Let X and Y be two continuous random variables with joint probability density function Calculate the positive constant b. Show the result with at least two decimal places. 5 -bcx cb - bzycb f(x,y) = 0 otherwise

Answers

Answer 1

The positive constant b is 0. This is obtained by setting the coefficient of the xy^2 term to zero in the equation derived from equating the integral of the joint probability density function to 1.

To compute the positive constant b, we need to calculate the integral of the joint probability density function (pdf) over the entire probability space and set it equal to 1 since it represents a valid probability density.

∫∫ f(x, y) dx dy = 1

Since the joint pdf is defined as:

f(x, y) = 5 - bcx * cb - bzycb

And it is zero otherwise, we can set up the integral as follows:

∫∫ (5 - bcx * cb - bzycb) dx dy = 1

To solve this integral, we need to determine the limits of integration. Since the joint pdf is not specified outside of the equation, we assume it is defined for all real values of x and y.

∫∫ (5 - bcx * cb - bzycb) dx dy = ∫∫ 5 - bcx * cb - bzycb dx dy

Integrating with respect to x first:

∫ (5x - bcx^2/2 * cb - bzy * cb) ∣∣ dy = 1

Now integrating with respect to y:

(5xy - bcxy^2/2 * cb - bzy^2/2 * cb) ∣∣ dy = 1

Since this equation holds for all real values of x and y, we can ignore the limits of integration.

Next, we can solve for b by equating the integral to 1 and simplifying:

(5xy - bcxy^2/2 * cb - bzy^2/2 * cb) = 1

Simplifying further:

5xy - bcxy^2/2 - bzy^2/2 = 1

Now, we can compare the coefficients of the terms on both sides of the equation:

- bc/2 = 0 (since there is no xy^2 term on the right-hand side)

Solving for b:

bc = 0

Since we are looking for a positive constant b, we can conclude that b = 0.

Therefore, the positive constant b is 0.

To know more about positive constant refer here:

https://brainly.com/question/31692182#

#SPJ11


Related Questions

calculate the exact distance between the points (8, -3) and (-2, 4). sophia calculus

Answers

The exact distance between the points (8, -3) and (-2, 4) can be calculated using the distance formula in mathematics.

The formula for finding the distance between two points (x1, y1) and (x2, y2) in a two-dimensional Cartesian coordinate system is given by: Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2). Using the coordinates (8, -3) and (-2, 4), we can substitute the values into the distance formula: Distance = sqrt((-2 - 8)^2 + (4 - (-3))^2) = sqrt((-10)^2 + (7)^2) = sqrt(100 + 49) = sqrt(149) ≈ 12.207

Therefore, the exact distance between the points (8, -3) and (-2, 4) is approximately 12.207 units.

To know more about the distance formula here: brainly.com/question/25841655

#SPJ11

What is the probability of getting a number greater than or equal to 5 when rolling a number cube numbered 1 to 6?

Answers

Answer:

There is a 1/3 (or 0.33%) probability of rolling a number greater than or equal to 5.

Step-by-step explanation:

First, find what numbers are greater than or equal to 5:

5 and 6

Find what options you can get on a number cube:

1, 2, 3, 4, 5, and 6

Out of the 6 possible outcomes, there are only 2 that will get a number greater than or equal to 5. Write this as a fraction:

2/6

Simplify:

1/3

Your grandmother always has a jar of cookies on her counter. One day while you are visiting, you eat 5 cookies from the jar. In the equation below, c is the number of cookies remaining in the jar and b is the number of cookies in the jar before your visit.

Answers

Answer:

b - 5 = c

Step-by-step explanation:

if you take the number of cookies before the visit (B) and then you eat 5, that would be (B - 5). after you eat the cookies, C is the amount left. so it’s a subtraction problem without 2 numbers. so the equation would be

b - 5 = c

or

before - 5 = after

answer the question true or false. the null distribution is the distribution of the test statistic assuming the null hypothesis is true; it is mound shaped and symmetric about the null mean .

Answers

False, the null distribution is the distribution of the test statistic assuming the null hypothesis is true; it is mound-shaped and symmetric about the null mean.

The null distribution is the distribution of the test statistic under the assumption that the null hypothesis is true. However, its shape and symmetry are not necessarily predetermined.

The null distribution can take various forms depending on the specific test and the underlying data. It may or may not be mound shaped or symmetric about the null mean. The shape and characteristics of the null distribution are determined by the specific hypothesis being tested, the sample size, and other factors.

Learn more about null distribution at

https://brainly.com/question/31692159

#SPJ4

what is 1/12 in simplest form

Answers

It cant be written any way else its already in its simplest form


[tex](2x5y6)(4x - 3y - 3) [/tex]

Answers

240x^2y-180xy^2-180xy

An experiment consists of tossing 3 fair (not weighted) coins, except one of the 3 coins has a head on both sides. Compute the probability of obtaining exactly 3 heads The probability of obtaining exactly 3 heads is

Answers

The probability of obtaining exactly 3 heads is 5/16.

We can find the probability of obtaining exactly 3 heads by considering the different ways in which this can happen.

First, suppose we toss the two normal coins and the biased coin with the two heads.

There is a probability of getting heads on each toss of the biased coin: 1/2

A  probability of getting heads on each toss of the normal coins: 1/2

Therefore, the probability of getting exactly 3 heads in this case is:

(1/2) * (1/2) * (1/2) = 1/8

Now suppose we toss the two normal coins and the biased coin with the two heads, but we choose to use the biased coin twice. In this case, we need to get two heads in a row with the biased coin, and then a head with one of the normal coins.

The probability of getting two heads in a row with the biased coin is: 1/2, and the probability of getting a head with one of the normal coins is: 1/2. Therefore, the probability of getting exactly 3 heads in this case is:

(1/2) * (1/2) * (1/2) = 1/8

Finally, suppose we use the biased coin and one of the normal coins twice each. In this case, we need to get two heads in a row with the biased coin, and then two tails in a row with the normal coin. The probability of getting two heads in a row with the biased coin is: 1/2,

and the probability of getting two tails in a row with the normal coin is :

(1/2) * (1/2) = 1/4.

Therefore, the probability of getting exactly 3 heads in this case is:

(1/2) * (1/2) * (1/4) = 1/16

Adding up the probabilities from each case, we get:

1/8 + 1/8 + 1/16 = 5/16

Therefore, the probability of obtaining exactly 3 heads is 5/16.

Learn more about Probability of tossing coins :https://brainly.com/question/22789432

#SPJ11

Prove that for any x e R, if x2 + 7x < 0, then x < 0. X E

Answers

To prove that for any real number x, if  x²+ 7x < 0, then x < 0, we can use the properties of quadratic functions and inequalities.

By analyzing the quadratic expression, we can determine the conditions under which it is negative. This analysis shows that the inequality x²+ 7x < 0 holds true when x is less than 0. Consider the quadratic expression x² + 7x. To determine when this expression is negative, we can factor it as x(x + 7). According to the zero product property, this expression is equal to zero when either x or (x + 7) is equal to zero. Thus, the two critical points are x = 0 and x = -7.

Now, let's analyze the behavior of the quadratic expression in the intervals (-∞, -7), (-7, 0), and (0, +∞). Choose a test point from each interval, such as -8, -3, and 1, respectively. Evaluating the expression x²⁺7x for these test points, we find that for -8 and -3, the expression is positive, and for 1, it is positive as well.

Learn more about quadratic expression click here:

brainly.com/question/10025464

#SPJ11

Find the inverse of the following matrix. Write entries as integers or fractions in lowest terms. If the matrix is not invertible, type "N" for all entries. -5-1021 A = -2-5 9 1 2 -4

Answers

The inverse of matrix A is given by;

A^-1 = |5/139   -189/139 29/139 |

         |-10/139 129/139 -27/139 |
         |-5/139   19/139 -3/139  |

The given matrix is A =

| -5  -10  21 |
| -2   -5   9 |
|  1    2  -4 |

To find the inverse of a matrix, first find the determinant of that matrix. The determinant of matrix A is given as;

|A| = -5(-5(-4) - 2(9)) - (-10)(-2(-4) - 1(21)) + (21)(-2(2) - 1(-5))

|A| = -5(10) + 100 - 21(9)

|A| = -50 + 100 - 189

|A| = -139

Thus, the determinant of matrix A is -139. Now, we can use the formula of inverse of a 3x3 matrix;

A^-1 = 1/|A| * |(b22b33 - b23b32)  (b13b32 - b12b33)  (b12b23 - b13b22)|
| (b23b31 - b21b33)  (b11b33 - b13b31)  (b13b21 - b11b23)|
| (b21b32 - b22b31)  (b12b31 - b11b32)  (b11b22 - b12b21)|

where b is the cofactor of each element of matrix A.

The cofactor of element aij is denoted as Aij and given as Aij = (-1)i+j|Mij|.

Thus, the cofactors of matrix A are;

|-5  -10  21|
| -2  -5  9 |
|  1   2 -4 |

M11 = | -5  9 |
         |  2 -4 |

M12 = | -2  9 |
          |  2 -5 |

M13 = | -2 -5 |

M21 = | -10 21 |
         |   2 -9 |

M22 = |  -5 -21 |
           |  -2  5 |

M23 = |  -2 -2 |

M31 = | -10 -5 |
         |  2  9 |

M32 = |  -5 -9 |
          |  2  2 |

M33 = |  -2 -2 |

Now we can find the inverse of matrix A as follows;

A^-1 = 1/-139 * |(5   189  -29)|
                      |(-10 -129  27)|
                      |(-5   19  -3) |

Hence, the inverse of matrix A is given by;

A^-1 = |5/139   -189/139 29/139 |

         |-10/139 129/139 -27/139 |
         |-5/139   19/139 -3/139  |

To learn more about matrix

https://brainly.com/question/28180105

#SPJ11

Which dot plot represents the data in this frequency table?

Number 3 4 5 7 8
Frequency 3 2 4 2 3

Answers

Answer:

Im so sorry im late! The answer is A i just took the quiz!

Step-by-step explanation:

The correct dot plot is given in option 1.

What is a dot plot?

Any data that may be shown as dots or tiny circles is called a dot plot. Given that the height of the bar created by the dots indicates the numerical value of each variable, it is comparable to a bar graph or a simple histogram. Little amounts of data are shown using dot plots.

As per the given data:

There are 4 options, with each option represented by a diagram also the number and frequency table is given

Number:     3 4 5 7 8

Frequency: 3 2 4 2 3

We can find the correct diagram of the dot plot by observing the number of cross against each value of the number on the line and then matching the obtained value with the given number and frequency table.

Hence, the correct dot plot is given in option 1.

To learn more about dot plot, click:

brainly.com/question/22746300

#SPJ3

PLEASE HELP!!!! 69 points my guy!!!

Answers

Answer:

D. f(q) = 2q + 3

Step-by-step explanation:

Given equation:

6q = 3s - 9

q is independent variable, we need to solve it for s:

6q = 3s - 93s = 6q + 9s = 2q + 3

Correct choice is

D. f(q) = 2q + 3

Can somebody help me!!??

Answers

Answer:

D) 8

Step-by-step explanation:

We're looking for [tex]x[/tex], which means the 7x and 5x will have the SAME x.

7(8) = 56

For the C corner, it is cornered as a 90 degree angle, so that means the (7x) + 34 degrees NEEDS to equal 90.

7(8) = 56 + 34 = 90!!

Now we have to see if 5(8) is correct

5(8) = 40 + 50 [The degree mark] = WHICH EQUALS 90 TOO..

Therefore, the answer is D) 8

hey guys could yall solve this problem for me? thanks

Answers

Answer:

Given ABCD ~ EFGH

FG = BC(EF/AB)

FG = 7(9/6)

FG = 63/6

FG = 10.5

GH = CD(EF/AB)

GH = 11(9/6)

GH = 99/6

GH = 16.5

EH = AD(EF/AB)

EH = 12(9/6)

EH = 108/6

EH = 18

What does the best fit line estimate for the y value when x is 100

Answers

you can’t estimate a variable if the letter has no meaning, you cannot do this problem w this information

The best fit line estimate for the y value when x is 100 in this case is 205.

What is Equation?

Two or more expressions with an Equal sign is called as Equation.

To determine what the best fit line estimate for the y value is when x is 100.

Assuming that you have a linear regression model with the equation y = mx + b, where "m" is the slope and "b" is the y-intercept, you would need to know the values of "m" and "b" to estimate the y value for a given x value.

If you have these values, you can substitute x = 100 into the equation and solve for y.

The resulting value will be the estimated y value for the given x value.

If the equation of the best fit line is y = 2x + 5, then the estimated y value when x is 100 would be:

y = 2(100) + 5

y = 200 + 5

y = 205

Hence, the best fit line estimate for the y value when x is 100 in this case is 205.

To learn more on Equation:

https://brainly.com/question/10413253

#SPJ2

Can someone answer all of them? Tysm!​

Answers

In a river bank

you can put the answers from the end

1.) 1/12

2.) 2/13

3.) 8/41

4.) 1/4

5.) 11/74

6.) 2/35

7.) 15/58

8.) 5/18

9.) 1/7

10.) 1/13

Find the general solution to the differential equation dy xoay + 3y = x2 dx b) Find the particular solution to the differential equation dy dx = (y + 1)(3x2 – 1) E subject to the condition that y = 0 at x = 0 c) Find the particular solution to the differential equation dy dx = y X- subject to the condition that y = 2 at x = 1

Answers

a) The differential equation is y = [tex]e^{(4x)/x}[/tex] + 3 b) The particular solution is y = [tex]e^{x^3 - x}[/tex] - 1 c) The particular solution to the differential equation is given by the equations is y = 2x or y = -2x.

a) To find the general solution to the differential equation:

x(dy/dx) + 3y = [tex](e^{4x})/{x^2}[/tex]

We can start by rearranging the equation:

dy/dx = [[tex](e^{4x})/{x^2}[/tex] - 3y]/x

This equation is linear, so we can use an integrating factor to solve it. The integrating factor is given by:

μ(x) = e^(∫(1/x) dx) = [tex]e^{ln|x|}[/tex] = |x|

Multiplying both sides of the equation by the integrating factor:

|x| * dy/dx - 3|xy| = [tex]e^{(4x)/x}[/tex]

Now, let's integrate both sides with respect to x:

∫(|x| * dy/dx - 3|xy|) dx = ∫([tex]e^{(4x)/x}[/tex]) dx

Using the properties of absolute values and integrating term by term:

∫(|x| * dy) - 3∫(|xy|) dx = ∫([tex]e^{(4x)/x}[/tex]) dx

Integrating each term separately:

∫(|x| * dy) = ∫([tex]e^{(4x)/x}[/tex]) dx + 3∫(|xy|) dx

To integrate ∫(|x| * dy), we need to know the form of y. Let's assume y = y(x). Integrating ∫[tex](e^{4x)/x}[/tex] dx gives us a natural logarithm term.

Integrating 3∫(|xy|) dx can be done using different cases for the absolute value of x.

By solving these integrals and rearranging the equation, you can find the general solution for y(x).

b) To find the particular solution to the differential equation:

dy/dx = (y + 1)(3x² - 1)

subject to the condition that y = 0 at x = 0.

We can solve this equation using separation of variables. Rearranging the equation:

dy/(y + 1) = (3x² - 1) dx

Now, let's integrate both sides:

∫(dy/(y + 1)) = ∫((3x² - 1) dx)

The left-hand side can be integrated using the natural logarithm function:

ln|y + 1| = x³ - x + C1

Solving for y, we have:

[tex]y + 1 = e^{x^3 - x + C1}\\y = e^{x^3 - x + C1} - 1[/tex]

Using the initial condition y = 0 at x = 0, we can find the particular solution. Substituting these values into the equation:

0 = [tex]e^{0 - 0 + C1}[/tex] - 1

1 = [tex]e^{C1}[/tex]

C1 = ln(1) = 0

Therefore, the particular solution is:

y = [tex]e^{x^3 - x}[/tex] - 1

c) To find the particular solution to the differential equation:

x(dy/dx) - y = y

subject to the condition that y = 2 at x = 1.

We can simplify the equation:

x(dy/dx) = 2y

Now, let's separate variables and integrate:

(1/y) dy = (1/x) dx

Integrating both sides:

ln|y| = ln|x| + C2

Simplifying further:

ln|y| = ln|x| + C2

ln|y| - ln|x| = C2

ln(|y/x|) = C2

|y/x| =  [tex]e^{C2}[/tex]

Since we are given the initial condition y = 2 at x = 1, we can substitute these values into the equation:

|2/1| = [tex]e^{C2}[/tex]

2 =    [tex]e^{C2}[/tex]

C2 = ln(2)

Therefore, the particular solution is:

|y/x| = [tex]e^{ln(2)}[/tex]

|y/x| = 2

Solving for y, we have two cases:

y/x = 2

y = 2x

y/x = -2

y = -2x

So, the particular solution to the differential equation is given by the equations:

y = 2x or y = -2x.

The complete question is:

a) Find the general solution to the differential equation

x dy/dx + 3y = (e⁴ˣ)/(x²)

b) Find the particular solution to the differential equation dy/dx = (y + 1)(3x² - 1)

subject to the condition that v = 0 at x = 0

c) Find the particular solution to the differential equation

x dy/dx (y) = y

subject to the condition that y = 2 at x = 1

To know more about equation:

https://brainly.com/question/14686792


#SPJ4

Luis's car used 4/5



of a gallon to travel 29 miles. At what rate does the car use gas, in miles per gallon?

Answers

Answer:

36.25 miles per gallon

Step-by-step explanation:

4/5 = .8

29/.8 = x/1

cross-multiply:

.8x = 29

x = 36.25

A certain statistic bˆ is being used to estimate a population parameter B. The expected value of bˆ is equal to B. What property does bˆ exhibit?

Answers

Answer:

Unbiased

Step-by-step explanation:

If b^ is equal to B this means that it is an unbiased estimator. When there is an absence of bias, we have an unbiased estimator. As an unbiased estimator it gives accurate information most of the time. The result it gives is not over estimated and also it is not underestimated.

Expected value = true value

Parameter estimates are correct on average

Thank you

The radius of a circle is 3 kilometers. What is the circle's area

Answers

Answer:

28.27

Step-by-step explanation:

A=πr2=π·32≈28.27433

Answer:

If you're using 3.14 for pi, it's 28.26

Step-by-step explanation:

Question 8 of 9
Carlita has a swimming pool in her backyard that is rectangular with a length of 26 feet and a width of 16
feet. She wants to install a concrete walkway of width c around the pool. Surrounding the walkway, she
wants to have a wood deck that extends w feet on all sides. Find an expression for the perimeter of the wood
deck.

Answers

Then, the width of the pool covered by the concrete walkway is 16 + 2c feet (2c feet on each side), and the length of the pool covered by the concrete walkway is 26 + 2c feet (2c feet on each end).

We have given a rectangular swimming pool with a length of 26 feet and a width of 16 feet. We need to find the perimeter of the wood deck that surrounds the concrete walkway of width c around the pool and extends w feet on all sides.

Let's solve the given problem as follows:Firstly, let's calculate the dimensions of the concrete walkway. Let the width of the concrete walkway be 'c' feet.

Then, the width of the pool covered by the concrete walkway is 16 + 2c feet (2c feet on each side), and the length of the pool covered by the concrete walkway is 26 + 2c feet (2c feet on each end).

So, the dimensions of the pool and concrete walkway are (26 + 2c) ft. x (16 + 2c) ft.The dimensions of the wood deck that surrounds the concrete walkway by w feet on all sides will be (26 + 2c + 2w) ft. x (16 + 2c + 2w) ft.Now, let's write the expression for the perimeter of the wood deck.P = 2(Length + Width)P = 2[(26 + 2c + 2w) + (16 + 2c + 2w)]P = 2[42 + 4c + 4w]P = 84 + 8c + 8wThe expression for the perimeter of the wood deck is 84 + 8c + 8w. Hence, the answer is 84 + 8c + 8w.

For more such questions on pool

https://brainly.com/question/28063924

#SPJ8

Knowledge and Understanding 14. Simplify (1112 - 6vw - 3wa)-(-702 + vw + 13w). 15. Which of the following is equivalent to the expression (5a + 26 - 4c)? a. 25a2 + 20ab - 40ac +482 - 16bc + 1602 b. 25a2 + 10ab - 20ac + 482 - 86C + 16c2 + c. 25a2 + 482 + 1602 d. 10a + 4b-8c 16. Expand and simplify. (b + b)(4 - 5)(25 - 8) 17. Simplify. P-2 3p + 3 X 9p +9 P + 2 3r2 - 18. Simplify. 63 62 po* + 5m3 - 15r + 12 2m2 + 2r - 40 19. Simplify. xi21 4 X + 2 3 x-1

Answers

14. (1112 - 6vw - 3wa)-(-702 + vw + 13w) = 1814 - 7vw - 3wa - 13w

15. The equivalent of the expression (5a + 26 - 4c) is 25a2 + 10ab - 20ac + 482 - 86c + 1602 + c.

16.  (b + b)(4 - 5)(25 - 8) = -34

14. Simplify (1112 - 6vw - 3wa)-(-702 + vw + 13w).

Given expression is (1112 - 6vw - 3wa)-(-702 + vw + 13w)

⇒ 1112 - 6vw - 3wa + 702 - vw - 13w

⇒ 1814 - 7vw - 3wa - 13w

15. We are to find the equivalent of the expression (5a + 26 - 4c).

a. 25a2 + 20ab - 40ac +482 - 16bc + 1602

b. 25a2 + 10ab - 20ac + 482 - 86C + 1602

c. 25a2 + 482 + 1602

d. 10a + 4b-8c5a + 26 - 4c

= 5a - 4c + 26 = 25a2 - 20ac +482 - 4c2 + 52 - 8ac

= 25a2 - 20ac + 482 - 4c2 + 10a - 8c = Option (b)

⇒ 25a2 + 10ab - 20ac + 482 - 86c + 16c2 + c.

16. Expand and simplify. (b + b)(4 - 5)(25 - 8)

Given expression is (b + b)(4 - 5)(25 - 8) = 2b(-1)(17) = -34

To learn more about simplification

https://brainly.com/question/28008382

#SPJ11

solve the equation 3a - 6 = -12.

Answers

Answer:

a=-2

Step-by-step explanation:

3a−6=−12

Step 1: Add 6 to both sides.

3a−6+6=−12+6

3a=−6

Step 2: Divide both sides by 3.

3a/ 3 = −6/ 3

a=−2

It’s a=2

I looked up the answer lol

CAN SOMEONE HELP PLS :D will mark brainliest ;)

Answers

Answer: the second one/ \/36/6

Step-by-step explanation:

A whale is at the surface of the ocean to breathe. What is the whale's elevation?

Answers

0 because it’s at the surface

PARK is a parallelogram. Find the value of x.

Answers

Answer: 40

Step-by-step explanation:

Consider the triple integral defined below: = f(x, y, z) dv 2y² 9 Find the correct order of integration and associated limits if R is the region defined by 0 ≤ ≤1-20≤x≤2- and 0 ≤ y. Remember that it is always a good idea to sketch the region of integration. You may find it helpful to sketch the slices of R in the zy-, zz- and yz-planes first. Hint: There are multiple correct ways to write dV for this integral. If you are stuck, try dV=dz dzdy s s s f(x, y, z) ddd I=

Answers

The correct order of integration and associated limits for the given triple integral I = ∫∫∫[f(x, y, z)] dx dy dz with limits: 0 ≤ x ≤ 1 - 2y, 0 ≤ y, 0 ≤ z ≤ 2y²

The correct order of integration and associated limits for the given triple integral, let's first examine the region of integration R and its slices in different planes.

Region R is defined by 0 ≤ z ≤ 2y² and 0 ≤ x ≤ 1 - 2y.

1.Slices in the zy-plane: In the zy-plane, z is restricted to 0 ≤ z ≤ 2y², and y is unrestricted. Therefore, the integral can be written as:

I = ∫∫∫ f(x, y, z) dV = ∫∫∫ f(x, y, z) dz dy dx

2.Slices in the zx-plane: In the zx-plane, z is unrestricted, and x is restricted to 0 ≤ x ≤ 1 - 2y. Therefore, the integral can be written as:

I = ∫∫∫ f(x, y, z) dV = ∫∫∫ f(x, y, z) dx dz dy

3.Slices in the yz-plane: In the yz-plane, y is unrestricted, and z is restricted to 0 ≤ z ≤ 2y². Therefore, the integral can be written as:

I = ∫∫∫ f(x, y, z) dV = ∫∫∫ f(x, y, z) dy dz dx

Considering the given hint, we can choose any of the above orders of integration as all of them are correct ways to write the integral. However, for simplicity, let's choose the order: I = ∫∫∫ f(x, y, z) dz dy dx.

Now, let's determine the limits of integration for each variable in this order:

∫∫∫ f(x, y, z) dz dy dx = ∫∫ [∫[f(x, y, z) dz] from z=0 to z=2y²] dy dx

The innermost integral with respect to z is evaluated from 0 to 2y². The next integral with respect to y is evaluated from 0 to a certain limit determined by the region R. Finally, the outermost integral with respect to x is evaluated from 0 to 1 - 2y.

Therefore, the order of integration and the associated limits for the triple integral are:

I = ∫∫∫ f(x, y, z) dz dy dx

I = ∫∫ [∫[f(x, y, z) dz] from z=0 to z=2y²] dy dx

I = ∫∫∫[f(x, y, z)] dx dy dz with limits: 0 ≤ x ≤ 1 - 2y, 0 ≤ y, 0 ≤ z ≤ 2y²

To know more about  order of integration click here :

https://brainly.com/question/30286960

#SPJ4

complete the table... plz help ​

Answers

Answer:

3=20

4=15

5=12

Step-by-step explanation:

Consider the following second order linear ODE y" - 5y + 6y = 0, where y' and y" are first and second order derivatives with respect to x. (a) Write this as a system of two first order ODEs and then write this system in matrix form. (b) Find the eigenvalues and eigenvectors of the system. (e) Write down the general solution to the second order ODE. (a) Using your result from part 3 (or otherwise) find the solution to the following equation. y' - 5y + y = 32

Answers

a. System in the matrix form is x' = Ax where A = [tex]\left[\begin{array}{ccc}0&1\\-5&6\end{array}\right][/tex] and x = [y, u].

b. The eigenvalues of the system are λ₁ = 5 and λ₂ = 1 and eigenvector are v₁ and v₂ = v₁, and v₁ is any non-zero value.

c. The general solution is equal to y(x) = c₁ × [tex]e^{(5x)[/tex] × [v₁] + c₂× [tex]e^{(x)[/tex]× [v₂].

a. Solution to the equation. y' - 5y + y = 32 is y(x) = c₁ × [tex]e^{(5x)[/tex] + c₂ × [tex]e^{(x)[/tex].

(a) To write the second order linear ODE as a system of two first order ODEs,

Introduce a new variable u = y'.

Then, we have,

u' = y'' - 5y + 6y

   = -5y + 6u

Now, write this as a system of two first order ODEs,

y' = u

u' = -5y + 6u

To express this system in matrix form,

Define the vector x = [y, u] and the matrix A = [tex]\left[\begin{array}{ccc}0&1\\-5&6\end{array}\right][/tex]

The system can then be written as,

x' = Ax

(b) To find the eigenvalues and eigenvectors of matrix A, solve the characteristic equation,

|A - λI| = 0

where I is the identity matrix.

Substituting the values of A, we have,

[tex]|\left[\begin{array}{ccc}0&1\\-5&6\end{array}\right][/tex] [tex]-\lambda\left[\begin{array}{ccc}1&0\\0&1\end{array}\right]|[/tex] = 0

[tex]\left[\begin{array}{ccc}-\lambda&1\\-5&6-\lambda\end{array}\right][/tex] = 0

(-λ)(6-λ) - (-5)(1) = 0

λ²- 6λ + 5 = 0

Factoring the quadratic equation, we get,

(λ - 5)(λ - 1) = 0

So the eigenvalues are λ₁ = 5 and λ₂ = 1.

To find the corresponding eigenvectors,

solve the equation (A - λI)v = 0 for each eigenvalue.

Let us start with λ = 5

(A - 5I)v = 0

[tex]|\left[\begin{array}{ccc}1&1\\-5&6\end{array}\right]|[/tex] v = 0

v₁ + v₂ = 0

-5v₁ + v₂ = 0

From the first equation, we get v₂ = -v₁.

Substituting this into the second equation, we have -5v₁ - v₁ = 0,

which simplifies to -6v₁ = 0.

This implies v₁ = 0, and consequently, v₂ = 0.

So, for λ = 5, the eigenvector is v₁ = 0 and v₂ = 0.

Now, let us find the eigenvector for λ = 1.

(A - I)v = 0

[tex]|\left[\begin{array}{ccc}-1&1\\-5&5\end{array}\right][/tex] v = 0

-v₁ + v₂ = 0

-5v₁ + 5v₂ = 0

From the first equation, we get v₂ = v₁.

Substituting this into the second equation, we have -5v₁ + 5v₁ = 0,

which simplifies to 0 = 0.

This implies that v₁ can be any non-zero value.

So, for λ = 1, the eigenvector is v₁ and v₂ = v₁, where v₁ is any non-zero value.

(e) The general solution to the second order ODE can be expressed using the eigenvalues and eigenvectors as follows,

y(x) = c₁ ×[tex]e^{(\lambda_{1} x)[/tex] × v₁ + c₂ × [tex]e^{(\lambda_{2} x)[/tex]× v₂

Plugging in the values we found earlier, the general solution becomes,

y(x) = c₁ × [tex]e^{(5x)[/tex] × [v₁] + c₂× [tex]e^{(x)[/tex]× [v₂]

where [v₁] and [v₂] are the eigenvectors corresponding to the eigenvalues λ₁ = 5 and λ₂ = 1 respectively.

(a) To find the solution to the equation y' - 5y + y = 32,

Use the general solution obtained above.

Comparing the equation with the standard form y' - 5y + 6y = 0,

The equation corresponds to the case where λ₂ = 1.

Substitute λ = 1, v₁ = 1, and v₂ = 1 into the general solution.

y(x) = c₁ × [tex]e^{(5x)[/tex] × [1] + c₂ × [tex]e^{(x)[/tex] × [1]

Simplifying this expression, we have,

y(x) = c₁ × [tex]e^{(5x)[/tex] + c₂ × [tex]e^{(x)[/tex]

Learn more about matrix here

brainly.com/question/31976942

#SPJ4

for what positive values of k does the function y=sin(kt) satisfy the differential equation y′′ 64y=0?

Answers

The function y = sin(kt) satisfies the differential equation y'' - 64y = 0 for pospositiveypospositiveyitiveitive values of k that are multiples of 8.

To determine the values of k for which the function y = sin(kt) satisfies the given differential equation, we need to substitute y into the equation and solve for k. Let's start by finding the first and second derivatives of y with respect to t.
The first derivative of y with respect to t is y' = kcos(kt), and the second derivative is y'' = -k^2sin(kt). Substituting these derivatives into the differential equation gives us:
(-k^2sin(kt)) - 64sin(kt) = 0Simplifying the equation, we get:
sin(kt) = -64*sin(kt)/k^2
We can divide both sides of the equation by sin(kt) (assuming sin(kt) is not zero) to get:
1 = -64/k^2
Solving for k^2, we find k^2 = -64. Since k must be positive, there are no positive values of k that satisfy this equation. Therefore, there are no positive values of k for which the function y = sin(kt) satisfies the given differential equation y'' - 64y = 0.

learn more about differential equation here

https://brainly.com/question/32538700



#SPJ11

Is this statement true or false? You calculate a finance charge by subtracting the cost of the purchase from the total payment,​

Answers

Answer:

True

Step-by-step explanation:

Brainliest?

Answer:

I Believe the answer is True

Step-by-step explanation:

Other Questions
1. if you are asked to write an essay about environmental pollution, which of the following topics will be the least useful for your argument? And the silken sad uncertain rustling of each purple curtainWhat sound devices are used in this excerpt?A. alliteration and rhymeB. repetition and rhymeC. alliteration and repetitionD. rhyme and suspense assume that amazon says that they can prove that they are not a monopsony in the labor market. what specific information might they need to find to support their claim? How to estimate disturbance term and its variance in econometricmodel Count the number of strings of decimal digits of length 6 with the following proper-ties.a) all even digitsb) begin and end with the same digitc) contains at least one 0d) contains exactly three 7se) contains exactly two 3s or exactly three 4s Morales, president of Tradewind Industries, Inc., would have actual implied authority to:a. issue corporate stock.b. remove a vice-president of the company from office.c. bind the company in a sale in the ordinary course of the company business.d. set the amount for production bonuses of the other officers. Find the Maclaurin series for the function -czby using partial fractions or otherwise. Output (Q): 0 1 2 3 4 5 6Total Cost (TC): $24 $33 $41 $48 $54 $61 $69Refer to the table shown here. Diminishing marginal returns starts to occur between units:2 and 3.3 and 4.4 and 5.5 and 6. The probability of drawing a bluemarble from a bag containingthese marbles is 1/2.If you replace the marble each time,predict how many times a blue marblewill be chosen out of 50 draws Let k, h be unknown constants and consider the linear system: + 5% = 6y 7 T - -31 = 4 z + 7 y -3 -9z+10y + hz = k This system has a unique solution whenever h If he is the (correct) value entered above, then the above system will be consistent for how many value(s) of k? Question 1 1 pts What was one detrimental effect caused by chain stores according to anti-chain store activists in the 1920s? Edit View Insert Format Tools Table 12pt Paragraph BIU TV: 0 words starting with cyclohexene, propose a reasonable synthesis of the cyclohexene derivative. a toy car is placed 13.0 cm from a convex mirror. the image of the car is upright and one-sixth as large as the actual car. calculate the mirror's power in diopters. On January 1, 2021 the national government provided a grant to Brgy ACYFA2 amounting to 24,000,000 intended to construct a new barangay hall provided that the said construction was finihsed August 15, 2021 for an amount of P32,000,000 with best estimate of the useful life at 40 yearsOn December 31, 2022 how much should be the ending balance of the recorded contra asset against the building barangay hall The most beautiful things in the world cannot be seen or touched, they are felt with the heart" means 1. Besides the fact that the customers have different ways to buy products, what are the major advantages of this kind of omni-channel strategy? 2. Evaluate the opportunities and risks involved when a formerly pure e-commerce company like Zalando opens a brick-and-mortar store. 3. In view of the recent Coronavirus pandemic, how do you think a) brick-and-mortar retailers and b) purely e-tailers (like Amazon) have altered their operational strategy? what is significant about the last lines of the chapter? what idea is lost or ""incommunicable forever""? the nurse provides care for a client diagnosed with asthma. The client has a prescription for albuterol and beclomethasone metered-dose inhalers. Which client action indicates to the nurse that further teaching is needed? (Select all that apply.)1. Using a spacer with both inhalers.2. Rinsing the mouth after taking the beclomethasone metered-dose inhaler.3. Writing down how many doses have been taken from the metered-dose inhalers.4. Using the beclomethasone inhaler, waiting 5 minutes, then taking the albuterol inhaler.5. Avoiding the use of a spacer to prevent bronchospasm. If a 90% confidence interval for the difference of means 1 2 contains all negative values, what can we conclude about the relationship between 1 and 2 at the 90% confidence level?We can conclude that 1 = 2.We can conclude that 1 > 2.We can not make any conclusions.We can conclude that 1 < 2. According to its blackbody curve, the sun puts out most of its light as what color?