Let S be the level surface g(x, y, z) = 4 where g(x, y, z) = x4 + y® + 32º. Let F be the vector field Vg ||V9||' F = and let G be the vector field G = Vg × (0,0,3). (a) Show that the flux of F through S is equal to the surface area of S (up to a sign). (b) Compute the flux of G through S. Hint: Your answers should not be long!

Q: Find the domain of definition of the function 3r Vx + 5 X - 5 y = log10 (,2. x² – 10x +24, -

A: Introduction :

Q: Using Laplace transform, solße y" +y = cos x, where y (0) = 0 =y'(0).

A: Use the following formulae, to obtain the solution. Ly=YsLy'=sYs-y0Ly''=s2Ys-sy0-y'0Lcosat=ss2+a2L-1...

Q: Use the portion of the curve r=3-3sin(theta) that’s in the first quadrant to answer parts a and b. a...

A: Use the following formulae, to obtain the solution. The arc length of the curve r=fθ, where θ1≤θ≤θ2...

Q: :Let p, q, r be three mutually lar vectors of the same If a vector x satisfies {b x (1 – x)} × b + {...

A:

Q: For questions 39-41 consider the following: 1 The Maclaurin series expansion for f(x)= is 1-x+x? -x°...

A: We will find out the required Maclaurian series.

Q: find the integrating factor (xy2-y)dx + (x2y-3x)dy = 0

A: find the integrating factor (xy2-y)dx + (x2y-3x)dy = 0

Q: Let (t) = t if 0<t<1 and (t + 1) = t. Compute: L{v}

A: We find the Laplace transform of given function by using this theorem: 

Q: Class category frequency Cf 80-84 3 40 75-79 3 37 70-74 4 34 65-69 30 60-64 25 55-59 19 50-54 10 45-...

A: The formula for standard deviation is S=∑f·x2-∑f·x2NN-1 Now, f is the frequency, x is the mid-point ...

Q: Given the table below generated by function f(x)=x². 6 | 7 | 8 49 64 2 3 4 | 5 10 100 9. f(x) 4 9 16...

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Q: (ii1) Let y(x) 2 Cnx" be a power series solution to y" + P(x)y'+ Po(x)y = 0 with initial conditions ...

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Q: ind the indefinite integral and check the result by differentiation. ' f (x) dx, where f (x) = (/T- ...

A: In the given question, concept of Indefinite Integral is applied. Indefinite Integral Indefinite int...

Q: Suppose A is the matrix for T: R3 → R³ relative to the standard basis. Find the diagonal matrix A' f...

A:

Q: Find the values of (eigenvalues) for which the given problem has a nontrivial solution. Also determi...

A: The given problem is to find the eigenvalues and eigenfunctions of given nontrivial problem, we can ...

Q: For questions 35-38 consider the following equation: x*= -kin(a+ bx*) Solve x using the Newton-Raphs...

A: According to newton raphson method  Suppose Solution of equation f(x) = 0  is needed where f(x) is  ...

Q: 7). Given functions F(x, y) = (x²y x³ – y + 4, ) and G(u, v) = (u² + v, v) compute the Jacobian deri...

A: Please find the answer in next step.

Q: 3. (x + 3y – 4)dx + (x + 4y - 5)dy = 0

A:

Q: (c) In the proof of Proposition 3, the following statement is not justified: "However, since x is no...

A:

Q: Question 1: If a, b and c are unit vectors, then la - b|2 + |b – c[² + |c – a|2 does not exceed A) 4...

A:

Q: For a function f, the Newton's interpolatory divided-difference formula gives the interpolating poly...

A: The general Newton's divided-difference interpolation polynomial can be defined as: Pnx=y0+(x-x0)f[x...

Q: 2.21 Solve Laplace's equation, v?u = 0 0 <x < T 0 < y < T subject to boundary conditions u(x,0) = si...

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Q: Let f E R[a, b] (which implies that f is bounded). 1. For any partition of a, b], show that U (2f, P...

A:

Q: Give an example of a non-zero vector field that is not irrotational and not incompressible.

A: We find an example of a non-zero vector field that is not irrotational and not incompressible. 

Q: find Parametric equatŁions Far the lihes 1 The line through (L11) Parallel tathe Z gris 2-The like t...

A: We solve for parametric equations.

Q: Consider solving the linear system 2x1 + x2 – x3 + 2x4 4.x1 + 5x2 – 3x3 + 6x4 -2x1+ 5x2 – 2x3 + 6x4 ...

A:

Q: If a, b e Z, then a? – 4b – 3 + 0 -

A:

Q: Suppose the price to sell some commodity is a linear function of output. If prices are 550691 R.O fo...

A: Given, the price to sell some commodity is a linear function of output. if prices are  650691 R.o fo...

Q: уах + %3D

A: In the given question, concept of Integrating factor is applied. Integrating Factor An integrating f...

Q: Let (t) = t if 0 <t<1 and (t+ 1) = t. Compute: L{}

A: Given that  ψt=t if 0≤t&lt;1 and ψt+1=t. i.e. ψt is a periodic function with period 1. Now, as we kn...

Q: f(t) = e2t cos 5t S- 2 (s – 2)² + 25 2s + 4 s(s² + 4) %3D Ans. f(t) = (sin t –- cos t)² %3D Ans.

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Q: (d) Show that Theorem 1 does not hold for n = 1 and n = 2. That is, show that the multiplicative gro...

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Q: {6} = I ( (b) T = [4,9) %3D (c) T = [-4,9] -

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Q: Find the projection matrix P that projects vectors in R onto W Let W be the subspace of R spanned by...

A: The inverse of a 2×2 matrix is calculated using the formula: a  b c  d -1=1deta  b c  d d  -b -c  a ...

Q: O Can Jefferson's method ever result in an Alabama paradox?

A: We have to state whether Jefferson's method ever result in an Alabama paradox.

Q: If the vectors ai + j+ k, i + bj + k and i +j+ ck (a # b ± c ± 1) are coplanar, then the value of [1...

A:

Q: Mark has a poultry farm. He is constructing 15 pens with each pen measuring 1 1/2 meters by 2 1/4 me...

A:

Q: Prove that if x is rational and x = 0, then 1/x is rational.

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Q: Find the maximum quantity of flow (in gallons) that could take place from A to H through the given n...

A: Given , A Weighted graph we have to maximize the quantity of flow in between A to H

Q: 1. Given: 1. Vector i= (1,1,1) (in standard basis) 2. The linear transform (in standard basis) T: R→...

A: Given :  1. Vector x⇀=1,1,1 (in standard basis) 2. The linear transform (in standard basis) T :ℝ3→ℝ3...

Q: The Northfork Feed Company makes a feed mix from four ingredients (x1 = pounds of oats, x2 D pounds ...

A: According to the given conditions, we will construct the constraints as inequalities in mathematical...

Q: 3. Let V = e" cos(qr), with p= r In(ryz), q = z cos(ry) and r = 2 tan-(y). Ae when r= y = 2 = 1. By ...

A:

Q: Vx ER (|x – 3| > 3 → x² > 6x)

A:

Q: y'= csc x + y cot x 2.

A:

Q: If 8000 dollars is invested in a bank account at an interest rate of 8 percent per year, Find the am...

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Q: K. 9. If f (x) = prove that f (xr) is an even function. %3D et -1 2

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Q: V3 1 2 V3 1 A = and Q = 1 %3D 2 PAPT then P (02005)PT equal to 1/2

A: Introduction :

Q: Assume the rate at which the zombies spread is jointly proportional to the number of encounters betw...

A: Please check next steps for the solution.!

Q: Activity 2.3 Complete the table below by finding the unknown. Nominal Interest Interest Compound Mat...

A:  

Q: Let G be a (p, q) graph. Prove that the sum of the degrees of the vertices of G equals twice the siz...

A: The given graph G=p, q, consists of two sets, p=VG, of vertices or nodes of G, and q, of 2-element s...

Q: O Drove that: ৭ २ - 5 2

A: Given: z is a complex number. To prove: tan-1z=i2lni+zi-z

Q: Indonesia's population in 2000 amounted to 211 million people, the growth rate is 4% per year. What ...

A: