Thus, the curl of the vector field F = (x2 − y2) i + 4xy j is (2x − 2y) k.
The curl of a vector field is a measure of how much the field rotates around a point. To compute the curl of the given vector field F = (x2 − y2) i + 4xy j, we need to calculate the cross product of the gradient operator (del) and F.
Using the formula for the curl, we have:
curl F = (∂Fz/∂y − ∂Fy/∂z) i + (∂Fx/∂z − ∂Fz/∂x) j + (∂Fy/∂x − ∂Fx/∂y) k
Where Fx, Fy, and Fz are the components of F in the x, y, and z directions, respectively.
In this case, F has no z-component, so we can simplify the formula to:
curl F = (∂Fy/∂x − ∂Fx/∂y) k
Now, let's calculate the partial derivatives:
∂Fx/∂y = 0 - (-2y) = 2y
∂Fy/∂x = 2x - 0 = 2x
Therefore, the curl of F is:
curl F = (2x − 2y) k
This means that the field rotates around the z-axis with a magnitude proportional to the difference between x and y. The curl is zero when x equals y, which corresponds to a point of no rotation.
In summary, the curl of the vector field F = (x2 − y2) i + 4xy j is (2x − 2y) k.
Know more about the gradient operator (del)
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A landscaping company charges customers a
one-time fee and an hourly rate of $10. For 1
hour of service, the company charges $35.
3. Which equation represents the total
charge t for h hours of landscaping?
Ot=10h
=10h+25
0
=250 + 10
Answer:
t = 10h +25
Step-by-step explanation:
let x be the one-time fee
hourly rate is $10
From given condition,
35 = x + 10*1
x = 35 - 10
x = 25
Therefore equation will be
t = 10h +25
License plates for motorcycles are different in each state. In New York they have five letters and in Maine they have four letters. How many more possibilities are there for license plates in New York? I feel like I'm overthinking this, someone help pls
Answer:
Not very many due to the fact that new york is more then just a busy place.
Step-by-step explanation:
Hope this helps Sorry if not
Is y=-7 horizontal or vertical
Answer:
Horizontal
Step-by-step explanation:
Answer:
Y=7 is a horizontal line :)
Step-by-step explanation:
(The equation can be written as y=0x+7 ). Thus, y will always be 7 , creating a horizontal line.
how do you calculate the midpoint of question e)? I am very desperate. please help
Answer:
(-1,-1)
Step-by-step explanation:
Midpoint equation: [tex](\frac{x_2+x_1}{2}, \frac{y_2+y_1}{2})[/tex]
= [tex](\frac{-5/2+1/2}{2},\frac{-1/2-3/2}{2} )[/tex]
= [tex](\frac{-2}{2},\frac{-2}{2})[/tex]
=(-1,-1)
Use the formula and plug it in :)
If micheal invests $2000 in the bank at a rate of 5.5% for 6 years how much interest will he make?
help me plz
Answer: 14,533.79 don´t take my word for it
Step-by-step explanation:
Future Value of Annuity Due
P = 2,000
r = 5.5% (0.055)
n = 6
1.055 * (2,000 * [(1 + 0.055)^6 - 1)/(0.055)])
= 14,533.79
PLS NEED DONE ASAP 10 MINUTES TILL DUE
Find the value of x.
A. 90
B. 70
C. 20
D. 50
Answer: B. 70
Step-by-step explanation:
i actually can't tell but i think this is right
Please help the problem is in the picture below.
its either a or d but positive its a
What are 3 of the 6 essential principles in Jefferson's Inaugural Address ?
brainliest if u get it right
Step-by-step explanation:
above guy is right. i donot about this.sorry and thanks.
8. Find 51% of 140. Round to the nearest tenth if necessary.
0 274.5
0 7,140.0
0 71.4
0 1.4
Answer:
0 1.4 is the answer
Step-by-step explanation:
well if you round thats why
Answer:
71.4
Step-by-step explanation:
Looked it up
Alice, Bob, and Christy are setting up aquariums. The design of each aquarium is below. Alice has enough pebbles to cover 9 square feet. Does she have enough to put a layer of pebbles on the bottom of Aquarium A?
Answer:
Step-by-step explanation:
Yes, she does
Answer:
Yes, she does
Step-by-step explanation:
Which equation has no solution?
6(5x+4)=3(10x+7)
6 times open paren 5 x plus 4 close paren is equal to 3 times open paren 10 x plus 7 close paren
18x+17=2(9x+8)+1
18 x plus 17 is equal to 2 times open paren 9 x plus 8 close paren plus 1
4(3x−7)=8(2x+3)
Answer:
The answer of the question is 6(5x+4)=3(10x+7)
Simplify:
3b - 3 and 3.5b + 4
Step-by-step explanation:
3b-3=3(b-1)
3.5+4=7,5
can you please help me with this? 50pts if it's correct.
2) Add the following:
4a2 + b2 – 3ab, 3a2 – 7b2 + 8ab and a2 – b2 + 2ab
Answer:
8a2-8b2+7ab
Step-by-step explanation:
Putting together all of the a2 gets you to 8a2
Putting together all of the b2 gets you to -8b2
Putting together all of the ab gets you to 7ab
Name three collinear points and non collinear points
I want all the answers please
A right triangle has legs 2m and 3m in length. What is the
length of its hypotenuse?
Answer:
First option) √13 m
Step-by-step explanation:
Using the Pythagorean theorem. 2^2+3^2=c^2
4+9=c^2
13=c^2
c=3.61
3.61 meters
Using the figure below, identify the sum of the angles. Then identify the measurement of the missing angles.
Answer:
x = 135
Step-by-step explanation:
The angles at the bottom are right angles (90°)
The sum of interior angles in this rectangle is equal to 720°
Find the sum of interior angles
4x + 180 = 720 subtract 180 from both sides
4x = 540 divide both sides by 4
x = 135 this is also giving us the measure of missing angles.
Select the correct answer. One factor of the polynomial 213 3r2 – 3x + 2 is (t – 2), which expression represents the other factor, or factors, of the polynomial? A. (21 + 1) (1 - 1) B. (2r2 + 1) OC. (212 - I + 1) OD. (2x - 1)(1 + 1)
Answer:
(x - 2)(x + 1)(2x -1)
Step-by-step explanation:
We use synthetic division as a tool for factoring the given expression. The coefficients of the terms given are {2, -3, -3, 2}. If x - 2 is a factor of this expression, then 2 is a root. We perform synthetic division as follows:
2 / 2 -3 -3 2
4 2 -2
-------------------------------
2 1 -1 0
Next, we determine whether or not (2x - 1)(x + 1) represents the remaining factor(s). Using -1 as divisor, we get:
-1 / 2 1 -1
-2 1
---------------------
2 -1 0
Since the remainder is zero, x + 1 must be a factor and (2x - 1) the third factor. Answer D is correct.
The solution is, (x - 2)(x + 1)(2x -1), is the expression represents the other factor, or factors, of the polynomial.
What are Polynomials?Polynomials are sums of k-xⁿ terms, where k can be any number and n can be any positive integer.
here, we have,
We use synthetic division as a tool for factoring the given expression. The coefficients of the terms given are {2, -3, -3, 2}. If x - 2 is a factor of this expression, then 2 is a root. We perform synthetic division as follows:
2 / 2 -3 -3 2
4 2 -2
-------------------------------
2 1 -1 0
Next, we determine whether or not (2x - 1)(x + 1) represents the remaining factor(s). Using -1 as divisor, we get:
-1 / 2 1 -1
-2 1
---------------------
2 -1 0
Since the remainder is zero, x + 1 must be a factor and (2x - 1) the third factor. Answer D is correct.
Hence, The solution is, (x - 2)(x + 1)(2x -1), is the expression represents the other factor, or factors, of the polynomial.
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If the ratio of milk cartons to juice boxes is 13:x and there are 39 milk cartons
and 18 juice boxes, what is the value of x?
Answer:
6
Step-by-step explanation:
Just write the amount of milk cartons and juice cartons as a fraction and simplify it
39/18 the biggest common divisor for this is 3 so we divide the fraction by 3
13/6 x = 6
g(-4) and g(4)=
Using the graph
Answer:
g(-4) = 1 g(5) = -3
Step-by-step explanation:
Step 1: Recognize this is in function notation
In funcion notation what is in the brackets are the x coordinates of the point
Step 2: Solve
We see the first one is g(-4) so we head to the left side of the x-axis and look for a point on the line that has the x value of -4. We see that at x = -4 y is equal to 1 so g(-4) is equal to 1
Next we take a look at g(5) so we look at the right side of the x-axis and see that the line crosses x=5 at y=-3 so the value of g(5) is -3
A scalene triangle has
A. No line of symmetry
B. one line of symmetry
C. two line of symmetry
D. three line of symmetry
Answer:A
scalene triangle is a triangle that has three unequal sides
Step-by-step explanation:
how to divide 134 800 by 240 using long method?
Answer:
sumando
Step-by-step explanation:
sumando 240 134800 veces
6x – 8y = -94
-X + 8y = 49
a. Subtract to eliminate y.
b. Subtract to eliminate x.
c. Add to eliminate y.
d. Add to eliminate x.
Answer:
photomath, assistant in mathematics, will decompose everything and give the correct answer.
please help me with this
Answer:
Y=MX+C is the equations of a straight line where C is the constant (y intercept)
Looking at a and b and the two graphs c and d
The function c represents the lowest value of the y intercept which is at -3
Just want answers/brainliest if right!
Answer:
the first one is D, the second is B, hope this helps
Step-by-step explanation:
magbigay ng apat elektronikong
Answer:
Digital electronics.
Analogue electronics.
Microelectronics.
Circuit design.
Step-by-step explanation:
One direction or Jonas brothers (only one right answer)
Answer:
one direction
Step-by-step explanation:
of course one direction
Please find the value of x
asap pls pls plslsspslsss
Answer:
The answer is the first one: y=3x+1
Step-by-step explanation:
For this question, you have to substitute different values of x and y in the table into the equation shown below the table.
y = 3x + 1
Sub x=4 and y=13
13 = 3(4) + 1
13 = 12 + 1
13 = 13
Sub x=2 and y=7
7 = 3(2) + 1
7 = 6 + 1
7 = 7
Sub x=0 and y=1
1 = 3(0) + 1
1 = 0 + 1
1 = 1
Sub x=-2 and y=-5
-5 = 3(-2) + 1
-5 = -6 + 1
-5 = -5
Hope it helps :)