5

Find the gradient field F = Vq for the potential function Q AxBy - 3ye...

Question

Find the gradient field F = Vq for the potential function Q AxBy - 3ye

Find the gradient field F = Vq for the potential function Q AxBy - 3ye



Answers

Find the gradient field $\mathbf{F}=\nabla \varphi$ for the follow. ing potential functions $\varphi$. $$\varphi(x, y)=x / y$$

This question gives us a function and access to find dysfunctions radiant. The function of three variables X, y and Z. We have e to the negative Z time sign of X plus y the functions Grady int equal to the sub x the sub y p sub z where this is shorthand for the partial derivative of fee with respect to X piece of why a shorthand for the partial derivatives of the With respect to y And then he follows the same pattern for peace of X. First we look at what we won't care about. That's going to be a e to the negative Z. It's a function in terms of Z, and that has nothing to do with X, so it will act as a constant when we take the partial derivatives for this will have to use the chain roll a little bit so first well, right into the negative, because we can be confident that will stay. Now we take the derivative of the outside of this part the derivative of Sign, which is just co sign of X plus y. Then we have to multiply by the derivative of the inside the derivative of X plus y with respect to X is just one since why it's treated the constant and in excess of the first power. So this is going to be easy to the negative z co sign of X plus y for feasible I we're going tohave the same each of negative z start. Since this also doesn't have anything to do with why, then we will also have to the derivative of sign, which is co sign X plus y. And now we take the derivative of this inside X plus y. With respect to y well, we're gonna also have one intimate skates. Accessories is a constant and why still has the first power? So this will be each the negatives, the co sign of experts. Why, for the last one piece obscene. Well, look at the other part as the constant term since it is a function of X and y not having anything to do is eat. So first will write this out front, and now we'll take the partial derivative of Z with respect to eat the negative. Z luckily will just take a negative one down here, so we just have negative each of the negative Z as are derivative. So are partial derivative with respect to Z is going to be negative e the negative z time sign of X plus y. So in this case, two of our partial derivatives were actually the exact same thing. So then the Grady And if he will be easy the negative Zied co sign of explosive lie into the negative Z sign. I mean, come sign of experts. Why again and then negative e to the negative sign of exports. Why and then this will be our Grady int of the function.

Question gives us a scaler function and wants us to calculate the radiant field. So our function the of X comma y, is equal to X squared. Why minus y squared X. So our Grady int f is equal to radiant of C is going to be equal to the partial of thieves. Respect to X comma, the partial V with respect. Why by definition So see some experts another notation for partial of the with respect to X For our first term here, we're going to treat Why is the constant So it's just gonna come out here? Then we use the power rules. Then we have two X. Then we do the other term minus just why squared? Because we treat westward of the constant and the X goes away. This is going to be equal to X y minus y squared piece of X, the partial derivative of the expected ex. I mean, why, I'm sorry. So we have X squared. Why? Well, just like with negative y squared x, we treat exit the constant here and then the widest goes waste. We have X squared minus Weiss. We're done x again, which we exit The constant and the needs of power rules. So we have to live. So this is going to be equal to X squared minus two X y. So we have both of our partial derivatives here. Cease of accent, piece of y now called the Men. So the Grady int of the is going to be equal to our first piece of x two x y minus Y squared comma X squared minus two X y, and this is going to be equal to our ingredient field.

This question gives us a function and wants us to compute the radiant field of this function. The function gives us the square root of X comma y, or we can write. This is X Y so 1/2 power. When you multiply two things and put into the same power, you could distribute the power. So we have it like this. This will make it a bit easier to answer our questions. So, by definition, the Grady int of sea going to be equal to this piece of ex Thomas he supplied The sub X is supposed to represent the partial derivative of theme. Prospective X Piece of y is a partial derivative of the respect Why? So we'll need to find these two things. Piece of X. So what do we do with the why we keep a constant? Because it is viewed as a constant We the power rule on X to move the 1/2 down. Then we subtract one from 1/2 to get negative 1/2 and then why stays along for the ride for peace? Of why? Well, actually end up doing the same thing, except for what we'll have x to the half being are constant part, so we'll put a 1/2 down here. We'll have wide to the negative 1/2 times X to the 1/2. So putting it back in terms of square roots as we saw this would be a square root of why, over two times the square root of X. Because we have this negative over here, we put it down in the denominator with two. Likewise, this would be the square root of X over two square root of wine. So then our radiant field grating a fee would be the square root of why over two square root of X times, the square root of X over two square feet of why?

So given a role of X Y is equal to X over y me or to find row. We're starting ingredient of rule. And so what is that? So that will be a vector in the following form. Where rows of X and Rosa B. Y or the partial derivatives of the row with respect to X and Y respectively. All right, so what does Rosa Becks? Well, Rosa, Becks, Why one over? Why is just a constant So it will just be in one of her. Why, since access to the first power. And when there's a rose a boy Well, why is to the negative first? So you'll get negative. X is a constant why you squared. Alright, so thus, ingredient is this the vector as such.


Similar Solved Questions

5 answers
MarutAnutVan,(m Autmmn im W"na) Im ianiiuai Va wnnrntotn Uuvutun4uurt mnn Nen 4n N
MarutAnut Van,(m Autmmn im W"na) Im ianiiuai Va wnnrntotn Uuvutun4uurt mnn Nen 4n N...
5 answers
Pex Ficd &hc { Intcrrnta , multiplicity, intarocnt d(r) (1 - 1J(r + 3)(I _ 2)Gd bchaviotKnsth U Erph81 5+4 2) Find t8 - vertical and horrizontal asyptotes (if tbcy cxist) for e(r) = 21 _ 10x
Pex Ficd &hc { Intcrrnta , multiplicity, intarocnt d(r) (1 - 1J(r + 3)(I _ 2) Gd bchaviot Knsth U Erph 81 5+4 2) Find t8 - vertical and horrizontal asyptotes (if tbcy cxist) for e(r) = 21 _ 10x...
5 answers
Problem 4: A research conducted by GFK for marketing research, the survey said that close to 70% of the customers prefer to use a credit card for purchasing transactions and the rest prefer to pay cash: Using binomial formula, find the probability that in a Sample of 26 people, the number who will hold this view is A) exactly 22B) At least 4 C) At most }
Problem 4: A research conducted by GFK for marketing research, the survey said that close to 70% of the customers prefer to use a credit card for purchasing transactions and the rest prefer to pay cash: Using binomial formula, find the probability that in a Sample of 26 people, the number who will h...
5 answers
1 1 1 3 3 1 3 tind tk? prebability that the [erson Find the proberility 2 L TdoDacr C) 0.0846 Oco selected 1 8 Ji 1 IH 0.300 1 1 1 who 1 0linc data shows of age one 1 Zcan 1 1 4 %haxhe 1 1 H 2 I Tz (v beclecen ovet 1
1 1 1 3 3 1 3 tind tk? prebability that the [erson Find the proberility 2 L TdoDacr C) 0.0846 Oco selected 1 8 Ji 1 IH 0.300 1 1 1 who 1 0linc data shows of age one 1 Zcan 1 1 4 %haxhe 1 1 H 2 I Tz (v beclecen ovet 1...
5 answers
(1point)Evaluate the Integral##10 cos(In(x)) dx,X>0Note: Use an upper-case "C for the constant of integratlon
(1point) Evaluate the Integral ##10 cos(In(x)) dx, X>0 Note: Use an upper-case "C for the constant of integratlon...
4 answers
Question 0f 12 Inolcs IO moles . Whai i5 the generic acid HA has pH = 4,00 with : solution containing bufler based on logIO(A VIHAJ = and 0.030 moles OH Use the Henderson Hasselbach equation pH = pK pH after the addition of the ratio of moles when everything in the same volute remember that the ratio of consentrations MzI
Question 0f 12 Inolcs IO moles . Whai i5 the generic acid HA has pH = 4,00 with : solution containing bufler based on logIO(A VIHAJ = and 0.030 moles OH Use the Henderson Hasselbach equation pH = pK pH after the addition of the ratio of moles when everything in the same volute remember that the rat...
1 answers
The strain at point $A$ on a beam has components $\epsilon_{x}=450\left(10^{-6}\right), \epsilon_{y}=825\left(10^{-6}\right), \gamma_{x y}=275\left(10^{-6}\right), \epsilon_{z}=0$. Determine (a) the principal strains at $A$, (b) the maximum shear strain in the $x-y$ plane, and (c) the absolute maximum shear strain.
The strain at point $A$ on a beam has components $\epsilon_{x}=450\left(10^{-6}\right), \epsilon_{y}=825\left(10^{-6}\right), \gamma_{x y}=275\left(10^{-6}\right), \epsilon_{z}=0$. Determine (a) the principal strains at $A$, (b) the maximum shear strain in the $x-y$ plane, and (c) the absolute maxim...
5 answers
Problem 4.9. On any given weekday, the number students that arrive at the University Center between 7:0Oam 8.0Oam has Poisson distribution with mean 30_ What is the probability that the first student arrives after 7:0Sam? >> Set up the integral, do NOT compute it. the second student arrives before 7:05am? >>> Set Up the integral, do NOT compute it:
Problem 4.9. On any given weekday, the number students that arrive at the University Center between 7:0Oam 8.0Oam has Poisson distribution with mean 30_ What is the probability that the first student arrives after 7:0Sam? >> Set up the integral, do NOT compute it. the second student arrives be...
5 answers
If the function T : Rn R" is a linear transformation, then show that the set below is a subspace of RnE2021 = { € €R" T(z) = 20212}.Is there anything special about 2021 in the definition? If it were replaced by another scalar; would it still be a subspace?
If the function T : Rn R" is a linear transformation, then show that the set below is a subspace of Rn E2021 = { € €R" T(z) = 20212}. Is there anything special about 2021 in the definition? If it were replaced by another scalar; would it still be a subspace?...
5 answers
The information below is summary of the duration of time in minutes that a random sample of customers spend drinking coffee on Friday evening: The cafe manager thinks the average time taken by the customers from 15 minutes: Is the manager supported by these data? Use a 0.05 to finish acup of coffee is different Assume the variable i5 normally distributed: mean (T) standard deviation (s) number 0f values 1435 1.76
The information below is summary of the duration of time in minutes that a random sample of customers spend drinking coffee on Friday evening: The cafe manager thinks the average time taken by the customers from 15 minutes: Is the manager supported by these data? Use a 0.05 to finish acup of coffee ...
5 answers
[12 points] Let S be a non-empty set of real numbers and let S denote the closure of S_ Prove that $ = 0{F | F is a closed set and S € F}
[12 points] Let S be a non-empty set of real numbers and let S denote the closure of S_ Prove that $ = 0{F | F is a closed set and S € F}...
5 answers
3. Show that the following conditions on field F are equivalent:(a) Every nonconstant polynomial in F[z] has & root in F (b) Every irreducible polynomial in F[z] is linear: (c) Every nonconstant polynomial in F[z] can be factored as a product of linear polynomials in Flz]: A field F is said to be algebraically closed if it satisfies any one and hence all) of the above conditions. The Fundamental Theorem of Algebra states that is algebraically closed.
3. Show that the following conditions on field F are equivalent: (a) Every nonconstant polynomial in F[z] has & root in F (b) Every irreducible polynomial in F[z] is linear: (c) Every nonconstant polynomial in F[z] can be factored as a product of linear polynomials in Flz]: A field F is said to ...
5 answers
Considcr the Markov Chain with state space{1,2,3_ 5,6} and transition matrixFind thc recurrent and transicnt states. Calculate the hitting probabilities for x € SR:
Considcr the Markov Chain with state space {1,2,3_ 5,6} and transition matrix Find thc recurrent and transicnt states. Calculate the hitting probabilities for x € SR:...
5 answers
IdeAolog (8x 3)= log (x+3) + log 9Rewrite the given equation without logarithms Do not solve for x
IdeAo log (8x 3)= log (x+3) + log 9 Rewrite the given equation without logarithms Do not solve for x...
2 answers
W13 Q9 HomeworkAnsweredFor plant 1,test the research hypothesis that the mean oxygen level is less than 5 ppm. Report the p-value: Hint: R command t.test() could be useful:Type your numeric answer and submit0.067609097You are incorrect
W13 Q9 Homework Answered For plant 1,test the research hypothesis that the mean oxygen level is less than 5 ppm. Report the p-value: Hint: R command t.test() could be useful: Type your numeric answer and submit 0.067609097 You are incorrect...
5 answers
3) How many milliliters of 4.00 M NaCl are required to prepare 1,500. mL of 140. mM NaCI?What will be the concentration of the diluted solution from problem #3 when expressed in molar and micromolar units?
3) How many milliliters of 4.00 M NaCl are required to prepare 1,500. mL of 140. mM NaCI? What will be the concentration of the diluted solution from problem #3 when expressed in molar and micromolar units?...
5 answers
Question 10 Homework UnansveredHow many moles ofNH; must be added to dissolve 0.010 mol of Agclin 100.0 mLH;o? Type your numeric answer and submit
Question 10 Homework Unansvered How many moles ofNH; must be added to dissolve 0.010 mol of Agclin 100.0 mLH;o? Type your numeric answer and submit...

-- 0.064006--