = Length 1 * Length 2

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

Area = √13 * √52

Evaluate

Area = 26

Hence, the area of the rectangle ABCD is 26 square units

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Answer:

  26 square units

Step-by-step explanation:

You want the area of the rectangle with vertices A(4, 1), B(0, 7), C(3, 9) and D(7, 3).

Pick's theorem

The area of a polygon whose vertices are grid points can be found using the formula ...

  A = i + b/2 -1

where i is the number of grid points inside the polygon, and b is the number of grid points on the boundary.

Application

In addition to the given vertices, the points (2, 4) and (5, 6) lie on the boundary, for a total of 6 boundary points.

Counting the points on the graph that lie completely within the boundary of the rectangle, we see there are 24.

The area is ...

  A = 24 +6/2 -1 = 26 . . . . square units

<95141404393>

What is the next 2 numbers in the sequence?

343,131413,11131114113

Answers

Answer:

111113111114111113 and 111111131111111411111113

Step-by-step explanation:

Here we want to know the next two numbers in the sequence.

The key here is that we shall be placing the same number of digit 1 between each of the digits 3 4 3

We went from a single 1 to triple, so the next will be 5 digit 1 and the next will be 7 digit 1

So the next number after the third will be;

111113111114111113

The next number after this will be;

111111131111111411111113

in △ABC, B=51°, b=35, and a=36. what are the two possible values for angle A to the nearest tenth of a degree?
Select all that apply:
a. A = 129.9°
b. A = 53.1°

Answers

Both options a. A = 129.9° and b. A = 53.1° are correct.

To find the possible values for angle A in triangle ABC, we can use the Law of Sines, which states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant.

Using the Law of Sines, we have sin(A)/a = sin(B)/b. Plugging in the given values, we get sin(A)/36 = sin(51°)/35.

To find the two possible values for angle A, we can solve the equation sin(A)/36 = sin(51°)/35. Taking the arcsine of both sides, we have A = arcsin((sin(51°)/35)*36).

Calculating this expression, we find two possible values for angle A:

A ≈ 53.1° (rounded to the nearest tenth)

A ≈ 129.9° (rounded to the nearest tenth)

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If a1= 7 and an = -4an-1 + n then find the value of a5

If a1= 7 and an = -4an-1 + n then find the value of a5

Answers

Answer:

a₅ = 1701

Step-by-step explanation:

\(a_1=7\\\\a_n=-4a_{n-1} + n\\\\a_2 = -4*a_1 + 2\\\\\)

    = -4*7 + 2

    = -28 + 2

   = -26

a₃ = -4a₂ + 3

    = -4*(-26) + 3

    = 104 + 3

    = 107

a₄ = -4a₃ + 4

    = -4*107 + 4

   = -428 + 4

  = -424

a₅ = -4a₄ + 5

    = -4*(-424) + 5

    = 1696 + 5

   = 1701

Find X Find Y PLEASE HELP ME

Find X Find Y PLEASE HELP ME

Answers

Answer is x= 8 and y= 21

Step by step

Let’s break this down

We know straight angle AB = 180 degrees so the sum of all angles will = 180

We know there is a right angle EOG = 90
Let’s solve the two angles inside this right angle. The sum of EOF = 27 and FOG = 3y will = 90 degrees (right angle)

Our equation is 27 + 3y = 90

Subtract 27 from both sides to isolate y

27 -27 +3y = 90 - 27
Combine

3y = 63

Divide both sides by 3 to solve y

3/3 y = 63/3

y = 21

So now let’s solve for x

Since we know EOG is 90 degrees, we know the other two unknown angles AOE = x and BOG = 8x + 18 sum will equal 90 degrees, because all straight angles sum = 180

So our equation is
x + 8x + 18 = 90

Combine like terms

9x + 18 = 90

Subtract 18 from both sides to isolate x

9x +18 -18 = 90 -18

Combine

9x = 72

Divide both sides by 9 to solve

9/9 x = 72/9

x = 8

Check your work

x + 27 + 3y + 8x + 18 = 180

(8) + 27 + (3)(21) + (8)(8) + 18 = 180

8 + 27 + 63 + 64 + 18 = 180

180 = 180

Problem solved!

Please help me! giving out brianliest!

Please help me! giving out brianliest!

Answers

Answer:

Hmm, remember to use distributive property with the fraction and the numbers in the parenthesis.

Step-by-step explanation:

"Jade and Jackson go to Cracker Barrel and order $62.60 worth of food. They want to tip their waiter 20%. They also have to pay a tax of 5% on the original bill. What is the final cost of the meal?"
I just need help please!!!!!!

Answers

Answer:

78.25

Step-by-step explanation:

First find the tip.

62.60 * 20%

62.60*.2 = 12.52

Then find the tax

62.60 * 5%

62.60 * .05

3.13

Now add the cost of the food, tip, and tax.

62.60+12.52+3.13

78.25

(q19) Which is an even function?

(q19) Which is an even function?

Answers

The even function in the context of this problem is given as follows:

A. \(f(x) = -x^4\)

What are even and odd functions?

In even functions, we have that the statement f(x) = f(-x) is true for all values of x.In odd functions, we have that the statement f(-x) = -f(x) is true for all values of x.If none of the above statements are true for all values of x, the function is neither even nor odd.

The fourth power function has the same output values for x and -x, meaning that:

\(-x^4 = -(-x)^4\)

Hence option A gives the even function in the context of this problem.

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Solve by graphing :

-x + 3y = -9
y = -x + 1

Answers

Step-by-step explanation:

the answer from the graph is;

(3 , -2)

Solve by graphing :-x + 3y = -9y = -x + 1

John has $200 in his bank account. He saves $40 of his allowance each month. Kyle has $100 in his bank account but he is saving $50 each month. After how many months will Kyle have at least as much money as John has?​

Answers

Answer:

It will take Kyle 10 months to have at least as much money as John. At 10 months both will have 600$

Step-by-step explanation:

John has $200 in his bank account. He saves $40 of his allowance each month. Therefore:

John = 40n+200

Where n is the number of months.

Kyle has $100 in his bank account but he is saving $50 each month.  Therefore:

Kyle = 50n+100

To see how much until they are equal or in other words, does Kyle have at least as much money as John has, we make equations equal.

40n+200=50n+100

200=10n+100

100=10n

10=n

Thus, we see that it will take 10 months for Kyle to have at least as much money as John has. We can quickly test this:

John:

John = 40n+200

John = 40(10)+200

John = 600$

Kyle:

Kyle = 50n+100

Kyle = 50(10)+100

Kyle = 600$

Thus, we see that it will take 10 months for Kyle to have at least as much money as John has.

Find the exact value of x

Answers

Answer:

well, the value of x is unknown

Kelly brought a pair of sneakers for 35.00 she also brought a pile of different laces. Each set of laces,l, costs 3.00. Write a variable expression to show how Kelly could calculate her total cost

Answers

Answer:

35+3I

Step-by-step explanation:

35+3I

35+3I is the adneee

let U={0,1,2,3,4,5,6,7,8,9} be the universal set and A={0,2,4,6,8,9} B={1,3,6,8} and C={0,2,3,4,5} find A'×C'​

Answers

Answer:

A'={1,3,5,7}

C'={1,6,7,8,9}

A' × C' = { (1,1),(1,6),(1,7),(1,8),(1,9),(3,1),(3,6),(3,7),(3,8),(3,9),(5,1),(5,6),(5,7),(5,8),(5,9),(7,1),(7,6),(7,7),(7,8),(7,9) }

in performing a lower-tailed z-test for one mean, the value of the test statistic was z=0.51, which would yield a p-value of 0.695. group of answer choices true

Answers

The given statement "In performing a lower-tailed z-test for one mean, the value of the test statistic was z=0.51, which would yield a p-value of 0.695." is true because we perform null hypothesis.

In a lower-tailed z-test for one mean, we test a null hypothesis that the population mean (μ) is greater than or equal to a certain value, against an alternative hypothesis that the population mean is less than that value.

To perform the test, we calculate the z-test statistic using the sample mean, sample standard deviation, sample size, and the hypothesized population mean. If the calculated z-test statistic falls in the rejection region (below the critical value), we reject the null hypothesis and conclude that the population mean is less than the hypothesized value.

In this case, the calculated z-test statistic is 0.51, which falls in the non-rejection region (above the critical value) for a lower-tailed test with a significance level of 0.05. Therefore, the p-value is greater than 0.05, and we do not reject the null hypothesis. The statement that the p-value is 0.695 is consistent with this conclusion.

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Twice Jack's age plus 5 is 21. Write and solve an equation. How old is Jack? Responses A32 B88 C52 D13

Answers

21-5=16
16 divided by 2 = 8


In both the Vendor Compliance at Geoffrey Ryans (A) and
Operational Execution at Arrows Electronics there are problems and
challenges. Integrate the problems and challenges from both
cases.

Answers

In both the Vendor Compliance at Geoffrey Ryans (A) and Operational Execution at Arrows Electronics cases, there are common problems and challenges. These include issues related to vendor management.

One of the key problems faced by both companies is vendor compliance. This refers to the ability of vendors to meet the requirements and standards set by the company. Both cases highlight instances where vendors fail to meet compliance standards, leading to disruptions in the supply chain and operational inefficiencies. This problem affects the overall performance and profitability of the companies.

Another challenge faced by both companies is operational execution. This encompasses various aspects of operations, including inventory management, order fulfillment, and delivery. In both cases, there are instances where operational execution falls short, leading to delays, errors, and customer dissatisfaction. This challenge requires the companies to streamline their processes, improve communication and coordination, and enhance overall operational efficiency.

Overall, the problems and challenges in both cases revolve around effective vendor management, supply chain optimization, and operational excellence. Addressing these issues is crucial for both companies to improve their performance, meet customer demands, and maintain a competitive edge in the market.

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jorge matrinez is making a buisness trip by car. After driving half the total distance he finds he has averaged only 20 mph, because of neuemrous traffic tieups. what must be his average soeed for the second half of the trip if he is to average 40mph

Answers

Answer:

Let's assume that the total distance of the trip is D miles. Jorge has already covered half of the distance i.e. D/2 miles at an average speed of 20 mph. Let's call the time taken to cover this distance T1.

We can use the formula: Average speed = Total Distance / Total Time

We know that the overall average speed for the entire trip is 40 mph. So, for the remaining half of the trip, Jorge needs to cover another D/2 miles at an average speed of 40 mph. Let's call the time taken to cover this distance T2.

Now we can write two equations:

1. 20 mph = (D/2) / T1  => T1 = (D/2) / 20

2. 40 mph = (D/2) / T2  => T2 = (D/2) / 40

We need to find out the average speed in the second half of the trip. Let's call it S2.

We know that the total time taken for the entire trip is T1 + T2.

Total time = T1 + T2 = (D/2) / 20 + (D/2) / 40 = D/30

We can again use the formula: Average speed = Total Distance / Total Time

So, we have:

D = D

Total time = D/30

Total distance = D/2 + D/2 = D

Average speed = Total distance / Total time

40 mph = D / (D/30)

40 mph = 30

This is not possible as the average speed cannot be higher than the maximum speed (which is 40 mph in this case). So, it means that there is no way for Jorge to achieve an average speed of 40 mph for the entire trip.

Step-by-step explanation:

Air is being pumped into a spherical balloon at the rate of 7 cm³/sec. What is the rate of change of the radius at the instant the volume equals 36n cm³ ? The volume of the sphere 47 [7] of radius r is ³.

Answers

the rate of change of the radius at the instant the volume equals 36π cm³ is 7 / (36π) cm/sec.

The volume V of a sphere with radius r is given by the formula V = (4/3)πr³. We are given that the rate of change of the volume is 7 cm³/sec. Differentiating the volume formula with respect to time, we get dV/dt =(4/3)π(3r²)(dr/dt), where dr/dt represents the rate of change of the radius with respect to time.

We are looking for the rate of change of the radius, dr/dt, when the volume equals 36π cm³. Substituting the values into the equation, we have: 7 = (4/3)π(3r²)(dr/dt)

7 = 4πr²(dr/dt) To find dr/dt, we rearrange the equation: (dr/dt) = 7 / (4πr²) Now, we can substitute the volume V = 36π cm³ and solve for the radius r: 36π = (4/3)πr³

36 = (4/3)r³

27 = r³

r = 3  Substituting r = 3 into the equation for dr/dt, we get: (dr/dt) = 7 / (4π(3)²)

(dr/dt) = 7 / (4π(9))

(dr/dt) = 7 / (36π)

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Which of the following is/are correct? (Select all that apply. You have only one submission for this question.) If u and v are parallel, then either u.v=jul lvl or u. V-lul lvl. The vector projuv is parallel to v If u and v are orthogonal, then u xv = 0. The expression u. (vw) is meaningful and the result is a scalar. Suppose u: O. If u xv=uxw, it follows that vw. If u and v are parallel, then u xv = 0. The expression u u can be negative

Answers

The correct statements are If u and v are orthogonal, then u × v = 0. The vector proj_v u is parallel to v. If u and v are parallel, then u × v = 0.

The statement "If u and v are parallel, then either u · v = |u||v|" is incorrect. The correct statement is "If u and v are parallel, then u · v = |u||v|".

The statement "The expression u.(vw) is meaningful and the result is a scalar" is incorrect. The expression u.(vw) is not meaningful because the dot product is only defined for vectors of the same dimension.

The statement "Suppose u: O. If u × v = u × w, it follows that v = w" is incorrect. The correct statement is "Suppose u ≠ 0. If u × v = u × w, it follows that v - w is parallel to u".

Finally, the statement "The expression u · u can be negative" is incorrect. The dot product u · u is always non-negative, and is only equal to zero if and only if u = 0

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Fair flow allocation with hard constrained links (a) By inspection, x max−min

=( 3
1

, 3
1

, 3
1

, 3
1

). (b) (proportional fairness) Let p l

denote the price for link l. Seek a solution to the equations x 1

= p 1

+p 2

+p 3

1

x 2

= p 1

+p 2

1

x 3

= p 1

1

x 4

= p 2

+p 3

1

x 1

+x 2

+x 3

≤1, with eqaulity if p 1

>0
x 1

+x 2

+x 4

≤1, with eqaulity if p 2

>0
x 1

+x 4

≤1, with eqaulity if p 3

>0

Clearly x 1

+x 4

<1, so that p 3

=0. Also, links 1 and 2 will be full, so that x 3

=x 4

. But x 3

= p 1

1

and x 4

= p 3

1

, so that p 1

=p 2

. Finally, use 2p 1

1

+ 2p 1

1

+ p 1

1

to get p 1

=p 2

=2, yielding x pf

=( 4
1

, 4
1

, 2
1

, 2
1

). Flows 1 and 2 use paths with price p 1

+p 2

=4 and each have rate 4
1

. Flows 3 and 4 use paths with price p 1

=p 2

=2 and each have rate 2
1

Answers

The problem involves fair flow allocation with hard-constrained links. By solving equations and considering constraints, the proportional fairness solution results in flow rates of (4/1, 4/1, 2/1, 2/1) with corresponding prices for links (p1, p2, p3) being (2, 2, 0).

By inspection, we find that the maximum-minimum flow allocation is (3/1, 3/1, 3/1, 3/1).

To achieve proportional fairness, we introduce price variables (p1, p2, p3) for each link and solve the following equations:

x1 = p1 + p2 + p3

x2 = p1 + p2

x3 = p1

x4 = p2 + p3

x1 + x2 + x3 ≤ 1, with equality if p1 > 0

x1 + x2 + x4 ≤ 1, with equality if p2 > 0

x1 + x4 ≤ 1, with equality if p3 > 0

From the equations, it is clear that x1 + x4 < 1, which implies p3 = 0. Additionally, since links 1 and 2 are full, we have x3 = x4. Using x3 = p1 and x4 = p3, we find p1 = p2.

Finally, we can solve 2p1 + 2p1 + p1 = 1 to obtain p1 = p2 = 2. Thus, the solution is x_pf = (4/1, 4/1, 2/1, 2/1). Flows 1 and 2 use paths with a price of p1 + p2 = 4 and have a rate of 4/1 each, while flows 3 and 4 use paths with a price of p1 = p2 = 2 and have a rate of 2/1 each.

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Complete question:

Consider a fair flow allocation problem with hard-constrained links. By inspection, the maximum-minimum flow allocation is found to be (3/1, 3/1, 3/1, 3/1). Seeking a solution for proportional fairness, where the price for each link is denoted as (p1, p2, p3), solve the given equations and constraints to determine the flow rates and prices that satisfy the system. Explain the steps involved in finding the solution and provide the resulting flow rates and corresponding link prices.

19.2 + X = -60.7
Solve for X

Answers

Answer:

-79.9

Step-by-step explanation:

-60.7-19.2=-79.9

Answer: -79.9

Step-by-step explanation:

Subtract 19.2 from both sides of the equation to isolate the X.

0 + X = -60.7 - 19.2

X = -79.9

You can also check your answer by plugging in X into the equation and seeing if it equals -60.7

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