1. If r = xi + yj + zk and r = |r|, show that (i) div 0, %3D (ii) div (grad ") = n (n + 1) r" - 2 (АMIЕТЕ, Jne 2010) (iii) div (r 4) = 30 + r grad %3D

Q: The revenue per month earned by the Couture clothing chain at timetisR(t) =N(t)S(t),whereN(t) is the…

A: Given query is to find the rate of change of average revenue per store per month.

Q: 35 Find the extrem poinbs of Pcxy)=xy Subject to X+y=20.

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Q: 2 al S ex+y dydx

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Q: In a test of Ho:p=0.4 against H: p 0.4, a sample of sizc 100 produces Z 31•28 for the value of the…

A: Hey there! Thank you for posting the question. Since there are multiple questions posted, we will…

Q: |(7) In general, SUT S (SUT)', but (SU T)' S°UT. Pra

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Q: .'( , "ג oa3 (125x*y)" 学 A: 125 2 3 $%% 1/3 5メ Y C: D: VONE OF THESE

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: Find the values of x,y and z using Gauss Jordan method.

A: We have given a system of equations ,  3x + 4y + z = 102x - 3y + 5z + 9 = 0x + 2y - z = 6 This…

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A: "Since you have posted a question with multiple subparts, we will solve first 3 sub-parts for you.…

Q: 22. Solve 0 0, x > 0, Urr + Uyy = 0, u (x, 0) = f (x), u (x, 1) = 0, u (0, y) = 0, и (х, у). O…

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Q: 3. Find an orthonormal pair one of whose members is proportional to (4, -3).

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Q: Solve the FO pooblems1olouing itial-value = cosx- simtys dy |3| being us FOboth-oodes (4) Rusnga-…

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Q: 15. Solve Orx + Pyy 0, -a < x < a, 0 < y < ∞, 8o, 0 < |x| < a, Oy (x, 0) = 0, || а. $ (x, y) → 0…

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Q: /9 – 2° dz Integrate: z4

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Q: a²z If z = In(x² + y²)., find ax2 ay?

A: Here we have;  z=ln(x2+y2) ...................(1) partial derivative with respect to x

Q: Subject to: 2x +y 28 ,x and y 20 4x +y2 12 2x + 3y 2 12 inet is the velue of y in oraer to minimize…

A: Given query is to find tha value of y to minimise the C.

Q: 1. re (x, y, z) x). Ly). (z}} - *(*. y, z) . (x)S(x), ly), (z]} (x)E (x, y, z}

A: If x is element then it belong to set And {x} it will be subset of set

Q: 2) Eliminate the arbitrary enstant, 4 y= x*+ Cix + Cz e-X

A: Given problem:- Eliminate the arbitrary constants. of y= x² + C₁x + C₂ e-x

Q: show that Ф (x, y, z) = аф PDE : агф дуг + дуг I х2 +у2 +Z2 024 072 satisfies the

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Q: (3) A study on optimizing revenue from a website considered dividing cus- tomers into two groups…

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Q: (2x+4) + 1 x² +2x- 10 dx = x² (x² + 4x +5) (2x +4) +1) dx- x² + 4x+5, Consider dx evaluate | x² + 4x…

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Q: In the manufacturing of a chemical adhesive, 3% of all batches have raw materials from two different…

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Q: 1. Compute for de terminant using pivotal etemente method. -3 D= 4. -6 -3 9. 5

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Q: (a) Consider the ARMA(2,1) process {Xt}, 0.45 X 1–0.05.X, 2 + € – 0.2q-1 where

A: a) Given ARMA(2, 2) process is,…

Q: If q x2 yz3 %3D =, the small increment in q with &r=8y=8z=±0.1 can be approximately calculated by…

A: We will use partial derivatives to calculate the required quantity.

Q: 1 Find the Nahee af the falloding in togreals's Jet X+1 3. 8. +3. -4+3 da -2 2 JX -9. 2. Lett-lx 9.…

A: You don't mention which question i have to solve. And you already solved them. I go through all the…

Q: In the manufacturing of a chemical adhesive, 3% of all batches have raw materials from two different…

A: The events A and B are defined as follows: A : A batch is formed from two different lots B : A lot…

Q: 2. Determine Var(Y) when Y 3X1 +2X2 with Var(X1) 1, Var(X2) 5, Cov(X, X2) 2, E X1} 3, аnd E{X} 4.

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Q: (4) Evaluate : + yz') dV if Q= {(x, y,z): x:[-1, 1], y:[3, 4], z:[0, 2]}

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Q: 2. Integrate: S w5 V7+ w3 dw 3. Find S (6-+ - sV) de

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Q: If Saz dy = In|ly +1- Inly +2| + c, then S- %3D y2+3y+2 dt = e2t +3et+2 In(e' + 1) + In(e + 2) + c…

A: The objective is to find the correct option

Q: 11. Prove the absorption law x +xy=x using the other laws in Table 5.

A: To prove: x+xy=x We use the following identities (1) x=x·1 (2) 1+x=1 (3) xy+z=xy+xz    ( This is…

Q: 6. The total revenue, in dollars, from the sale of z units of a product is given by R(z) ==…

A: The graph of y = g (x) is concave upward on those intervals where  g"(x) &gt; 0. The graph of y = g…

Q: 2): Consider the DE y" – y" – 6y = 0 -

A: Follow the procedure given below.

Q: S x2 +2x-10 (2x+4) + 1 JE + 4x +5) Consider dx = x² (x² + 4x + 5) (2x+4) + 1 dx- x² + 4x +5 dx ,…

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Q: 4. For a fully discrete whole life insurance of 10,000 on (45): (i) Beth net and gross premiums are…

A: I proceeded to get 78.5221 for the gross premium

Q: 10 Consider A :3D and y:= Find all re R that minimize || Ar - y|l2.

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Q: Find y' if exy = e 4x -esy-

A: NOTE: Refresh your page if you can't see any equations. .

Q: 15. If mOT = (27x + 3)', mRT = (9x - 5)° and MZRST = (10x – 2)°, find mRT. %3D %3D R S.

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Q: 3) yv1+x²dx + x/1+y?dy = 0 (1+v1+x²)(1+/1+y²) Ans: V1+ x² +/1+ y² In +c (Bali, 2007) xy

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Q: Find the antiderivative of: dt/(1-7t)^3 where  u = 1-7t

A: To find antiderivative

Q: 8. Theorem h° = %3D

A: The figure given below represents the circle. From the angle subtended by the same arc theorem, The…

Q: 7) [[3embch5y] dvl [jel*5) dy] „In[sec h 5y]

A: Using rule of logarithm &amp; integration formula of sech(x)

Q: 12 Sf x² ydxdy 01 In2 2 11₂ SS 2xe dxdy 0-1 3 1 2xy SS- -dxdy 10x+1 4√x 2 S S x²y dydx 00 11-y S S…

A: Note:As per our guidelines we are supposed to answer only one question if there are multiple…

Q: Find y' if y= In coshv tanh v. y =sech v-2tanh v O None of the above O Option 4 y=tanh'y y'=tanhv –…

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Q: In the manufacturing of a chemical adhesive, 3% of all batches have raw materials from two different…

A: Given data in the manufacturing of a chemical adhesive 3% of all batches have raw materials from two…

Q: Suppose that the true model is () E+ and that it satishes MR1-MR6, but you estimate by OLS (II) W=…

A: From the given information, I yi=γxi+ei The OLS estimator of γ is, γ^=∑i=1Nxiyi∑i=1Nxi2 II…

Q: 1 Detemine una segunda solución en: 9y"- 9y = 0 ; y;=e .Considere C;=-2; C,=0

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.