Calculate curl and divergence of the given vector fields a) f(x,y,z) = (x - y)i + e- xj + xye?k b) f(x,y,z) = x+ sin(yz)i + z cos(xz) / + yeSxy k.
Answers
The divergence of vector field f(x, y, z) is given values div(f) = 1 + zy cos(yz) - z sin(xz) + ye²(Sxy) + xy e²(Sxy) ×cos(Sxy).
To calculate the curl and divergence of the given vector fields, each vector field separately:
a) Vector field f(x, y, z) = (x - y)i + e²(-x)j + xyek
The curl of a vector field F = P i + Q j + R k is given by the following formula:
curl(F) = V × F = (dR/dy - dQ/dz)i + (dP/dz - dR/dx)j + (dQ/dx - dP/dy)k
calculate the curl for vector field f(x, y, z):
P = x - y
Q = e²(-x)
R = xy
compute the partial derivatives:
dP/dz = 0
dQ/dx = -e²(-x)
dR/dy = x
dP/dy = -1
dQ/dz = 0
dR/dx = y
These values into the curl formula,
curl(f) = (x - 0)i + (-e²(-x) - y)j + (-1 - (x - y))k
= xi - e²(-x)j - k
So, the curl of vector field f(x, y, z) is given by curl(f) = xi - e²(-x)j - k.
The divergence of a vector field F = P i + Q j + R k is given by the following formula:
div(F) = V · F = dP/dx + dQ/dy + dR/dz
calculate the divergence for vector field f(x, y, z):
P = x - y
Q = e²(-x)
R = xy
compute the partial derivatives:
dP/dx = 1
dQ/dy = 0
dR/dz = 0
values into the divergence formula,
div(f) = 1 + 0 + 0
= 1
So, the divergence of vector field f(x, y, z) is given by div(f) = 1.
b) Vector field f(x, y, z) = (x + sin(yz))i + (z cos(xz))j + (ye²(Sxy))k
Curl:
Using the same formula as before, Calculate the curl for vector field f(x, y, z):
P = x + sin(yz)
Q = z cos(xz)
R = ye²(Sxy)
Compute the partial derivatives:
dP/dz = y cos(yz)
dQ/dx = -z sin(xz)
dR/dy = e²(Sxy) + xy e²(Sxy) × cos(Sxy)
dP/dy = z cos(yz)
dQ/dz = cos(xz) - xz sin(xz)
dR/dx = y² e²(Sxy) × cos(Sxy)
values into the curl formula,
curl(f) = (y cos(yz) - (cos(xz) - xz sin(xz)))i + ((e²(Sxy) + xy e²(Sxy) × cos(Sxy)) - (z cos(yz)))j + ((z sin(xz) - y² e²(Sxy) ×cos(Sxy)))k
Simplifying further:
curl(f) = (xz sin(xz) + y cos(yz) - cos(xz))i + (e²(Sxy) + xy e²(Sxy) ×cos(Sxy) - z cos(yz))j + (z sin(xz) - y² e²(Sxy) × cos(Sxy))k
So, the curl of vector field f(x, y, z) is given by curl(f) = (xz sin(xz) + y cos(yz) - cos(xz))i + (e²(Sxy) + xy e²(Sxy) × cos(Sxy) - z cos(yz))j + (z sin(xz) - y² e²(Sxy) × cos(Sxy))k.
Divergence:
Using the same formula as before, calculate the divergence for vector field f(x, y, z):
P = x + sin(yz)
Q = z cos(xz)
R = ye²(Sxy)
compute the partial derivatives:
dP/dx = 1 + zy cos(yz)
dQ/dy = -z sin(xz)
dR/dz = ye²(Sxy) + xy e²(Sxy) ×cos(Sxy)
values into the divergence formula,
div(f) = 1 + zy cos(yz) - z sin(xz) + ye²(Sxy) + xy e²(Sxy) ×cos(Sxy)
To know more about values here
https://brainly.com/question/30145972
#SPJ4
Related Questions
Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your answer as a function of t.) L-1 (4s/4s^2+1)
Answers
The inverse Laplace transform of \(L^{-1}\)(4s/(4s² + 1)) is \(e^{(-i/2t)\) + \(e^{(i/2t))/2\).
To find the inverse Laplace transform of \(L^{-1}\)(4s/(4s² + 1)), we can use partial fraction decomposition.
Step 1: Factorize the denominator of the Laplace transform.
4s² + 1 = (2s + i)(2s - i)
Step 2: Write the partial fraction decomposition.
4s/(4s² + 1) = A/(2s + i) + B/(2s - i)
Step 3: Clear the fractions.
4s = A(2s - i) + B(2s + i)
Step 4: Solve for A and B.
Comparing coefficients:
4 = 2A + 2B (coefficient of s terms)
0 = -Ai + Bi (constant terms)
From the second equation, we can see that A = B. Substituting this into the first equation:
4 = 4A
A = 1
So, B = 1 as well.
Step 5: Rewrite the partial fraction decomposition.
4s/(4s² + 1) = 1/(2s + i) + 1/(2s - i)
Step 6: Take the inverse Laplace transform.
\(L^{-1}\)(4s/(4s² + 1)) = \(L^{-1}\)(1/(2s + i)) + \(L^{-1}\)(1/(2s - i))
Using Theorem 7.2.1, the inverse Laplace transforms of the individual terms can be found:
\(L^{-1}\)(1/(2s + i)) = \(e^{(-i/2t)/2\)
\(L^{-1}\)(1/(2s - i)) = \(e^{(i/2t)/2\)
Therefore, the inverse Laplace transform of \(L^{-1}\)(4s/(4s² + 1)) is:
\(L^{-1}\)(4s/(4s² + 1)) = \(e^{(-i/2t)/2\) + \(e^{(i/2t)/2\).
Learn more about the inverse Laplace transform at
https://brainly.com/question/30404106
#SPJ4
Please help me with this page it’s hard
Answers
Answer:
I can't really answer but you could download photomath it basically answers these questions by itself
Step-by-step explanation:
hope this is enough
b) no, the equation isn't a linear function as it takes the form of a parabola (x^2-bx).
Q5) y=x+6, y= x^2+6 and y=2x+6 go through the point of (0,6). This is because, if you substitute 0 for x in all the three equations, y is always equal to 6.
Q6) the line is a linear function because it is a straight line that has a slope and a y intercept. To figure out the equation of the line, you have two points, (-2,0) and (0,3). To no the gradient, you do 3-0 divided by 0+2, which is 3/2. Then, you choose on random point and substitute it in y=mx+b
3= 3/2*0+b
So you get 3=b
So, the equation of the line is y= 3/2x+3
I need help again.ASAP
Answers
Answer:
Last Option: y=2x-2
please hurry I really need help!
13. The table shows the times of runners completing a
marathon. To qualify for the next marathon, a
runner's time must be less than 3 hours. Which
runners qualify?
Cho
Kevin
Runner
Ojas
Sydney
Time (h)
3-1/
3.2
8
30
13
360
3-
Answers
Answer:
Step-by-step explanation:
the answer is 30
Which is more, 49 ounces or 3 pounds?
Answers
Answer:
The answer is 49
Step-by-step explanation:
Because 48 oz is 3 pounds but their one more there for.
What type of number is 0.2681?
A. Natural
B. Whole
C. Integer
D. Rational
Answers
Answer:
D. (Rational)
Step-by-step explanation:
Natural : Counting numbers (1,2,3...)
Whole : Natural numbers including 0 (NO DECIMALS/FRACTIONS)
Integer : Whole numbers and their opposites (positive, negative.)
Rational : Any number that can be written as a fraction/decimal, a number that can terminate or repeat.
In this case, 0.2681 is rational because it is a terminating decimal.
Help, please! I will mark you!
Answers
Answer:
It's the first one
Step-by-step explanation:
DO NOT SEND LINKS OR I'LL REPORT! Find the value of X, it's a parallelogram. Offering 50 points
Answers
Answer:Whats the question or add a picture
Answer:
127 degree I guess because I don't see a picture
Step-by-step explanation:
is the picture showing 53 degrees
Mrs. Thakur invested Rs 8000 at an interest rate of 8% per annum. Find the total amount that he will get after 2 years, if the interest is compounded annually.
Answers
Mrs. Thakur will receive Rs 9331.2 after 2 years, with an interest rate of 8% compounded annually.
How to determine the amount after tow yearsTo find the total amount Mrs. Thakur will receive after 2 years,
We need to calculate the compound interest.
The formula for compound interest is: A = P * (1 + r/100)^n
Where A is the final amount, P is the principal (Rs 8000),
r is the interest rate (8%), and n is the number of years (2).
So,
A = 8000 * (1 + 8/100)^2
A = 8000 * (1.08)^2
A = 8000 * 1.1664
A = 9331.2
Therefore, Mrs. Thakur will receive Rs 9331.2 after 2 years
Read more about compound interest at
https://brainly.com/question/24274034
#SPJ1
A ditributor of computer oftware want to obtain ome cutomer feedback concerning it newet package. Three thouand cutomer have purchaed the package. Aume that 600 of thee cutomer are diatified with the product. Twenty cutomer are randomly ampled and quetioned about the package. Let X denote the number of diatified cutomer ampled. (a) Find the denity for X. (b) Find E[X] and Var X. (c) Set up the calculation needed to find P[X ? 3]. (d) Ue the binomial table to approximate P[X ? 3]
Answers
(a) The distribution of X is binomial with parameters n = 20 and p = 600/3000 = 1/5 since we are randomly selecting 20 clients without replacement and interested in the proportion of happy consumers. Given below is the probability density function for this binomial distribution.
f(x) is equal to (n pick x) * p * x * (1-p) (n-x)
Where p and 1-p are the probability of success and failure, respectively, and n pick x is the binomial coefficient, which is equal to n!/(x! * (n-x)!).
(b) The formula for the anticipated value of X, or E[X], is
E[X] = np = 20 * (1/5) = 4
Var X, the variance of X, is defined as follows:
Var X = np(1-p) = 20*1/5*4/5=3.2
(c) The cumulative distribution function of the binomial distribution's formula can be used to get P[X >= 3]:
Sum(i=3 to n) f for P[X >= 3] (i)
Summarizing from I = 3 to 20 and substituting the values from the density function, we obtain:
Sum(i=3 to 20) = P[X >= 3] [(20 pick I (1/5)*i*4/5*(20-i)]
(d) We must determine the value of the cumulative distribution function at x = 3, which is equivalent to the likelihood of receiving three or fewer successes out of 20 trials, in order to approximate P[X >= 3] using the binomial table. By using n = 20 and p = 1/5 to calculate the value of the cumulative distribution function at x = 3 in the binomial table, it is possible to determine this probability. P[X >= 3]'s estimated value is 0.586.
To know more about cumulative distribution function at :
brainly.com/question/15291240
#SPJ4
in a class of 33 student 18 play football 1"basketball and 7 play both games how many students play non of the games
Answers
Answer:
20
Step-by-step explanation:
I'm pretty sure its 20 but I could be wrong but 20 is my best guess.
Answer:
16 of the 33 plays none.
Step-by-step explanation:
From the list, we get that 18 students play football, 1 basketball, and 7 both.
What we need to do here is add up 18 and 1
then we subtract 19 by 7 to cancel out the people who play both
and then subtract the total number of 33 by 17,
which gives you 16.
use partial fractions to find the integral partial\:fractions\:\int \frac{16x-130}{x^2-16x 63}\:dx
Answers
The solution to the integral is ∫ (16x-130) / (x²-16x+63) dx = -ln|x-9| + 41ln|x-7| + C
Now, let's get into the details of the problem. We are given the integral:
∫ (16x-130) / (x²-16x+63) dx
To solve this integral, we first need to factor the denominator. We can factor it using the quadratic formula, which gives us:
x²-16x+63 = (x-9)(x-7)
Therefore, we can rewrite the integral as:
∫ (16x-130) / [(x-9)(x-7)] dx
To apply this technique, we need to first write the fraction as:
(16x-130) / [(x-9)(x-7)] = A/(x-9) + B/(x-7)
where A and B are constants that we need to find. We can find A and B by multiplying both sides by the common denominator and then equating the numerators. This gives us:
16x - 130 = A(x-7) + B(x-9)
Now, we can solve for A and B by substituting values of x that make one of the terms zero. For example, if we substitute x=9, we get:
16(9) - 130 = A(9-7) + B(9-9)
Simplifying this expression gives us:
2A = -2
Therefore, A = -1.
Similarly, if we substitute x=7, we get:
16(7) - 130 = A(7-7) + B(7-9)
Simplifying this expression gives us:
-2B = -82
Therefore, B = 41.
Now that we have found A and B, we can rewrite the original fraction as:
(16x-130) / [(x-9)(x-7)] = -1/(x-9) + 41/(x-7)
Using this decomposition, we can integrate the original function by integrating each term separately. This gives us:
∫ (16x-130) / [(x-9)(x-7)] dx = ∫ [-1/(x-9) + 41/(x-7)] dx
= -ln|x-9| + 41ln|x-7| + C
where C is the constant of integration.
To know more about integral here
https://brainly.com/question/18125359
#SPJ4
pls help asap if you can!!!!!
Answers
Answer:
x = 24
Step-by-step explanation:
if a and b are parallel then
62 and 5x - 2 are same- side interior angles and sum to 180° , that is
5x - 2 + 62 = 180
5x + 60 = 180 ( subtract 60 from both sides )
5x = 120 ( divide both sides by 5 )
x = 24
thus for a to be parallel to b , then x = 24
2 box plots. The number line goes from 28 to 33. For Company A Monthly Sales, the whiskers range from 28 to 32, and the box ranges from 31 to 31.8. A line divides the box at 31.25. For Company B monthly sales, the whiskers range from 30 to 33, and the box ranges from 32 to 32.8. A line divides the box at 32.5. Which measure of center would you use to compare the populations represented by the box plots? Which measure of variability would you use to compare the populations represented by the box plots?
Answers
Answer:the answer for the first one is MEDIAN for the second one is INTERQUARTILE RANGE (IQR)
Answer:
Step-by-step explanation: it is MEDIAN for the second one is INTERQUARTILE RANGE
work out the area of this shape
Answers
Answer: 127
Step-by-step explanation:
the image has steps
Answer:
the answer is 127 cm^2 ig
the manager of a neighborhood plant nursery measured the height of every tree on the lot. The mean height of the trees was 75 inches and the median height was 62 inches. What was the shape of the distribution?
symmetric
roughly symmetric
skewed to the left
skewed to the right
Answers
Answer: D. skewed to the right
Step-by-step explanation:
just took it
Answer:
skewed to the right
This is the right answer Edge 2020
Step-by-step explanation:
Step 1: Subtract 3 from both sides of the inequality.
Step 2: __________
Step 3: Divide both sides of the inequality by the coefficient of x.
What is the missing step in solving the inequality 5 – 8x < 2x + 3?
Add 2x to both sides of the inequality.
Subtract 8x from both sides of the inequality.
Subtract 2x from both sides of the inequality.
Add 8x to both sides of the inequality.
Answers
Answer:
D. Add 8x to both sides of the inequality.
Step-by-step explanation:
y=¼x-3
what are the x and y intercepts
Answers
Answer:
1/4× and 3y
this is the answerr
f(x) = xe-x ce-x, for what positive value of c does f have an absolute minimum at x = -5?
Answers
The positive value of c that makes the function f(x) = xe^(-x)ce^(-x) have an absolute minimum at x = -5 is approximately 16.05.
To find the value of c that gives an absolute minimum at x = -5, we need to analyze the behavior of the function. First, we differentiate f(x) with respect to x to find the critical points. The derivative of f(x) is f'(x) = -x^2e^(-2x)ce^(-x). Setting f'(x) = 0 and solving for x, we find x = 0 as a critical point.
However, we are interested in finding the value of c that results in an absolute minimum at x = -5. Plugging x = -5 into f(x), we get f(-5) = -5e^(5)c^(-5)e^(5). Since e^5 is positive, to minimize f(-5), c should be as large as possible. Taking the limit as c approaches infinity, we find that f(-5) approaches 0.
Therefore, c should be a large positive value. Calculating the exact value, we find c ≈ 16.05 gives an absolute minimum at x = -5 for the function f(x).
Learn more about derivative here:
https://brainly.com/question/29020856
#SPJ11
Ciara measured the length, x, of each of the insects she found underneath a rock. She recorded the lengths in the table below. Calculate an estimate of the mean length of the insects she found. Give your answer in millimetres (mm). Length (mm) 0≤x≤10 10≤x≤20 20≤x≤30 Frequency 5 6 9
Answers
The estimate of the mean length of the insects Ciara found is 17 millimeters (mm).
To calculate an estimate of the mean length of the insects Ciara found, we need to find the weighted average of the lengths using the given frequencies.
Let's denote the lower limits of the length intervals as L1 = 0, L2 = 10, and L3 = 20.
Similarly, denote the upper limits as U1 = 10, U2 = 20, and U3 = 30.
Next, we calculate the midpoints of each interval by taking the average of the lower and upper limits.
The midpoints are M1 = (L1 + U1) / 2 = 5, M2 = (L2 + U2) / 2 = 15, and M3 = (L3 + U3) / 2 = 25.
Now, we can calculate the sum of the products of the frequencies and the corresponding midpoints.
This gives us (5 \(\times\) 5) + (6 \(\times\) 15) + (9 \(\times\) 25) = 25 + 90 + 225 = 340.
Next, we calculate the sum of the frequencies, which is 5 + 6 + 9 = 20.
Finally, we divide the sum of the products by the sum of the frequencies to find the weighted average, which is 340 / 20 = 17.
Therefore, the estimate of the mean length of the insects Ciara found is 17 millimeters (mm).
Thus, the mean length of the insects Ciara found is approximately 17 millimeters (mm).
For similar question on mean length.
https://brainly.com/question/16971437
#SPJ8
NEED HELP ASAP!!! what’s the two column proof for 13x-11+8x-25=90??
Answers
The value of x = 6 of the given expression '13x-11+8x-25 = 90' using the two-column proof.
What are expressions?An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division, etc.) You can think of expressions as being similar to phrases. A phrase in language may contain an action on its own, but it does not constitute a complete sentence. You must substitute a number for each variable and carry out the arithmetic operations in order to evaluate an algebraic expression. Since 6 + 6 equals 12, the variable x in the example above is equal to 6.So, the value of x:
Now, the value of x in expression'13x-11+8x-25 = 90' by two columns proof:(Refer to the image attached below)
x = 6Therefore, the value of x = 6 of the given expression using the two-column proof.
Know more about expressions here:
https://brainly.com/question/723406
#SPJ13
i never really understood what this was could u help
Answers
Answer:
1. f(4) or f(n)= 28
2. f(-2) or f(n)= -2
(please consider marking brainliest <3 )
Step-by-step explanation:
n=4 n=-2
f(n)= 5(n)+8 f(n)= 5(n)+8
f(n)= 5(4)+8 f(n)= 5(-2)+8
(n)= 20+8 f(n)= -10+8
f(n)=28 f(n)=-2
F(4)=5(4)+8
20+8=28
Determine the coordinates of W(-7 , 4) after a reflection in the line y = 9
Answers
The coordinates of W(-7, 4) after a reflection in the line y = 9 are (-7, -2).
The line y = 9 represents a horizontal line at y = 9 on the coordinate plane.
To reflect a point across a line, we need to find the same distance between the point and the line on the opposite side.
The line y = 9 is 5 units below the point W(-7, 4), so we need to reflect the point 5 units above the line.
We subtract 5 from the y-coordinate of the point W(-7, 4) to find the new y-coordinate after reflection: 4 - 5 = -1.
The x-coordinate remains the same, so the coordinates of the reflected point are (-7, -1).
However, the reflected point is still below the line y = 9. To bring it above the line, we need to reflect it again.
This time, we add 10 to the y-coordinate of the reflected point: -1 + 10 = 9.
The final coordinates of W(-7, 4) after reflection in the line y = 9 are (-7, -1).
Therefore, the coordinates of W(-7, 4) after a reflection in the line y = 9 are (-7, -1).
For more such questions on coordinates , click on:
https://brainly.com/question/17206319
#SPJ8
Someone help please, thanks.
Answers
Answer: x>16/3
Step-by-step explanation :0
# [4-5{1-(4-3+1)}] of 100% equals
a) 50%
b)-1%
c)zero
d)100%
Answers
Answer:
To solve this, we need to first evaluate the given expression. We can do that by simplifying the contents of each bracket, starting with the innermost one:
[4-5{1-(4-3+1)}]
⇒ [4 - 5{1 - (2)}]
⇒ [4 - 5{-1}]
⇒ 4 - (-5)
⇒ 4 + 5
⇒ 9
Now we can calculate what 9 out of 100 is:
9 of 100 = \(\frac{9}{100}\)
⇒ 9%
WHATS THE SLOPE OF THE RED LINE AND THE BLUE LINE?? and is the line parallel?? PLEASE I NEED THIS DONE
Answers
Answer:
The slopes of both lines are 2/3, and since they have different y-intercepts they are parallel.
Step-by-step explanation:
In order to find slope, you need to find the rise and run of the line, since slope is rise/run. Lets use the red line as an example: There are two points , (0,1) and (-2,-1) where there are solid points. Once you locate solid points, you can then count how many units up or down (rise) and how many left or right (run). If you do this on paper the lines should form a right triangle with the line as the hypotenus. Since we went up 2, right 3, the slope would be 2/3.
Hope this helps :)
Can anyone help me out?
Answers
Answer:
55° because 2and 6 are corresponding angles (they are equal)
6 and 8 are vertically opposite angles (they are equal)
Step-by-step explanation:
hope this is helpful
Raj tells his daughter, “Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be.” Find the present ages of Raj and his daughter. Also, verify the present age of Raj and his daughter graphically
Answers
The present ages of Raj and his daughter are respectively: 42 years and 12 years.
How to solve Algebra Word Problems?Present Age of Raj =y years
Present Age of daughter =x years
According to Question :
7 Years ago,
y − 7 = 7(x − 7)
⇒ 7x − y − 42 = 0.............(1)
And 3 Years from now
y + 3 = 3(x + 3)
⇒ 3x − y + 6 = 0............(2)
From eq (1) and eq (2)
Subtract eq 2 from eq 1 to get:
7x − 3x − y + y − 42 − 6 = 0
⇒ 4x = 48
⇒ x = 12
Putting x = 12 in Equation (2). we get,
(3 × 12) − y + 6 = 0
⇒ y = 42
Read more about Algebra Word Problems at: https://brainly.com/question/21405634
#SPJ1
(4y + 3)
(5x - 7)
(3x + 17°
X= ,y= ,
Answers
Answer:
Simplifying
4y + 3 = 5x + -7 + 3x + 17
Reorder the terms:
3 + 4y = 5x + -7 + 3x + 17
Reorder the terms:
3 + 4y = -7 + 17 + 5x + 3x
Combine like terms: -7 + 17 = 10
3 + 4y = 10 + 5x + 3x
Combine like terms: 5x + 3x = 8x
3 + 4y = 10 + 8x
Solving
3 + 4y = 10 + 8x
Solving for variable 'y'.
Move all terms containing y to the left, all other terms to the right.
Add '-3' to each side of the equation.
3 + -3 + 4y = 10 + -3 + 8x
Combine like terms: 3 + -3 = 0
0 + 4y = 10 + -3 + 8x
4y = 10 + -3 + 8x
Combine like terms: 10 + -3 = 7
4y = 7 + 8x
Divide each side by '4'.
y = 1.75 + 2x
Simplifying
y = 1.75 + 2x
i hope that helpsWhich of the following is the correct representation of permutation?
rPn
P (n,r)
C(n, r)
nCr
all the above