Thanks for the update. "Irrotational" means curl = zero, so we compute the curl, set it equal to zero, and solve for the constants.
[tex]\vec f(x,y,z) = (axy+z^3) \, \vec\imath + (3x^2-z) \, \vec\jmath + (bz^2-y) \, \vec k[/tex]
[tex]\nabla \times \vec f(x,y,z) = \left(\dfrac{\partial(bz^2-y)}{\partial y} - \dfrac{\partial(3x^2-z)}{\partial z}\right) \, \vec\imath - \left(\dfrac{\partial(bz^2-y)}{\partial x} - \dfrac{\partial(axy+z^3)}{\partial z}\right) \, \vec\jmath \\ ~~~~~~~~~~~~ + \left(\dfrac{\partial(3x^2-z)}{\partial x} - \dfrac{\partial(axy+z^3)}{\partial y}\right) \, \vec k[/tex]
[tex]\nabla \times \vec f(x,y,z) = 3z^2 \, \vec\jmath + (6-a)x \, \vec k[/tex]
At this point, all we can conclude is that a = 6 to make the k-component vanish. Unfortunately there's no zeroing out the j-component, so the field as given is *not* irrotational.
As I mentioned in comments, if the i-component had instead been [tex]axy+bz^3[/tex], we would have ended up with
[tex]\nabla \times \vec f(x,y,z) = 3bz^2 \, \vec\jmath + (6-a)x \, \vec k[/tex]
in which case we would have b = 0.
I'll continue working with this "fixed" field to find Φ, if only to give you an idea of how to proceed. We want a scalar function Φ(x, y, z) such that the given vector field is the gradient of f. This would entail solving the partial differential equations,
[tex]\dfrac{\partial\Phi}{\partial x} = axy+bz^3 = 6xy[/tex]
[tex]\dfrac{\partial\Phi}{\partial y} = 3x^2 - z[/tex]
[tex]\dfrac{\partial\Phi}{\partial z} = bz^2-y = -y[/tex]
Let's start with the last equation. Integrating both sides with respect to z yields
[tex]\Phi(x,y,z) = \displaystyle \int (-y) \, dz = -yz + g(x,y)[/tex]
Now differentiate both sides with respect to y :
[tex]\dfrac{\partial\Phi}{\partial y} = -z + \dfrac{\partial g}{\partial y} = 3x^2 - z \implies \dfrac{\partial g}{\partial y} = 3x^2[/tex]
Integrate both sides of the latter PDE with respect to y to solve for g :
[tex]g(x,y) = \displaystyle \int 3x^2 \, dy = 3x^2y + h(x)[/tex]
Now we differentiate Φ with respect to x :
[tex]\Phi(x,y,z) = -yz + 3x^2y + h(x) \\\\ \dfrac{\partial\Phi}{\partial x} = 6xy + \dfrac{dh}{dx} = 6xy \implies \dfrac{dh}{dx} = 0[/tex]
Integrate to solve for h :
[tex]h(x) = \displaystyle \int 0 \, dx = C[/tex]
where C is an arbitrary constant.
So the scalar function whose gradient is our "fixed" field f is
[tex]\Phi(x,y,z) = -yz + 3x^2y + C[/tex]
AB = 3(2x + 7), BC = 2x - 3, AC = 6x + 6
Answer:
^
Step-by-step explanation:
Help please thank you
Answer:
12 gallons
Step-by-step explanation:
Please help me with math area finding
Answer:
832.5
Step-by-step explanation:
if you multiply the height by the base and then divide by 2 you will get this answer (it's the formula)
IMPORTANT: Jamie says that the expressions 6x-2x+4 and 4(x+1)are not equivalent because one expression has a term that is subtracted and the other does not. Do you agree? Explain.
20 pts and Brainliest!
I need an answer similar to how this answer looks:
Yes, because in the expression 2(2n-1) you will first need to multiply 2 by 2n, your result is 4n, and then you multiply 2 by 1, you get 2, so the answer will be 4n-2, as mentioned up in the problem. So yes, Chris is correct.
Answer:
The reasoning of Jamie is incorrect
Step-by-step explanation:
No, because in the expression 4(x+1) you will first need to multiply 4 by x, your result is 4x, and then you multiply 4 by 1, you get 4, so the answer will be 4x+4, as mentioned up in the problem.
Also in the expression 6x-2x+4 ,you will first need to subtract 2x from 6x, your result is 4x ,and then you add 4 , so the answer will be 4x + 4
Finally,we obtain
6x-2x+4 = 4x + 4 and 4(x+1) = 4x + 4
Conclusion:
The reasoning of Jamie is NOT correct.
Answer:
Np Jamie is wrong
Step-by-step explanation:
No, because in the phrase 4(x+1), you must first multiply 4 by x, which gives you 4x, and then multiply 4 by 1 to get 4, giving you 4x+4, also, in the phrase 6x-2x+4, you must subtract 2x from 6x to get 4x, and then add 4 to get 4x + 4x.
Our final solution is:
4(x+1) = 4x + 4 and 6x-2x+4 = 4x + 4
Find the solution to the system of equations.
3x + y + z = 6
3x - y + 2z=9
y+ Z=3
O A. x = 2, y=-1, z = 5
O B. x = 1, y = 0, z = 3
O C. x = 5, y = -2, z = 6
O D. x = 2, y = 1, z = 4
Answer:
B. x = 1, y = 0, z = 3
Step-by-step explanation:
Systems of linear equations are readily solved by a suitable calculator or spreadsheet. The attached calculator display shows the solution to be ...
x = 1, y = 0, z = 3
__
There are several ways a calculator can solve these equations. The method shown here is to input the equations as an augmented matrix of their coefficients, and reduce it to row-echelon form. The right-most column of the reduced matrix is the set of variable values in the same order as the coefficients.
A graphing calculator can also be used to graph the equations. You may have to write one variable in terms of the others. (Here, it is convenient to let z=3-y.) The second attachment shows the solution (x, y) = (1, 0). This is sufficient to choose the correct answer. Or, you can finish the solution by substituting into the expression for z: z = 3 -y = 3 -0 = 3.
Many calculators will solve the system of equations after you enter it as presented in the problem statement.
Callie surveyed 50 people leaving the supermarket about the type of food they like. The table below shows the relative frequency
of the rows.
Does Not
Like Italian
Total
Like Italian
Like Chinese
1.00
Does Not
0.35
1.00
Like Chinese
Total
1.00
0.4
0.6
0.65
0.5
0.5
Based on this information, complete the two-way table below.
Like Italian
Does Not
Like Italian
Total
30
Like Chinese
Does Not
Like Chinese
Total
20
25
25
50
Reset
Submit
O 2022 Edmentum. All rights reserved
Answer:
left to right
12 18
13 7
Step-by-step explanation:
i got it wrong for the answer
An electronics store reduced the price of a TV from $1100 to $946. What was the percent of decrease?
Answer:
14%
Step-by-step explanation:
946/1100 = 0.86
1 - 0.86 = 0.14 = 14%
Answer: 14%
Answer:
14% decrease
Step-by-step explanation:
Percentage Decrease = [ (Starting Value - Final Value) / |Starting Value| ] × 100
Percentage Decrease = [ (1100 - 946) / |1100| ] × 100
Percentage Decrease = [ (154) / |1100| ] × 100
Percentage Decrease = [ 0.14] × 100
Percentage Decrease = 14
Find QR.
Write your answer as an integer or as a decimal rounded to the nearest tenth.
Answer:
QR ≈ 9.1
Step-by-step explanation:
using the cosine ratio in the right triangle
cos49° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{PR}{QR}[/tex] = [tex]\frac{6}{QR}[/tex] ( multiply both sides by QR )
QR × cos49° = 6 ( divide both sides by cos49° )
QR = [tex]\frac{6}{cos49}[/tex] ≈ 9.1 ( to the nearest tenth )
Make r the subject of t ＝6r^2 + 12t
[tex]\sf \dashrightarrow t = 6r^2 + 12t[/tex]
[tex]\sf \dashrightarrow -6r^2 = 12t-t[/tex]
[tex]\sf \dashrightarrow -6r^2 = 11t[/tex]
[tex]\sf \dashrightarrow 6r^2 = -11t[/tex]
[tex]\sf \dashrightarrow r^2 = -\dfrac{11t}{6}[/tex]
[tex]\sf \dashrightarrow r = \pm \sqrt{-\dfrac{11t}{6} }[/tex]
[tex]\dashrightarrow \sf r=\pm i\sqrt{\dfrac{11t}{6}}[/tex]
PLEASE HELP
An account has $325 and earns 4.5% interest. How much will the account be worth after 5 years using simple interest. Remember, money has 2 decimal
places.
Answer:
$398.13
Step-by-step explanation:
Which equation is correct?
A. cos x = 1/sin x
B. tan x = 1/csc x
C. cot x = 1/sec x
D. sec x = 1/cos x
Answer: D
Step-by-step explanation:
By definition, sec x = 1/cosx.
Answer:
B
Step-by-step explanation:
please say the answer step by step
2(10-4)2square+8
What is the image point of (-4, 2) after a translationm left 2 units and up 3 units?
Answer:
(-6,5)
Step-by-step explanation:
left 2 = x-2
up 3= y+3
BE4.5 (LO 2), AP The ledger of Pitt Company contains the following balances: Owner's Capital $30,000, Owner's Drawings $2,000, Service Revenue $58,000, Salaries and Wages Expense $39,000, and Supplies Expense $7,000. Enter the balances in T-accounts, post the closing entries, and underline and balance the accounts. Journalize and post closing entries using the three-column form of account. T-accounts
Based on the entries given, the balances when posted in T-accounts would be:
Owner's Capital a/c
Drawings $2,000 Balance c/d $30,000
Balance b/f $40,000 Income summary $12,000
$42,000 $42,000
Service revenue a/c
Cash $58,000
Profit and loss account $58,000
$58,000 $58,000
Salaries and Wages
Cash $39,000 Income summary $39,000
$39,000 $39,000
Supplies a/c
Cash $ 7,000 Income summary $7,000
$7,000 $ 7,000
Income summary a/c
Salaries and wages $39,000 Service revenue $58,000
Supplies expense $7,000
Capital a/c $12,000
$58,000 $58,000
Journal entries will be:
Date Account title Debit Credit
Owner's capital $2,000
Drawings $2,000
Date Account title Debit Credit
Income summary $46,000
Salaries and wages expense $39,000
Supplies expense $7,000
Date Account title Debit Credit
Service revenue $58,000
Income summary $58,000
Date Account title Debit Credit
Income summary $12,000
Owner's capital $12,000
What would be the closing balances?The closing balance will close off the temporary accounts which include expense accounts such as salaries and wages, and supplies. They will be sent to the Income summary account.
The owner's capital account will receive the profit for the period and will be debited for any drawings made. Accounts should always balance as shown above.
Find out more on closing account balances at https://brainly.com/question/24914390.
A simple random sample of 100 8th graders at a large suburban middle school indicated that 83% of them are involved with some type of after school activity. Find the 99% confidence interval that estimates the proportion of them that are involved in an after school activity. a) (0.733, 0.927) b) (0.653, 0.927) c) (0.633, 0.877) d) (0.783, 0.788) e) (0.733, 0.727) f) None of the above
Using the z-distribution, as we are working with a proportion, the 99% confidence interval is given by:
a) (0.733, 0.927).
What is a confidence interval of proportions?A confidence interval of proportions is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.In this problem, we have a 99% confidence level, hence[tex]\alpha = 0.99[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.99}{2} = 0.995[/tex], so the critical value is z = 2.575.
The other parameters are p = 0.83, n = 100, hence the bounds of the interval are given as follows.
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.83 - 2.575\sqrt{\frac{0.83(0.17)}{100}} = 0.733[/tex]
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.83 + 2.575\sqrt{\frac{0.83(0.17)}{100}} = 0.927[/tex]
Hence option a is correct.
More can be learned about the z-distribution at https://brainly.com/question/25890103
Prove that the value of the expression
(16^3–8^3)(4^3 +2^3) is divisible by 63.
Answer:
Step-by-step explanation:
16^3 - 8^3
Take out 8^3 as a common factor.
16^3 = 2^3 * 8^3
8^3(2^3 - 1)
8^3(8 - 1) = 8^3 * 7
(4^3 + 2^3) Expand
64 + 8 Combine
72
72 = 9 * 8
Conclusion
(8*3 * 7 )(9*8)
7*9 = 63
So any number containing 63 will divide into the reduced form of
(16^3–8^3)(4^3 +2^3)
Find the percent of change 7 players to 10 players
70%
hope it really helps...!!!
Find m RS
I NEED HELP PLS!!!!
Applying the chord theorem, since chords RS and TU are equal, then the measure of arc RS is: 106°.
What is the Chord Theorem?The chord theorem states that if two chords in a circle are equal in length, then their corresponding minor arcs will also be equal in measure.
Since chords RS = TU, therefore:
m(RS) = m(TU)
Substitute
8x - 14 = 7x + 1
8x - 7x = 14 + 1
x = 15
m(RS) = 8x - 14
Plug in the value of x
m(RS) = 8(15) - 14
m(RS) = 106°
Learn more about chord theorem on:
https://brainly.com/question/13950364
Please Help!!! . . . .
Answer:
10) a
11) the second step wound be to solve for -5^2
what is the digit 9 in this number 195,487
Answer:
In this case the number 9 would be located in the tens of thousands.
---
Thank you so much for participate in the community of Brainly.com
I hope help you :)
Kind regards, Antonio.
Nancy and Kevin collect coins. Nancy has x coins. Kevin has 9 coins fewer than five times the number of coins Nancy has. Write and simplify an expression for the total number of coins Nancy and Kevin have.
Answer:
x + (5x-9)
Step-by-step explanation:
x stands for the number of coins Nancy has
Kevin has 9 less than 5 times what Nancy has, so his part of the expression is 5x-9
To find the total number of coins they have, you have to add Nancy's number of coins x plus Kevin's number of coins 5x-9
x + (5x-9)
But you have to put parentheses around Kevin's 5x-9 so that part of the expression is calculated first, as per order of operations
Which inequality doesn't belong?
5/4≤2 8.5≥0.95 8.5≤7 10.00≤100
Answer:
8.5 < 7
Step-by-step explanation:
8.5 is less than 7.
doesn't verify mathematically.
If cos Θ = -0.1, find the value of cos (Θ + 2π) + cos(Θ + 4π).
Answer:
cos(Θ + 2π) + cos(Θ + 4π) = -0.2
Step-by-step explanation:
The cosine funciton is periodic with period 2π, so we have ...
cos(Θ) = cos(Θ + 2π) = cos(Θ + 4π) = -0.1
__
The sum is ...
cos (Θ + 2π) + cos(Θ + 4π) = -0.1 +(-0.1) = -0.2
It is possible that a distribution of data may not actually contain one of the measures of central tendency. Which one might that be?
Question 3 options:
Range
Mode
Mean
Median
Answer:
Mode
Step-by-step explanation:
PLATO users. There will always be a MEDIAN because there is always a middle number. There will always be a MEAN because you add the numbers. There will always be a RANGE because there is a high and a low number. There will sometime be no MODE if there is no reoccurring numbers.
Pleeeeeeeeeseee help meee!!!
Answer:
y= 44
Step-by-step explanation:
you know 4y so just
×11 and you get 44
A bakery sold 224 chocolate cupcakes in a day, which was 56% of the total number of cupcakes sold that day. How many total cupcakes did the bakery sell that day?
Hence, 440 cupcakes were sold on that day.
The bakery sold a total of 400 cupcakes that day, with 224 of them being chocolate cupcakes, representing 56 precent of the total.
Use the concept of percentage defined as:
A figure or ratio that may be stated as a fraction of 100 is a percentage. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion, therefore, refers to a component per hundred.
Given that,
A bakery sold 224 chocolate cupcakes in a day.
The 224 chocolate cupcakes represent 56% of the total number of cupcakes sold that day.
To find the total number of cupcakes sold,
Use the percentage given and some simple math.
If 56% of the cupcakes sold were chocolate cupcakes and that amounts to 224 cupcakes,
Set up the following equation:
0.56 x Total number of cupcakes = 224 cupcakes
To find the total number of cupcakes,
Divide both sides of the equation by 0.56:
Total number of cupcakes = 224 cupcakes / 0.56
Calculating this,
The bakery sold a total of 400 cupcakes that day.
Learn more about the percentage visit:
https://brainly.com/question/24877689
#SPJ3
choose the ratio equivalent to 10/9
30/27, 20/18...
Solution:There are infinitely many ratios equivalent to 10/9.Here are some of them:30/2720/18100/9060/54Hope it helps.
Do comment if you have any query.
find x in the right triangle
Answer:
C. √147
Step-by-step explanation:
Set the values of the triangle up in the Pythagorean Theorem.
a² + b² = c²
x² + 7² = 14²
Take 7 and 14 to the power of 2.
x² + 49 = 196
Subtract 49 from both sides.
x² = 147
Take the square root of both sides. There will only be one answer since lengths cannot be negative.
x = √147
Answer:
C
Step-by-step explanation:
using Pythagoras' identity in the right triangle.
the square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
x² + 7² = 14²
x² + 49 = 196 ( subtract 49 from both sides )
x² = 147 ( take square root of both sides )
x = [tex]\sqrt{147}[/tex]
⭐ Question 2
What is...
three times the sum of seven plus two divided by the square root of four
Hint: Try doing seven plus two first.
using podmas rule:
P - parenthesisO - OrderD - DivisionM - MultiplicationA - AdditionS - subtraction==============
[tex]\dashrightarrow \sf 3 * (7+2) \ \div \ \sqrt{4}[/tex]
[tex]\dashrightarrow \sf 3 \ * \ 9\ \div \ \sqrt{4}[/tex]
[tex]\dashrightarrow \sf 3 \ * \ 9\ \div \ 2[/tex]
[tex]\dashrightarrow \sf 3 \ * \ 4.5[/tex]
[tex]\dashrightarrow \sf \ 13.5[/tex]
Answer:
13.5
Step-by-step explanation:
[tex]3*(7+2)/\sqrt{4}[/tex]
You use PEDMAS - priority of calculation
1) Paranthesis
2) Exponents
3) Divide or Multiple (whichever comes first, reading left to right)
4) Add or Subtract (whichever comes first, reading left to right)
so,
Parenthesis first:
[tex]7+2=9[/tex]
becomes
[tex]3*9/\sqrt{4}[/tex]
No exponents, so we skip this step
Left to right for multiply or divide: first comes multiply.
[tex]3*9 = 27[/tex]
becomes
[tex]27/\sqrt{4}[/tex]
Now, last one is divide:
[tex]27/\sqrt{4} = 27/2 = 13.5[/tex]
Determine the domain of the function in the correct set notation. {x|x ∈ R, x ≠ –3} {x|x ∈ R, x ≠ 3} {x|x ∈ R, x ≠ 2} {x|x ∈ R, x ≠ –2}
Answer:
a on edg
Step-by-step explanation:
i just did the question
The correct set notation for the domain of the function is {x | x ∈ R, x ≠ 3}. Option {x | x ∈ R, x ≠ 3} is the correct answer.
The domain of a function is the set of all possible input values (x-values) for which the function is defined.
In this case, the given function is:
F(x) = (x - 4)/(x - 3)
The function is defined for all real numbers (x ∈ R) except when the denominator (x - 3) becomes zero, as division by zero is undefined.
Therefore, we need to find the value of x that makes the denominator zero and exclude that value from the domain.
The denominator becomes zero when:
x - 3 = 0
x = 3
So, the domain of the function is {x | x ∈ R, x ≠ 3}. This set notation means that the function is defined for all real numbers except x = 3. Thus, the correct set notation for the domain of the function is {x | x ∈ R, x ≠ 3}. Option {x | x ∈ R, x ≠ 3} is the correct answer.
To learn more about the domain;
https://brainly.com/question/28135761
#SPJ3
The complete question:
F(x) = (x - 4)/(x - 3)
Determine the domain of the function in the correct set notation. {x|x ∈ R, x ≠ –3} {x|x ∈ R, x ≠ 3} {x|x ∈ R, x ≠ 2} {x|x ∈ R, x ≠ –2}