What is the value of x identify the missing justifications.

Answers

Answer 1

Where the above conditions are given in the equation,  x is 45.

How is this so?

Given equations are  -

m∠PQR = x + 7 ,

m∠SQR = x + 3 ,

and m PQR + m SQR = m PQS = 100

using those equations we need to find value of x.

Plug value of (m PQR = x + 7) and (m SQR = x + 3 ) into (m PQR + m SQR = m PQS = 100 )

(x+7) + ( x+3) = m PQS = 100

(x+7) + (x +3) = 100

Remove parenthesis

x+7 + x+3 = 100

Rearrange terms

x + x +3+7 = 100

Combine like terms

2x+10 = 100

2x= 100 - 10

2x=90

x=90/2

x=45

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Full Question:

Although part of your question is missing, you might be referring to this full question:

What is the value of x? Identify the missing justifications. M PQR = x + 7 , m SQR = x + 3 , and m PQR + m SQR = m PQS = 100


Related Questions

Point D is located at (-1, 6) on the coordinate plane. Point D is reflected over the
y-axis to create point D'. Point D'is then reflected over the r-axis to create point
D". What ordered pair describes the location of D"?

Answers

Answer:

(1, -6)

Step-by-step explanation:

After reflecting over y axis: (1, 6)

After reflecting (1, 6) over x axis: (1, -6)

I think you made a typo in your question. I think you meant "x-axis" instead of "r-axis"

Write an equation of the line through (-3,- 6) having slope17/16Give the answer in standard form.The equation of the line is

Answers

The equation of a line in Standard form is:

\(Ax+By=C\)

Where "A", "B" and "C" are Integers ("A" is positive).

The Slope-Intercept form of the equation of a line is:

\(y=mx+b\)

Where "m" is the slope and "b" is the y-intercept.

In this case you know that:

\(m=\frac{17}{16}\)

And knowing that the line passes through the point

\(\mleft(-3,-6\mright)\)

You can substitute values and solve for "b":

\(\begin{gathered} y=mx+b \\ -6=(\frac{17}{16})(-3)+b \\ \\ \\ -6=-\frac{51}{16}+b \\ \\ -6=-\frac{51}{16}+b \\ \\ -6+\frac{51}{16}=b \\ \\ b=-\frac{45}{16} \end{gathered}\)

Then, the equation of this line in Slope-Intercept form is:

\(y=\frac{17}{16}x-\frac{45}{16}\)

Now that you have this equation, you can write it in Standard form as following:

\(\begin{gathered} y+\frac{45}{16}=\frac{17}{16}x \\ \\ \frac{45}{16}=\frac{17}{16}x-y \\ \\ \frac{17}{16}x-y=\frac{45}{16} \end{gathered}\)

The answer is:

\(\frac{17}{16}x-y=\frac{45}{16}\)

The measure of an angle is 60.2°. What is the measure of its complementary angle?

Answers

Answer:

29.8° is the measure its complementary angle.

Step-by-step explanation:

Complementary angle = 90°

60.2° + x = 90°

x = 90° - 60.2°

x = 29.8°

Answer:

59.9° AND 120.1°

Step-by-step explanation:

Call the measure of one angle n. The other angle, which is 60.2° bigger, measures n + 60.2°.

Since the angles are supplementary, their measures must add to 180°. Set up an equation and solve for n.

n +  n +  60.2° =  180°

2n + 60.2° =  180°

2n+  60.2° − 60.2° = 180°− 60.2°

2n=  119.8°

2n÷  2 =  119.8°÷ 2

n= 59.9°

The first angle measures 59.9°. Now plug in n = 59.9° to find the measure of the other angle, n + 60.2°.

n+ 60.2° = 59.9° +  60.2°

=  120.1°

So, the two angles measure 59.9° and 120.1°.

tina has scheduled a dinner with friends in 4.5 hours. what is the probability that her simulation study will be done by then?

Answers

The approximate distribution (give distribution name and parameters) of the total length will be =  450 minutes

The estimated distribution of the total length of Tina's simulation study is a triangular distribution with a base worth of 2 minutes, a greatest worth of 4 minutes, and a mode (most reasonable worth) of (2+4)/2 = 3 minutes.

Since the simulation time is generally consistently distributed somewhere in the range of 2 and 4 minutes, the total simulation time will be the sum of 150 free random variables each with a triangular distribution.

Hence, the total simulation time will also have a triangular distribution with a base worth of 2 minutes x 150 = 300 minutes, a greatest worth of 4 minutes x 150 = 600 minutes, and a method of (300+600)/2 = 450 minutes.

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The complete question is:

Tina is running a simulation study on her laptop. The duration of each simulation is roughly uniformly distributed between 2 and 4 minutes. She needs to run 150 simulations and she runs all her simulations back-to-back. - What is the approximate distribution (give distribution name and parameters) of the total length of Tina's simulation study? Explain your answer

Can someone please help me answer this

Can someone please help me answer this

Answers

Answer:

1) a = 1.6          2) f = 0.53

Step-by-step explanation:

1) 6a = 10                      2) 48 = 90f

6a/6 = 10/6                       90f/90 = 48/90

a = 1.6                                f = 0.53

sorry i could only do the first two, i think those are right

x + 3y = 5
x + 2y = 3
Solve by using elimination​

Answers

Answer:

  (x, y) = (-1, 2)

Step-by-step explanation:

The variable x has the same coefficient in both equations, so we can eliminate x by subtracting one equation from the other. We notice the y-coefficient is greater in the first equation, so we want to subtract the second equation. This will ensure that the remaining y-term has a positive coefficient. (That is not required by the elimination method, but it helps reduce mistakes.)

  (x +3y) -(x +2y) = (5) -(3)

  y = 2 . . . . . . . simplify

  x =3 -2y = 3 -2(2) = -1 . . . . . use the second equation to find x

The solution is (x, y) = (-1, 2).

what percent of the youths surveyed prefer reading electronic books round your answer to the nearest tenth of a percent?

what percent of the youths surveyed prefer reading electronic books round your answer to the nearest

Answers

The percentage of youths surveyed that prefer reading electronic books is 54%

What is percentage of a number?

The percentage of a number represents a portion or fraction of that number expressed as a percentage. It is often used to describe a proportion or relative value.

To calculate the percentage of a number, you can use the following formula:

Percentage = (Part / Whole) * 100

To determine the percentage of youths that prefer electronic books is;

youths (electronic books) = number of electronic books(youth) / total number of youths.

youths (electronic books) = 40/(40 + 34) * 100

youths (electronic books) = 40/74 * 100

youths (electronic books) = 0.54 * 100

youths (electronic books) = 54%

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100 points please solve fast! Brainliest please!

100 points please solve fast! Brainliest please!

Answers

Answer:

21

Step-by-step explanation:

The number of rectangles and combinations:

1 rectangle = 62 rectangles = 53 rectangles = 44 rectangles = 35 rectangles = 26 rectangles = 1

Total

6 + 5 + 4 + 3 + 2 + 1 = 21

Now the number of,

Rectangles and combinations are,

→ 1 rectangle = 6

→ 2 rectangles = 5

→ 3 rectangles = 4

→ 4 rectangles = 3

→ 5 rectangles = 2

→ 6 rectangles = 1

Then the total number is,

→ 6+5+4 + 3+2+1

→ 15 + 6 = 21

Hence, total number is 21.

in the capgemini iot industry 4.0 case, what dimension focuses on the way that smart products are equipped with computing power that enables autonomous decision-making and self-learning processes based on algorithms?

Answers

The capgemini iot industry 4.0 case provide an entire end-to-end transformation, we encourage human-centered design and ground-breaking innovation.

The new era of digitization, known as smart industry, includes industry 4.0 but expands well beyond it. Disruptive technologies and data enable use cases that were not previously possible, such as multi-physics modelling, remote operations, digitization of products and processes, driver less cars, linked products, reinvented consumer experiences, and novel as-a-service business models.

We work with customers to uncover new business model options, address industry obstacles, and navigate complicated ecosystems so they can gain and maintain a competitive edge. Using our expertise in engineering, technology, IT, data, and consulting, we inject intelligence into our operations, products, and services. To provide an entire end-to-end transformation, we encourage human-centered design and ground-breaking innovation.

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explain how to break apart the addends to find the sum of 25 16

Answers

Answer:

The sum of 25 and 16 is 41.

Step-by-step explanation:

The sum of two numbers, 25 and 16, you can break apart the addends and add them separately to simplify the process. Here's how you can do it:

Break apart the numbers into their place values: For 25, you have 20 and 5, and for 16, you have 10 and 6. This step helps you work with the place values individually.

Add the tens place: In this case, you have 20 (from 25) and 10 (from 16). Adding them gives you 30.

Add the ones place: Now you add the ones place, which is 5 (from 25) and 6 (from 16). Adding them gives you 11.

Combine the sum of the tens place and the sum of the ones place: Take the sum of 30 (from step 2) and 11 (from step 3). Adding them together gives you 41.

So, the sun is 41.

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Please help itś due tomorrow, I will give points.

Please help it due tomorrow, I will give points.

Answers

Answer: 120

Step-by-step explanation:look up the answer on another site

Question on the photo pls help

Question on the photo pls help

Answers

2 time 5 + 2x + 2 + 2x + 4 + 2x - 3

find the value of of x sin(4x+30)°=cos(-2x+54)°

Answers

Answer:

fhxhfbccbbn

cfhjhkj

ffuhhoh

What does side LN equal?

What does side LN equal?

Answers

Answer:

MN = x(x + 1)/(x + 3)

Step-by-step explanation:

We are given;

MN/LN = PN/QN

From the diagram;

Let MN = y

LN = x + 1 + y

PN = x

QN = x + 3 + x = 2x + 3

Thus;

y/(x + y + 1) = x/(2x + 3)

Rearranging gives;

y(2x + 3) = x(x + y + 1)

2xy + 3y = x² + xy + x

x² + x = xy + 3y

x(x + 1) = y(x + 3)

y = x(x + 1)/(x + 3)

Thus; MN = x(x + 1)/(x + 3)

Please answer all of the questions!!! I am clueless!!!

Please answer all of the questions!!! I am clueless!!!

Answers

if number one is multiplication then the answer is (-301). number two is -94

d. scatter plot QUESTION 23 A chart that is recommended as an alternative to a pie chart is a a. stacked column chart. b. line chart. c. bar chart. d. box plot. QUESTION 24 A data visualization tool that updates in real time and gives multiple outputs is called a. a data dashboard. b. the GIS.

Answers

A chart that is recommended as an alternative to a pie chart is a - stacked column chart. A chart that is recommended as an alternative to a pie chart is a stacked column chart. Question 24: A data visualization tool that updates in real time and gives multiple outputs is called - a data dashboard.

A data visualization tool that updates in real time and gives multiple outputs is called a data dashboard. What is a scatter plot? A scatter plot is a type of diagram used to display two variables on a two-dimensional plot. The positioning of data points on a scatter plot graphically depicts the correlation between the two variables. To construct a scatter plot, two variables (independent and dependent variables) are plotted on a graph.

The independent variable is plotted on the horizontal (x) axis and the dependent variable is plotted on the vertical (y) axis. A point is plotted for each pair of values, and the pattern of the points suggests a relationship between the two variables.A scatter plot is useful in displaying the correlation between two variables. The correlation is positive if the points are in an upward direction. The correlation is negative if the points are in a downward direction. A lack of correlation, or random points, is suggested by a scatter plot with no apparent pattern.

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Which answer is equivalent to

Which answer is equivalent to

Answers

Answer:

A

Step-by-step explanation:

sorry if it is wrong

in exercises 29–34, solve the given system by forming x = a−1b, where a is the coefficient matrix for the system. 29. 2x1 + x2 = 4 30. X1 + X2 = 0 3.x1 + 2x2 = 2 2.x + 3x2 = 4 31. X- X2 = 5 32. 2xı + 3x2 = 1 3x - 4x2 = 2 3x + 4x2 = 7 33. 3x1 + x2 = 10 X1 - 12 = 10 -X1 + 3x2 = 5 2.x, + 3x2 34. X

Answers

To solve the given system of equations by forming x = a-1b, where a is the coefficient matrix for the system, we need to first write the system in matrix form Ax = b, where A is the coefficient matrix, x is the variable matrix, and b is the constant matrix. Then we can find the inverse of A and multiply it by b to get the solution for x.

For example, for exercise 29:

2x1 + x2 = 4

x1 + x2 = 0

We can write this system in matrix form as:

[ 2 1 ] [ x1 ] = [ 4 ]

[ 1 1 ] [ x2 ] = [ 0 ]

So, A = [ 2 1 ]

[ 1 1 ]

x = [ x1 ]

[ x2 ]

b = [ 4 ]

[ 0 ]

To find the inverse of A, we can use the formula:

A-1 = 1/(ad-bc) [ d -b ]

[ -c a ]

where a, b, c, and d are the elements of A.

So, A-1 = 1/(2-1) [ 1 -1 ]

[ -1 2 ]

= [ 1 -1 ]

[ -1 2 ]

Now we can multiply A-1 by b to get the solution for x:

x = A-1b

= [ 1 -1 ] [ 4 ]

[ -1 2 ] [ 0 ]

= [ 4 -4 ]

[ -4 0 ]

= [ 0 ]

[ 4 ]

So, the solution for the system is x1 = 0 and x2 = 4.

Similarly, we can solve the other exercises by following the same steps.

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PLEASE HELP!!!!!!!!!!!!!!!!

PLEASE HELP!!!!!!!!!!!!!!!!

Answers

There is only one pair of solution to the given system.

What is system of equations?In mathematics, a set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

Given is the system of equations as graphed.

The solution of the given system of equations is given by the total number of intersections of the graphed lines. These lines intersect at only one point (1, 4). So, there is only one pair of solution.

Therefore, there is only one pair of solution to the given system which is (1, 4).

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A solid with surface area 50units^2 is dilated by a scale factor of K to obtain a solid surface area 200units^2. Find the value of K.

Answers

The value of K is 2.

Let's denote the scale factor as K. The surface area of a solid after dilation is directly proportional to the square of the scale factor.

We are given that the initial surface area of the solid is 50 units^2, and after dilation, the surface area becomes 200 units^2.

Using the formula for the surface area, we have:

Initial surface area * (scale factor)^2 = Final surface area

50 * K^2 = 200

Dividing both sides of the equation by 50:

K^2 = 200/50

K^2 = 4

Taking the square root of both sides:

K = √4

K = 2

Therefore, the value of K is 2.

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1
Which line is pointing to the cell body?
A. 1
B. 2
C. 4
D. 5
2
3
4
5
Image by Dhp 1080

1Which line is pointing to the cell body?A. 1B. 2C. 4D. 52345Image by Dhp 1080

Answers

The line 2 is pointing towards the body of the cell, in the given image of a neuron.

What is cell body?

The soma, or cell body, is the spherical part of the neuron that houses the nucleus. The cell body is linked to the dendrites, which transport information to the neuron, and the axon, which sends information to other neurons.

When one neuron receives information from another, the dendrites send it to the cell body. Depending on the signal strength, the cell body may then send the information to the axon.

The cell body's role is to regulate all of the cell's functions. It has several important organelles that aid in this process. Organelles are tiny organelles found within cells that each perform a specific function. The nucleus is the most important organelle within the cell body.

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A magazine claimed that more than 55% of adults skip breakfast at least three times a week. To test this, a dietitian selected a random sample of 80 adults and ask them how many days a week they skip breakfast. 45 of them responded that they skipped breakfast at least three days a week. At Alpha equals 0.10 testy magazines claim

Answers

In conclusion, based on the given data and at a significance level of 0.10, there is not enough evidence to support the claim that more than 55% of adults skip breakfast at least three times a week according to the sample data.

To test the magazine's claim that more than 55% of adults skip breakfast at least three times a week, we can set up a hypothesis test.

Let's define the null hypothesis (H0) and the alternative hypothesis (Ha):

H0: The proportion of adults who skip breakfast at least three times a week is 55% or less.

Ha: The proportion of adults who skip breakfast at least three times a week is greater than 55%.

Next, we need to determine the test statistic and the critical value to make a decision. Since we have a sample proportion, we can use a one-sample proportion z-test.

Given that we have a random sample of 80 adults and 45 of them responded that they skip breakfast at least three days a week, we can calculate the sample proportion:

p = 45/80 = 0.5625

The test statistic (z-score) can be calculated using the sample proportion, the claimed proportion, and the standard error:

z = (p - P) / sqrt(P * (1 - P) / n)

where P is the claimed proportion (55%), and n is the sample size (80).

Let's calculate the test statistic:

z = (0.5625 - 0.55) / sqrt(0.55 * (1 - 0.55) / 80)

≈ 0.253

To make a decision, we compare the test statistic to the critical value. Since the significance level (α) is given as 0.10, we look up the critical value for a one-tailed test at α = 0.10.

Assuming a normal distribution, the critical value at α = 0.10 is approximately 1.28.

Since the test statistic (0.253) is less than the critical value (1.28), we fail to reject the null hypothesis.

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What is the point-slope form of the equation for the line with a slope of 6/19 that passes through the point (−1, 7/5)?

Answers

The point-slope form of the equation for the line with a slope of \(\frac{6}{19}\) that passes through the point\((-1,\frac{7}{5} )\) is \(6x-19y=-\frac{163}{5}\)

As per the question statement, we are supposed to find the point-slope form of the equation for the line with a slope of \(\frac{6}{19}\) that passes through the point\((-1,\frac{7}{5} )\) .

Before solving the question, we need to know about the point - slope form of the line i.e., \(y-y_{1} =m(x-x_{1} )\)

where m = slope = \(\frac{6}{19}\)

\(x_{1} =-1\) and \(y_{1} = \frac{7}{5}\)

Now substituting values, we get

\(y-\frac{7}{5} =\frac{6}{19} (x-[-1])\)

\(y-\frac{7}{5} = \frac{6}{19} (x+1)\)

\(19y - \frac{133}{5} = 6x+6\)

Rearranging,

\(6x-19y+6+\frac{133}{5} =0\)

\(6x-19y+\frac{163}{5} =0\)

\(6x-19y=-\frac{163}{5}\)

Hence our required equation is \(6x-19y=-\frac{163}{5}\)

Point slope form of equation: The equation of a straight line that passes through a particular point and is inclined at a specific angle to the x-axis can be found using the point slope form. Every point on a line must satisfy the equation for the line in order for it to exist. This implies that a line is represented by a linear equation in two variables.

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What is the value marginal product of labor if p = $10, mpl = $25, and apl = 40? multiple choice $400 $10,000 $250 $1,000

Answers

If P=$10, MPL= $25 and APL=$ 40, then the value of marginal product of labor is $250

The marginal product of labor (MPL) is the change in output that results from employing an added unit of labor.

The average product of labor (APL) is the total product of labor divided by the number of units of labor employed.

Here,

P= $10

The marginal product of labor (MPL)= $25

The average product of labor (APL)= $40

The value of marginal product of labor= P × The marginal product of labor (MPL)

The value of marginal product of labor= 10×25=$250

Hence, If P=$10, MPL= $25 and APL=$ 40, then the value of marginal product of labor is $250

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In figure, the side QR of ∆PQR is produced to a point S. If the bisectors of ∠PQR and ∠PRS meet at point T, then prove that ∠QTR= ½ QPR​

In figure, the side QR of PQR is produced to a point S. If the bisectors of PQR and PRS meet at point

Answers

Step-by-step explanation:

Mark her brainliest dude!!!!

In figure, the side QR of PQR is produced to a point S. If the bisectors of PQR and PRS meet at point

Write the fraction in simplest form. 3/9 *​

Answers

Answer:

the simplest form is ⅓...............

Select the correct answer.

Which expression is equivalent to the given expression?

In(2e/x)

A. In 2 – In

OB. In 2 + In

C. 1 + In 2 – In I

OD In 1 + In 2 – In r

Answers

The given expression In(2e/x) is equivalent to In 1 + In 2 + In x, which can be determined by breaking down the expression into its individual components and applying the properties of logarithms.

In(2e/x) = In(2) + In(e/x) = In(2) + In(e) - In(x) = In 1 + In 2 + In x

The given expression In(2e/x) is equivalent to In 1 + In 2 + In x. This can be determined by breaking the expression into its individual components and applying the properties of logarithms. The expression In(2e/x) can be broken down into In(2) + In(e/x). Applying the property that logarithms of products are equal to the sum of the logarithms of the individual components gives us In(2) + In(e) - In(x). Simplifying further, we get In 1 + In 2 + In x. Thus, the expression In(2e/x) is equivalent to In 1 + In 2 + In x.

In(2e/x) = In(2) + In(e/x)

= In(2) + In(e) - In(x)

= In 1 + In 2 + In x

The given expression In(2e/x) is equivalent to In 1 + In 2 + In x, which can be determined by breaking down the expression into its individual components and applying the properties of logarithms.

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Suppose John wants to open a learning center for high school students in his community. John wants to compare the average time area high school students spend studying per week with the regional average, 21.1 h. John surveys 28 randomly selected local high school students, asking how much time they spend studying in a typical week. Although he does not know the standard deviation of the underlying population, he is confident that the population is normally distributed because other studies indicate that study times are normally distributed, and graphs of his sample data indicate normality. Choose the correct test procedure that John should use to test if the mean weekly study time from his sample differs from 21.1 h. one-sample, right-tailed f-test for a mean one-sample, two-tailed f-test for a mean O one-sample, left-tailed z-test for a mean O one-sample, left-tailed r-test for a man O one-sample, two-tailed z-test for a mean

Answers

John should use a one-sample t-test to test if the mean weekly study time from his sample differs from 21.1 hours because the population standard deviation is unknown and the sample size is less than 30.

John wants to compare the average time area high school students spend studying per week with the regional average of 21.1 hours. He selects a sample of 28 local high school students and records how much time they spend studying per week to compare it to the regional average. John does not know the standard deviation of the underlying population, but he is confident that the population is normally distributed because other studies indicate that study times are normally distributed, and graphs of his sample data indicate normality.

To test if the mean weekly study time from his sample differs from 21.1 hours, John needs to use a one-sample t-test because the population standard deviation is unknown and the sample size is less than 30. The one-sample t-test is a statistical hypothesis test used to determine if there is a significant difference between the mean of a sample and a known or hypothesized population mean when the standard deviation of the population is not known.

It tests whether the sample mean is significantly different from the hypothesized population mean, taking into account the sample size and the sample standard deviation. The null hypothesis, in this case, is that there is no significant difference between the mean weekly study time of the local high school students and the regional average of 21.1 hours.

The alternative hypothesis is that there is a significant difference between the two means. John will calculate the t-test statistic using the sample mean, sample standard deviation, and sample size, and compare it to the critical t-value for his chosen level of significance (usually 0.05). If the t-test statistic is greater than the critical t-value, he can reject the null hypothesis and conclude that there is a significant difference between the mean weekly study time of the local high school students and the regional average of 21.1 hours

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Change from rectangular to cylindrical coordinates. (Let r ≥ 0 and 0 ≤ θ ≤ 2π.) (a) (−9, 9, 9) (b) (−8, 8 3 , 5)

Answers

(a) Cylindrical coordinates for (a): (r, θ, z) = (√162, 3π/4, 9)
(b) Cylindrical coordinates for (b): (r, θ, z) = (√256, 4π/3, 5)

Cylindrical coordinates can be defined as three sets of coordinates used to locate a point in a cylindrical coordinate system. In two dimensions, the position of a point can be expressed in Cartesian and polar coordinates. When polar coordinates are extended to the 3D plane, an additional coordinate is added. Together, these three measurements form cylindrical coordinates. Coordinates define both distance and angle.

The radial distance, azimuth, and height of the plane from a point are expressed in cylindrical coordinates. Cylindrical-coordinate systems can be used to describe systems with rotational symmetry.

To convert from rectangular coordinates to cylindrical coordinates, we use the following equations:

r = sqrt(x^2 + y^2)
theta (θ) = arctan(y/x)
z = z

For part (a), we have the rectangular coordinates (-9, 9, 9). Using the above equations, we get:

r = sqrt((-9)^2 + 9^2) = 9 sqrt(2)
theta = arctan(9/-9) = -π/4 (since the point is in the third quadrant)
z = 9

So the cylindrical coordinates for part (a) are (9 sqrt(2), -π/4, 9).

For part (b), we have the rectangular coordinates (-8, 8 sqrt(3), 5). Using the above equations, we get:

r = sqrt((-8)^2 + (8 sqrt(3))^2) = 16
theta = arctan(8 sqrt(3)/-8) = -π/3 (since the point is in the third quadrant)
z = 5

So the cylindrical coordinate for part (b) is (16, -π/3, 5).

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3. The system of equations for two liquid surge tanks in series is
A₁ dh'₁/dt = q'ᵢ - 1/R₁ h'₁, q'₁ = 1/R₁ h'₁
A₂ dh'₂/dt = 1/R₁ h'₁ - 1/R₂ h'₂ q'₂ = 1/R₂ h'₂
Using state-space notation, determine the matrices A,B,C, and D assuming that the level deviations are the state variables: h'₁ and h'₂. The input variable is q'ᵢ , and the output variable is the flow rate deviation, q'₂.

Answers

The surge tank is a vital component of a system in which the flow rate fluctuates significantly. The flow rate entering the tank varies significantly, causing the fluid level in the tank to fluctuate as a result of the compressibility of the liquid. The surge tank is utilized to reduce pressure variations generated by a rapidly fluctspace uating pump flow rate. To determine the matrices A,B,C, and D using state-space notation, here are the steps:State representation is given by:dx/dt = Ax + Bu; y = Cx + DuWhere: x represents the state variablesA represents the state matrixB represents the input matrixC represents the output matrixD represents the direct transmission matrixThe equation can be written asA = [ -1/R₁ 0; 1/R₁ -1/R₂]B = [1/A₁; 0]C = [0 1/R₂]D = 0Thus, the matrices A,B,C and D assuming that the level deviations are the state variables: h'₁ and h'₂. The input variable is q'ᵢ, and the output variable is the flow rate deviation, q'₂ are given by A = [ -1/R₁ 0; 1/R₁ -1/R₂]B = [1/A₁; 0]C = [0 1/R₂]D = 0.Hence, the required matrices are A = [ -1/R₁ 0; 1/R₁ -1/R₂], B = [1/A₁; 0], C = [0 1/R₂], and D = 0 using state-space notation for the given system of equations for two liquid surge tanks.

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