Find the resultant matrix ~

\( \begin{gathered} \begin{bmatrix} {5 } \\ 3 \\ 2 \\ \end{bmatrix}\end{gathered} \times \begin{gathered} \begin{bmatrix} {5 } \: \: \: 3 \: \: \: 2 \\ \end{bmatrix}\end{gathered}\)

Answers

Answer 1

                    \(\left[\begin{array}{ccc}5\\3\\2\end{array}\right] \times[5 \ \ \ 3 \ \ \ 2]\)

Matrix multiplications are defined if the number of columns in the first matrix is equal to the number of rows in the second matrix.

                    \(\bf{\left( \begin{array}{rrr} 5 \\ 3 \\ 2 \end{array}\right) \ \ (5 \ \ 3 \ \ 2)}\)

Multiply the first element of the array by the first element of the second array to get the element of the first row of the first column in the product array.

                    \(\bf{\left( \begin{array}{rrr} 5\times5 & & \\ & & \\ & & \end{array}\right)}\)

The remaining elements of the product matrix are obtained in the same way.

                        \(\bf{ \left( \begin{array}{rrr} 5\times5 & 5\times3 & 5\times2 \\ 3\times5 & 3\times3 & 3\times2 \\ 2\times5 & 2\times3 & 2\times2 \end{array}\right) }\)

Simplify each item by multiplying the individual terms.

                                 \(\left( \begin{array}{rrr} 25 & 15 & 10 \\ 15 & 9 & 6 \\ 10 & 6 & 4 \end{array}\right)\)

\(\huge \red{\boxed{\green{\boxed{\boldsymbol{\purple{Pisces04}}}}}}\)

Answer 2

\( \begin{gathered}\left[\begin{array}{ccc}5\\3\\2\end{array}\right] \times[5 \ \ \ 3 \ \ \ 2]\end{gathered} \\ \\ \begin{gathered}\bf{\left( \begin{array}{rrr} 5 \\ 3 \\ 2 \end{array}\right) \ \ (5 \ \ 3 \ \ 2)}\end{gathered} \)

\(\begin{gathered}\bf{ \left( \begin{array}{rrr} 5\times5 & 5\times3 & 5\times2 \\ 3\times5 & 3\times3 & 3\times2 \\ 2\times5 & 2\times3 & 2\times2 \end{array}\right) }\end{gathered} \)

\(\begin{gathered}\left( \begin{array}{rrr} 25 & 15 & 10 \\ 15 & 9 & 6 \\ 10 & 6 & 4 \end{array}\right)\end{gathered}\)


Related Questions

Which statement best explains the relationship
between lines FG and HJ?
O They are perpendicular because their slopes are
equal.
• They are perpendicular because their slopes are
negative reciprocals.
They are not perpendicular because their slopes are
equal.
O They are not perpendicular because their slopes are
not negative reciprocals.

Answers

Answer:

The answer is A

Step-by-step explanation:

Write an equation for the following problems and then solve.
1. Ten times a number added to five is nine times the number.
2. Twice the difference of a number and three is the sum of that number and four.
3. Three times a number is two times the difference of that number and one

Answers

Answer: 11,444,091,796,874

Step-by-step explanation: 10 x 2 = 20 + 5 = 25 to the power of nine = 3,814,697,265,625 divided by 2 = 1,907,348,632,812 - 953,674,316,406 = 476,837,158,203 x 3 = 1,430,511,474,609 x 4 = 5,722,045,898,437 so 3 x 2 = 6 - 1 = 5 x 5,722,045,898,437 = 11,444,091,796,874 I hope this helps

The numbers are:

1. 5

2. 10

3. -2

What is  Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

1. Ten times a number added to five is nine times the number.

let the number be x

Then, 10x + 5 = 9x

10x -9 x= 5

x= 5

2. Twice the difference of a number and three is the sum of that number and four.

let the number be w

Then, 2(w- 3) = w+ 4

2w - 6= w+ 4

w= 10

3. Three times a number is two times the difference of that number and one

let the number be y

Then, 3y = 2( y - 1)

3y= 2y- 2

y= -2

Learn more about equation here:

https://brainly.com/question/10413253

#SPJ2

A)
What are the coordinates of the vertex C'
B)
What is the length of the side A'B'?

A)What are the coordinates of the vertex C'B)What is the length of the side A'B'?

Answers

Answer:

(4 , 1)

Step-by-step explanation:

This is because to find the coordinate on a graph, it is written as ( x , y) and x is on 4 and y is on 1.

that's my opinion.

Nice question

Given square PQRS, determine the missing information.

P

R

4 cm

1

S

X =

y=

Ox= 4y = 4

Ox + 4y = 2 sqrt(2)

x = 4y = 4 sqrt(2)

x = 4y - 8 sqrt(2)

Answers

The missing information in the square is option(b) x = 4y = 4 √(2) and y = 4.

Given square PQRS, the task is to determine the missing information. A square is a quadrilateral with four equal sides and four equal angles.

The coordinates of the vertices of a square are (x,y), (x+4,y), (x+4,y+4) and (x,y+4).

The missing information, x and y, can be found by solving the equations that represent the sides of the square. We can start by solving for x.

The equation for the side PQ is x + 4y = 2 √(2). Solving this equation for x gives x = 4y - 8 √(2).

Similarly, the equation for the side RS is x + 4y = 4 √(2). Solving this equation for x gives x = 4y = 4 √(2).

Therefore, the missing information is x = 4y = 4 √(2) and y = 4.  

To know more about square here

https://brainly.com/question/14198272

#SPJ4

a baseball is thrown upward from a rooftop 60 feet high. the function h(t)= -16t²+68t+60 describe the ball's height above the ground h(t) in feet t seconds after it is thrown. how long will it take for the ball to hit the ground?

Answers

Therefore, it will take the ball approximately 5 seconds to hit the ground. To find the time it takes for the ball to hit the ground, we need to determine when the height h(t) becomes zero.

Given the function h(t) = -16t^2 + 68t + 60, we set h(t) equal to zero and solve for t:

-16t^2 + 68t + 60 = 0

To simplify the equation, we can divide the entire equation by -4:

4t^2 - 17t - 15 = 0

Now, we can solve this quadratic equation either by factoring, completing the square, or using the quadratic formula. In this case, factoring is the most efficient method:

(4t + 3)(t - 5) = 0

Setting each factor equal to zero:

4t + 3 = 0 --> 4t = -3 --> t = -3/4

t - 5 = 0 --> t = 5

Since time cannot be negative, we discard the solution t = -3/4.

Therefore, it will take the ball approximately 5 seconds to hit the ground.

Learn more about divide here:

https://brainly.com/question/15381501

#SPJ11

NEED HELP ASAP, I WILL GIVE YOU BRAINLIEST

Which one represents the recursive formula for the series -4, -1, 2,...? ​

NEED HELP ASAP, I WILL GIVE YOU BRAINLIEST Which one represents the recursive formula for the series

Answers

Answer:

sO THE ANSWER TO THIS QUESTION IS 2

Step-by-step explanation:

The correct answer is the last bubble

XY= 15 and YZ= 17 find XZ

Answers

Answer:

xz=255

Step-by-step explanation:

17 is prime so yz has to be 1*17

if that's the case xy=15*1

so 15*17=255

I need a good joke :D

Answers

Answer:

My life

Step-by-step explanation:

your life
explanation: none needed

Is the function w(n)=n(n−4)(m−6)−n^2
(n−8) quadratic? If so, write the function in the form w(n)=an^2
+bn+c and enter the values for a,b, and c below. If not, enter NA in each answer field. (f)

Answers

The given function w(n) = n(n−4)(m−6)−n^2(n−8) is not a quadratic function. Therefore, NA (not applicable) should be entered in each answer field.

A quadratic function is a function of the form f(x) = ax^2 + bx + c, where a, b, and c are constants. In the given function w(n), we have terms involving n, (n−4), (m−6), and (n−8), but none of these terms are multiplied by n^2. In a quadratic function, the highest power of the variable (in this case, n) should be 2.

Since the given function does not fit the form of a quadratic function, it cannot be expressed as w(n) = an^2 + bn + c. Instead, it remains in its original form, w(n) = n(n−4)(m−6)−n^2(n−8).

Therefore, NA is the correct answer.

To know more about quadratic functions, refer here:

https://brainly.com/question/18958913#

#SPJ11

(a) Find the 95% confidence interval for the proportion of auto accidents with teenaged drivers: ) (Use 4 decimals.) (b) What does this interval mean? We are 95% confident that of the 604 sampled accidents, the proportion with a teenaged driver falls inside the above interval. We are 95% confident that the percent of accidents with teenaged drivers is 15.1%. We are 95% confident that the proportion of all accidents with teenaged drivers is inside the above interval. We are 95% confident that a randomly chosen accident with a teenaged driver will fall inside the above interval. (c) What does the 95% confidence level mean? We expect that 95% of random samples of size 604 will produce □ ✓ that contain(s) the □ □ of accidents that had teenaged drivers. The confidence interval contradicts the assertion of the politician. The figure quoted by the politician is outside the interval. The confidence interval supports the assertion of the politician. The figure quoted by the politician is inside the interval. The confidence interval contradicts the assertion of the politician. The figure quoted by the politician is inside the interval. The confidence interval supports the assertion of the politician. The figure quoted by the politician is outside the interval.

Answers

To find the 95% confidence interval, we first find the standard error of proportion by using the formula: Standard error of proportion \(= sqrt [p * (1 - p) / n]\)where\(n = 604, p = 0.151\)

Using this information we can find the 95% confidence interval as follows:Lower limit\(= 0.151 - 1.96 * sqrt [0.151 * (1 - 0.151) / 604] = 0.1179Upper limit = 0.151 + 1.96 * sqrt [0.151 * (1 - 0.151) / 604] = 0.1841\)Thus the 95% confidence interval for the proportion of auto accidents with teenage drivers is (0.1179, 0.1841) (rounded to four decimal places)b)

we cannot be 100% certain that the true proportion of all auto accidents with teenage drivers is within the interval (0.1179, 0.1841), but we can be 95% confident. Answer: The confidence interval contradicts the assertion of the politician. The figure quoted by the politician is outside the interval.

To know more about limit visit:

https://brainly.com/question/12211820

#SPJ11

Can someone please help me with this

Can someone please help me with this

Answers

Answer: x = 40

The equation you would write would be 2x + x + 60 = 180.

This is because you have to add all the angles inside the triangle in order to get 180°. Then, you solve the equation.

2x + x + 60 = 180
Add all the like terms.
3x + 60 = 180
Subtract 60 on both sides.
3x = 120
Divide 3 on both sides.
x = 40

Oliver's family took a 4-hour-and-30-minute trip on a train. They left at 7:30 a.m.
What time did Oliver's family arrive?

Answers

Answer:

12pm

Step-by-step explanation:

7:30am + 4 hours and 30 minutes = 12 pm

Answer:

Well, assuming that they just drove for four and half hours straight, without the train stopping for any reason, they would arrive at 12:00pm

7 + 4  = 11

30 + 30 = 60, and since that 60 is an hour then...

11 + 1 = 12

Hope this helps(:

A triangle has one side that measures 5 ft, one side that measures 7 ft, and one side that measures 11 ft.

Answers

The perimeter of the triangle is 23 ft.

We have,

We can use the triangle inequality theorem to check whether this triangle can exist.

According to the theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Let's check whether this condition holds for the sides given:

5 + 7 = 12, which is greater than 11, so the condition holds.

5 + 11 = 16, which is greater than 7, so the condition holds.

7 + 11 = 18, which is greater than 5, so the condition holds.

Therefore, this triangle can exist.

To find the perimeter of the triangle, we simply add up the lengths of the three sides:

Perimeter = 5 + 7 + 11 = 23 ft

Therefore,

The perimeter of the triangle is 23 ft.

Learn more about triangles here:

https://brainly.com/question/25950519

#SPJ1

The triangle inequality theorem states that a triangle with sides of 5, 7, and 11 feet is feasible.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

Any two triangle sides' lengths added together must be bigger than the third side's length.

The first two sides' combined lengths are 5 + 7 = 12, which is longer than the third side's length (11).The length of the second and third sides added together is 7 + 11 = 18, which is likewise longer than the first side's length (5).The first and third sides' combined lengths are 5 + 11 = 16, which is longer than the second side's (7 total) length.

More about the triangle link is given below.

https://brainly.com/question/25813512

#SPJ1

Find the measure of unknown angle. Line p Il q
13. m2A=
14. m2B=
15. m2C=
16. m2D=
17. m2E-
18. m2F
19. m2G=
20. mZH
F
E
60°
H
100%
с
B
20

Answers

The value of x is 13 in the given parallel lines.

a and b are two parallel lines.

We have to find the value of x.

The angle of the straight line is 180 degrees.

12x-29+4x+1=180

Combine the like terms:

16x-28=180

Add 28 on both sides:

16x=180+28

16x=208

Divide both sides by 16:

x=208/16

x=13

Hence, the value of x is 13 in the given parallel lines.

To learn more on Angles click:

https://brainly.com/question/28451077

#SPJ1

Find the measure of unknown angle. Line p Il q13. m2A=14. m2B=15. m2C=16. m2D=17. m2E-18. m2F19. m2G=20.

4. What are the Z-scores for the following Confidence Interval levels? Remember, you MUST account for both tails of the curve, positive and negative, when identifying each. That means you will need to do a little math to obtain the correct z-value. 3 Points 68%= 85% = 99% =

Answers

In order to calculate the z-scores for the given Confidence Interval (CI) levels, we need to use the Z-table. It is also known as the standard normal distribution table. Here are the z-scores for the given Confidence Interval levels:1. 68% CI: The confidence interval corresponds to 1 standard deviation on each side of the mean.

Thus, the z-score for the 68% \(CI is ±1.00.2. 85% CI\): The confidence interval corresponds to 1.44 standard deviations on each side of the mean.

We can calculate the z-score using the following formula:\(z = invNorm((1 + 0.85)/2)z = invNorm(0.925)z ≈ ±1.44\)Note that invNorm is the inverse normal cumulative distribution function (CDF) which tells us the z-score given a certain area under the curve.3. 99% CI: The confidence interval corresponds to 2.58 standard deviations on each side of the mean. We can calculate the z-score using the following formula:\(z = invNorm((1 + 0.99)/2)z = invNorm(0.995)z ≈ ±2.58\)

Note that in general, to calculate the z-score for a CI level of (100 - α)% where α is the level of significance, we can use the following formula:\(z = invNorm((1 + α/100)/2)\) Hope this helps!

To know more about distribution visit:

https://brainly.com/question/29664127

#SPJ11

On a cave dive in Oahu, a scuba diver swims at an elevation of 20 3/4 ft relative to sea level. She notices a sea turtle above her and rises 6 ft to take its picture. At what elevation does the diver take the picture?

Answers

The elevation at which the diver takes the picture is -14 3/4 feet if, on a cave dive in Oahu, a scuba diver swims at an elevation of 20 3/4 ft relative to sea level.

What is a fraction?

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

On a cave dive in Oahu, a scuba diver swims at an elevation of 20 3/4 ft relative to sea level.

Let x be the elevation at which the diver takes the picture.

The value of x can be found as follows:

x = -20 3/4 + 6

x = -83/4 + 6

x = (-83 + 24)/6

x = -59/6

Or

x = -14 3/4 feet

Thus, the elevation at which the diver takes the picture is -14 3/4 feet if, on a cave dive in Oahu, a scuba diver swims at an elevation of 20 3/4 ft relative to sea level.

Learn more about the fraction here:

brainly.com/question/1301963

#SPJ1

|||
Calculator
3.05 Quiz: Volumes of Cones
What is the approximate volume of a cone with a height of 12 in. and radius of 9 in.?
Use 3.14 to approximate pi, and express your final answer to the nearest hundredth.
Enter your answer as a decimal in the box.
in³

|||Calculator3.05 Quiz: Volumes of ConesWhat is the approximate volume of a cone with a height of 12

Answers

Rounding to the nearest hundredth, the approximate volume of the cone is 1017.36 cubic inches.

How do we find volume of cone ?

To find the volume of a cone, we use the following formula:

V = 1/3 * π * r² * h

where V is the volume of the cone, π (pi) is a mathematical constant approximately equal to 3.14, r is the radius of the circular base of the cone, and h is the height of the cone.

To use the formula, we simply substitute the given values for r and h into the formula and simplify. Make sure that the radius and height are measured in the same units. The resulting volume will be in cubic units.

The formula for the volume of a cone is:

V = 1/3 * π * r² * h

where π is pi (approximately 3.14), r is the radius of the base of the cone, and h is the height of the cone.

Substituting the given values, we get:

V = 1/3 * 3.14 * 9² * 12

= 1/3 * 3.14 * 81 * 12

= 3.14 * 324

= 1017.36

Rounding to the nearest hundredth, the approximate volume of the cone is 1017.36 cubic inches.

Learn more about concept of Cone here

https://brainly.com/question/16394302

#SPJ1

There are 9 red, 8 blue, 5 green, and 15 white marbles in a jar. If I cannot see the marbles, what is the fewest number of marbles I must pick, without replacement, in order to guarantee that 3 of the marbles are of different colors?

Answers

Answer:

25

Step-by-step explanation:

select the points that are solutions to the system of inequalities. Select all that apply.

select the points that are solutions to the system of inequalities. Select all that apply.

Answers

The solution to the graph of the linear inequality is the point of intersection which is (-5, 3)

Graph of System of Linear Inequality

A system of linear inequalities in two variables consists of at least two linear inequalities in the same variables. The solution of a linear inequality is the ordered pair that is a solution to all inequalities in the system and the graph of the linear inequality is the graph of all solutions of the system

In this problem, to find the solution to the system of linear inequality, we have to find the point of intersection. This gives the exact solution to the graph.

Looking at this graph, the point of intersection is (-5, 3)

The solution to the graph is (-5, 3)

Learn more on graph of system of linear inequality here;

https://brainly.com/question/23093488

#SPJ1

for the following grouped frequency distribution table, what is the width of each class interval? x f 20-29 2 30-39 5 40-49 4 50-59 1

Answers

The width of each class interval from the given grouped frequency distribution table is 9.

What is a class interval?

In a frequency distribution, the numerical width of a class is referred to as the class interval. Data is organised into classes in a grouped frequency distribution. The class interval is determined by the difference between the upper and lower class limits.

The give class intervals are 20-29, 30-39, 40-49 and 50-59.

The size, or width, of a class interval is the difference between the lower and upper class boundaries and is also referred to as the class width, class size, or class length.

So, class width = Upper class - Lower class

29-20=9

39-30=9

Therefore, the width of each class interval is 9.

Learn more about the class interval here:

https://brainly.com/question/29027902.

#SPJ1

the data set that lists the temperatures in albany, ny each day in the month of february would be classified as what type of data?

Answers

The data set that lists the temperatures in Albany, NY each day in the month of February would be classified as time series data, as it represents a sequence of observations recorded over a specific period of time.

Time series data refers to a collection of observations or measurements taken at regular intervals over time. In the case of the temperatures in Albany, NY each day in the month of February, the data set represents a sequence of daily temperature measurements recorded over the specific period of February. The data set captures the variation and patterns of temperature changes throughout the month, allowing for analysis of seasonal trends, fluctuations, and other temporal patterns. Time series data is commonly used in various fields, such as weather forecasting, economic analysis, and environmental monitoring, to understand and predict trends and patterns over time.

To know more about data set,

https://brainly.com/question/30248009

#SPJ11

EASY BRAINLIEST PLEASE HELP!!
-if you answer correctly ill give you brainliest which will give you 100pts-

(if you put links or don't answer accordingly im reporting your account)

EASY BRAINLIEST PLEASE HELP!!-if you answer correctly ill give you brainliest which will give you 100pts-(if

Answers

Parallelogram

Answer:

solution given:

properties of parallelogram:

diagonal bisect each otherdiagonal are CONGRUENTat least two pair of opposite sides are CONGRUENTthe diagonal are not perpendicular.

Parallelogram

Explanation:-

The answer is rectangle if we omit condition 4.

But as diagonals are not perpendicular its parallelogram.

As Rectangle has diagonals bisecting each other and perpendicular .

Please Help I will do Brainliest for first and correct answer

Please Help I will do Brainliest for first and correct answer

Answers

Answer:

5

Step-by-step explanation:

41 - 32 = 9

5/9 x 9 = 5

benji keeps track of the number of frisbee golf holes on which he makes par or better. the table shows the number of holes benji has played during his round so far. if the ratio of holes with par or better to total holes played is equal to 0.4, on how many of the holes has benji made par or better?

Answers

Benji made par or better on 7 holes in his round so far.

the ratio of holes with par or better to total holes played is equal to 0.4. We need to determine on how many of the holes Benji has made par or better. Table that shows the number of holes Benji has played during his round so far is shown below: Number of holes played in round so far Holes played 6 12 18Number of holes with par or better Number of holes played

2x 6 0.4

The ratio of the number of holes with par or better to the total number of holes played is 0.4.So, (Number of holes with par or better) /

(Number of holes played) = 0.4

Number of holes with par or better

/ (6 + 12 + 18) = 0.42x / 36 = 0.4

Cross-multiplying the above equation, we get,

2x = 0.4 x 36 = 14.4Dividing by 2 on both sides, we get x = 7.2

For more question ratio

https://brainly.com/question/32490081

#SPJ8

When performing a statistical test, such as the Chi-Square test, what p-value indicates that the data differ significantly from that expected if the null hypothesis is true?

Answers

When performing a statistical test, such as the Chi-Square test, the p-value is a crucial component in determining the significance of the data compared to the null hypothesis. The p-value represents the probability of observing the given data, or more extreme results, assuming the null hypothesis is true. In general, a p-value threshold of 0.05 is used to determine statistical significance.

If the calculated p-value is less than or equal to 0.05, it indicates that the observed data significantly differ from what is expected under the null hypothesis. This means that there is a less than 5% chance of obtaining the observed data if the null hypothesis were true. Consequently, researchers often reject the null hypothesis in favor of the alternative hypothesis when the p-value is less than or equal to 0.05.

However, it is essential to note that the choice of the significance level is subjective and may vary depending on the field or specific study. In some cases, a more stringent threshold, such as 0.01, might be required to minimize the chances of false positives, while in other situations, a more lenient threshold, such as 0.10, may be acceptable.

In summary, a p-value of 0.05 or less typically indicates that the data differ significantly from what is expected under the null hypothesis in a statistical test like the Chi-Square test. However, the chosen threshold for significance may vary depending on the specific context and research objectives.

learn more about the Chi-Square test here: brainly.com/question/29415488

#SPJ11

grade 8 math's please.

grade 8 math's please.

Answers

The measure of one interior angle of the decagon is 144 degrees

Working out the measure of one interior angle of the decagon

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

The decagon

The sum of interior angles of a polygon is calculated as

Sum = 180 * (n - 2)

Where

n = number of sides

In a decagon, we have

n = 10

This means that

Sum = 180 * (10 - 2)

When evaluated, we have

Sum = 1440

The measure of one interior angle of the decagon is then calculated as

One interior angle = 1440/10

Evaluate

One interior angle = 144

Hence, the measure of one interior angle of the decagon is 144 degrees

Read more about interior angle at

https://brainly.com/question/24839702

#SPJ1

use the flux form of​ green's theorem to evaluate ∫∫r2xy+12y3 da​, where r is the triangle with vertices​ (0,0), (1,0), and​ (0,1). question content area bottom part 1 ∫∫r2xy+12y3 da=enter your response here ​(simplify your​ answer.)

Answers

To evaluate the given integral using Green's theorem, we need to express it in the flux form.  The result of the integral is -r/6.

Green's theorem states that for a region R bounded by a simple closed curve C, the flux of the vector field F = (P, Q) across C is equal to the double integral of the curl of F over R.

In this case, we have the vector field F = (r^2xy, 1/2y^3), where r is the position vector (x, y).

The flux form of Green's theorem is:

\(∫∫R (curl F) · dA = ∫∫R (∂Q/∂x - ∂P/∂y) dA\)

Let's calculate the curl of F:

∂Q/∂x = 0

∂P/∂y = 2rxy

So, the curl of F is given by\((∂Q/∂x - ∂P/∂y) = 0 - 2rxy = -2rxy.\)

Now, let's evaluate the integral using the flux form of Green's theorem:

∫∫R (-2rxy) dA

Since the region R is a triangle with vertices (0,0), (1,0), and (0,1), we can express it as:

\(R = {(x, y) | 0 ≤ x ≤ 1, 0 ≤ y ≤ 1 - x}\)

Now, we can rewrite the integral:

\(∫₀^(1-x) (-2rxy) dy = -2rxy²/2 ∣₀^(1-x) = -rxy² ∣₀^(1-x) = -r(x-x²)\)

Let's evaluate the inner integral first:

\(∫₀^(1-x) (-2rxy) dy = -2rxy²/2 ∣₀^(1-x) = -rxy² ∣₀^(1-x) = -r(x-x²)\)

Now, evaluate the outer integral:

\(∫₀¹ -r(x-x²) dx = -r(x²/2 - x³/3) ∣₀¹ = -r(1/2 - 1/3) = -r(3/6 - 2/6) = -r(1/6) = -r/6\)

Therefore, the result of the integral is -r/6.

Learn more about Green's theorem

https://brainly.com/question/27549150

#SPJ11

simplify the expression 22(5) − 8

Answers

Answer:The answer to the expression is 102.

Step-by-step explanation:

Answer:

102

Step-by-step explanation:

22(5)-8=102

Multiply and divide (left to right) 22(5) :   110

= 110 - 8

Add and subtract ( left and right) 110 - 8 :    102

Factor -3x^2-23x+8. Please Help

Answers

Answer:

-(x+8)(3x-1)

Step-by-step explanation:

Take out the - sign, then factor as if it is positive.

An automobile uses 17 gal of fuel to go 590 mi. how many gallons are required to travel 840 mi? (round your answer to one decimal place.)

Answers

Answer:

the car would use 49 gallons because you get a decimal of 49.49 so you would put got decimal to the nearest 1's place and that would be 49

Other Questions
Which word best describes Yun Ok? A. determined B. cautious C. gentle D. frightenedplz help whoever answers the question with a correct answer, i will mark brainlyest Which of the following shows the correct prediction the pattern in the size of atoms (atom radii) from left to right across the periodic table of the elements.The size of atoms will decrease from left to right because the increasing number of protons results in a greater pull on the electrons toward the nucleus.The size of atoms will increase from left to right because the increasing number of electrons tends to overcome the pull of the protons and increase the size of their orbitals.The size of atoms will increase from left to right because the increasing number of electrons occupy more space creating a larger atom.The size of atoms will decrease from left to right because the increasing number of electrons are adding mass to the outside which is pulled toward the center. Sketch the graph of the function below, including correct signs, x-intercepts and y-intercepts.f(x) = (x + 5)(x + 3)(x - 2)2 what is the area of the triangle shown below? 1. As America entered the second industrial age, after the US Civil War; a growing gap betweencapitalists and workers emerged. What did workers want; how did they go about getting whatthey wanted? What arguments did the new rich justify their position, and justify treatingworkers as they did?2. Although we like to think of ourselves as the "land of the free," some people in America weredenied rights and freedom, even after the Civil War. Who was denied freedom, and what didpeople being denied freedom mean when they said they wanted freedom? To what extent, ifany, does it seem to be true that the fight for the rights of one group of people denied freedomand equality is the fight for the rights of all people denied freedom and equality?3. What reforms did the Progressives want? What role do they see for state and federalgovernments? How and why do they feel they balance the role of governments with the needsof businesses and ordinary people? Interpret the data - Characterizing a viral DNA polymerase DNA polymerases are an essential component of prokaryotic cells and eukaryotic cells. They are also an essential component of DNA viruses, because these viruses contain a DNA-based genome that must be replicated in order for the virus to replicate. Bacteriophage 029 is a DNA virus that infects certain species of bacteria. The specific DNA polymerase from this virus is called 029 DNA polymerase. When researchers began to characterize 029 DNA polymerase in the early 1990s, they observed the following properties: Property 1: It can unwind parental double-stranded DNA, enabling it to use one of the strands as a template. Property 2: It can initiate DNA synthesis by attaching a nucleotide to the -OH group of a protein. Property 3: It not only has 5'3' polymerization activity but also 3'=-5'exonuclease activity. Property 4: It is highly efficient, carrying out thousands of polymerizations without detaching from the template. these observations were surprising because the dna polymerases of prokaryotic and eukaryotic cells exhibit only which one of these four properties? which of the following measurements could be the side lengths of a right triangle? "I'm holding on to pieces of us, That I just can't let go" Where is this line from? What song? What artist? which of these is the biggest Sirius, Canopus, Vega, Procyon, Capella, Pollux, Deneb, Altair, Antares, or Regulus follow the steps to find the area of the shaded region for the given reaction, what volume of o2 would be required to react with 4.8 l of co , measured at the same temperature and pressure? Let us have a dagger between our teeth, a bomb in our hands, and an infinite scorn in our heartsI need help on what this quote means? Need help fast , due today research on proximity and social attraction generally supports the view that group of answer choices familiarity breeds contempt. familiarity leads to liking. distance makes the heart grow fonder. proximity leads to affection and animosity with equal frequency. How can you use the career to-do list assignment in geb 3006 to explore career options? group of answer choices to quickly assess a patient's nervous system for dysfunction, what assessment should the healthcare professional perform as the priority? hacer el presente perfecto: elija positivo, negativo o pregunta1.(i/go/to the library today)____________2.(you/ keep a pet for three years)_____________3.(you/eat thai food before?)____________4.(it/ rain all day?) - verbo regular ___________5.(who/we/forget to invite?)___________6.(we/not/hear that song already)___________7.(he/not/forget his books)___________8.(she/steal all the chocolate!)____________9.(i/explain it well?) - verbo regular__________10.(who/he/meet recently?)___________11.(how/we/finish already?) - verbo regular___________12.(he/study latin) - verbo regular___________porfa es para hoy How do I find the area? Triangle ABC is s defined by the points A(2,3), B (3,4), and C(6,3). Find the perimeter of a triangle. Round to 2 decimal places if necessary. Please help me :( what is the role of the vertical prism when measuring horizontal phorias using the von graefe method? In the early 1900s, how did the development of mass transportation systems such assubways and trolleys impact urban areas?A) They led to a reduction in the need for ethnic neighborhoods in cities,B) They contributed to a geographic separation of socioeconomic classes,C) They reduced pollution in cities by ending problems with overcrowding,D) They created a labor shortage as workers left factories for transportation jobs.