Compute the flux of the vector field F(x, y, z) = 3xj + 3yk through the surface S, where S is the part of the surface Z z = y + 4 above the rectangle 0 ≤ x ≤ 2, 0 ≤ y ≤ 4, oriented upward. flux =

Q: HOW TO DERIVE du Ət

A: To derive the given value

Q: Calculate (ri(t) r₂(t)] and [ri(t) x r₂(t)] first by differentiating the product directly and then…

A: In the three dimensional space, a vector A→ has three components, namely the x-component written as…

Q: 7. Show that (a). (Z, +) # (Q, +). (b). (Q,+)# (Q\{0},.). (c). (R\{0},-) # (Q\{0},.). (d). (R\{0},-)…

A:

Q: Verify the formula [[F.nds = [ div F dV in the Divergence Theorem by evaluating the surface integral…

A: The function given is as follows: Fx, y, z=2xi^-yzj^+z2k^ With σ being the paraboloid z=x2+y2 capped…

Q: 6. (a) Let T: L²[0, 2π] → L²[0, 2π] be given by 2п Tf(x) = S cos(xt) f(t) dt. Show that (i) T is…

A:

Q: Refer to the following vectors below. A = 3i6j+2k B = −8ż −4j – 10k C=2i 3j9k D = -9i3j - 7k 1.…

A: Since you have asked multiple questions here, we will solve the first question for you. To get the…

Q: A simplified version of input-output analysis of a national economy has the following input-output…

A: Let A be the given matrix A=0.2450.1020.0510.0990.2910.2790.4330.3720.011 Let X=AMH where H= 1 unit…

Q: Prove that the dual of 1 is not isometric to 1¹, but contains a proper subspace that is isometric to…

A:

Q: 3 6 Let y = [8] Write y as the sum of two orthogonal vectors, one in Span {u} and one orthogonal to…

A:

Q: The table contains data on the admission price (in dollars) for one-day tickets to 10 theme parks in…

A: Use the formula for Interquartile range.

Q: Find a coterminal angle between 0° and 360° or between 0 and 2π radians. 1) 780°

A:

Q: A company manufactures x units of Product A and y units of Product B, on two machines, I and II. It…

A:

Q: Compute the product of C(90°)B(180°)A(−90°) using the points A(6,2), B(1, 2) and C(6,-3). What are…

A: Given: The product of rotations, C90°B180°A-90° and the points A6,2, B1,2 and C6,-3.   To determine:…

Q: COMPLEX ANALYSIS Please answer all questions Let F be the branch of log z, which is analytic in the…

A:

Q: Find the Maclaurin series of and give the radius of convergence. 1 1 Using your answer, evaluate L…

A: The given function is z1-z To find : (a) Maclaurin series of given function and radius of converges.…

Q: In Exercises 1-4, apply the Jacobi method to the given system of linear equations, using the initial…

A:

Q: SOLVE FOR THE LAPLACE TRANSFORM OF THE GIVEN EQUATION. STOLPE sin 3t t 4. f(t) gettyimages

A:

Q: 3. 2x₁ - x₂ x2 2 x₁ = 3x₂ + x3 = -x₁ + x₂ - 3x3 5. Apply the Gauss-Seidel method to Exercise 1. 6.…

A:

Q: Verify the formula J.F., F.ndS= =JJJ₂ div div F dV G in the Divergence Theorem by evaluating the…

A:

Q: Accumulate P180,000 for 5 years at 13% compounded semi-annually. (Note: accumulating an amount means…

A: When the interest is compounded, then the formula used is A=P1+rnnt , where, A is the final amount,…

Q: . If f is one-to-one and continuous on [a, b], prove that f must be strictly monotonic on [a, b].

A:

Q: Consider the following optimization problem: It is desired to know the dimensions of a rectangular…

A: The volume of a rectangular box is calculated by multiplying its length, width and height. The…

Q: Find the root of the following using the method indicated. |a| < 0.0001 1. f(x) = sin x + e -2, xo =…

A: 1. Given that,fx=sinx+ex-2x0=2The root of the following function is solved by using the Fixed…

Q: Alea would like to buy a $150,000 home. She plans to pay 16% as a down payment and will take out a…

A: Alea wants to buy a $150,000 home. She plans to pay 16% as a down payment and will take out a 35…

Q: Find T(t) and N(t) at the given point. r(t) = 6 cos(t)i + 6 sin(t)j + tk; t T() 6 37 0, √3/31 X N()…

A:

Q: For items 6-10. Refer to the figure at the right. Given: m ll u 6. Which pair of angles are…

A: Use the given diagram.

Q: Let G(x) = [² w(t) dt. -2 Find a function, w, and a number, a, such that G(x) = 4x−² – 1. w(x) = a "

A: Evaluation of the integral

Q: Using Cramer's rule find the x, y and z 2x-y+3z=-3 3x+3y-z=10 -x-y+z=-4

A:

Q: 13. Find the mass of a thin funnel in the shape of a cone z = √√x² + y², 1 ≤ z ≤ 4, if its density…

A:

Q: Let be a function that allows continuous second partial derivatives, we know that: Vf(x,y) = (16x³ -…

A:

Q: Find all possible solutions of the equation cos z = = 2√15.

A:

Q: A²-6 + 11 = 0 1-3 2 5 and by the theorem you have A²-64 + 111₂ = 0 Demonstrate the Cayley-Hamilton…

A:

Q: Find a sequence that accurately counts the ancestors of a male honeybee.

A: Male bees are known to have only one parent, a female. Female bees are known to have two parents, a…

Q: f(x)=x(40-x)/(20+9cos(x)) Let the function and the set V=[10,15,20,25,30]. Consider the set W of…

A: Given, The function f(x) = x(40-x)(20+9cos(x)) and the set V = [10,15,20,25,30]. The set W of pairs…

Q: f(x) = e²x cos(x)

A:

Q: 5. Find the work done by F = (x² + y)i + (y² + x)j + ze²k over the following paths from (1, 0, 0) to…

A:

Q: Question 1 A periodic function ƒ(x)= f(x+27) is given by -7≤X<0 2 f(x)= 7-X 0≤x≤a 2 (a) Sketch f(x)…

A: Fourier series and even and odd function

Q: 2.f(t) = cosh wt sin wt

A:

Q: 2. - 4x₁ + 2x₂ = -6 3x₁ - 5x₂ = 1

A:

Q: 9. A coffee company wants to determine the daily production levels of its three different blends of…

A: To represent the portions of regular, medium and dark used in the blends I, II and III in decimals,

Q: Series solution of variable-coefficient ODE Consider the variable coefficient linear second order…

A:

Q: dy/dx=sin(x)+1 using euler method h=0.01 y(0)=1 y(1)=?

A: Euler's method uses the formula: yn+1=yn+hf(xn,yn) to perform the iterations and to approximate the…

Q: Use the formula k(t) S k(t) = ||r' (t) × r"(t)|| X ||r' (t)||³ r(t) = t²i+t¹5j to find k(t).

A:

Q: Use the function to find the image of v and the preimage of w. T(V₁ V₂ V3) = (V₂ - V₁ V₁ + V₂, 2v₁),…

A:

Q: 2. (a) Let X = C[0, 1]. Define T: X→ X by. Tf(x) = xf(x) Show that (i) T is bounded (ii) Find || T…

A: Given- Let X = C0, 1. Define T : X → X by Tfx = xfx.  To Show- Show that T is bounded. Find T.

Q: 10. Let (G, *) be a group, and let H≤ G. Define N(H) = {x € G: x¹ *H* x = H} [Normalizer of H in G].…

A:

Q: b) Calculate the inclined angle λ and orthogonal rake angle yo, when yx =10°, yy =8°, qs=15°.

A: Solution :-

Q: 2. Let G be a group and suppose a E G generates a cyclic subgroup of order 2 and is the unique such…

A:

Q: Use Green's Theorem to evaluate the line integral Scox (y - x) dx + (2x - y) dy for the given path.…

A: The given integral is                                    ∫Cy-xdx+(2x-y)dy for the given path.…

Q: 7. Polly purchased a car. She paid P150,000 as down payment and pays P5,500 at the end of each month…

A: