Discuss the difference between harmonic and conjugate harmonic function. Also find the analytic function ƒ(z) = u(r, 0) + iv(r, 0), such that v(r,0) = r³ cos30 + rcos0 +5.

Q: 3 Find the area of the region bounded by 2x = y²+1 and the y-axis using the horizontal strip.

A: 2x = 3y2+ 1 Consider a horizontal strip at a distance y from x-axis of thickness dy.

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Q: - Obtain a numerical solution of the differential equation = y - 2x in dx the rang 1.0(0.2) 2.0,…

A: To find the solution of the first order differential equation dydx=fx,y with the initial condition…

Q: t tantln(t² + 1) nts on C where the tangen

A: Given that C be x=t(t2+1)-12y=2t-2tan-1t-lnt2+1, t∈[-3,3] therefore, dxdt=1t2+1-122t2(t2+1)-32…

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Q: 17. (15pts) Let relation G be a subset of the cross product of the natural numbers with the natural…

A: Using the definition of Reflexive relation,symmetry relation, Transitive relation, Antisymmetry…

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Q: 1. A city averages 14cm monthly precipitation in July 10cm in January. Assume that the monthly…

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Q: A mass of 1.25 kg stretches a spring 0.08 m. The mass is in a medium that exerts a viscous…

A: Please see the type of inputs.

Q: A. Given the set of equations below, 17x+6y+4z+5t=17 8x+22y+2z+4t=20 6x+3y+17z+7t=11 3x+4y+7z+19t=22…

A: Converting the given system to Augmented matrix form we get: [1764517822242063177113471922] now we…

Q: Solve for x. X= (Round to the nearest hundredth.) 45 C B

A: Let us consider a right angle triangle  sinC=ABACcosC=BCACtanC=ABBC

Q: 6. A shopper observes that whenever the price of butter goes up, the price of cheese goes up also.…

A: Given : A shopper observe that , When the price of butter goes up, the price of cheese goes up also…

Q: 10. Determine whether the equation y = 2x2 − 3x + 4 is a function.

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Q: III. Consider the parabola C: 2 - 4 = -(x - 2)² on the xz-plane. 1. Find the center-radius form of…

A: Given: C:Z-4=-x-22 To find: Equation

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Q: If f & R[a, b], then f is not continuous on [a,b].

A: Given statement statement:-  If  f∉Ra, b, then  f is not continuous on a, b.

Q: ・ Rephrase the initial value problems as integral equations yzyte, yco) 21 2 * x²= t-2² (0)=0 1 2

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Q: a) yp (t c) yp (t) = A cos(2t) + B sin(2t) d) y(t) = A cos(t) + B sin(t) Q21) One of the following…

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Q: in fuzzy graph What is the fuzzy forests ? And give an examples

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Q: Problem 14. Determine if the statements are true or false. ? ? 1. If the set of vectors U spans a…

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Q: Let G be a finite group and H a subgroup of G of order n. If H is the only subgroup of G of order n,…

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Q: Use undetermined coefficients to find the particular solution to y'' + 3y' 10y = 3e²t Y(t) = ₁² +₂e…

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Q: Find the differential equation whose general equation is y = C₁x + c₂ex. A. (x-1)y" - xy' + y = 0 B.…

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Q: b.) √4-1²-² √3x²+3y² TEN nates. z dz dy dx from Cartesian coordinates to spherical coordi-

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Q: Calculate the direction of P1P2 and the midpoint of line segment P1P2- P 13, 4, 6) and P 2(6, 0, 1)…

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Q: 4. The boat is travelling at 18 knots on a heading of 234°. The current is 8 knots, flowing from a…

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Q: Solve the following Differential Equations with Laplace Transforms y" - 6y + 15y = 2 sin (3t), y (0)…

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Q: in fuzzy graph

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Q: Verify that the indicated function y = (x) is an explicit solution of the given first-order…

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Q: 15. What is the sum of the 11th row of Pascal's triangle? a. 2048 b. 1024 C. 976 d. 2056

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Q: Determine the directional derivative of X²Yz +4XZ² at the point P(1,-2,1) in direction a=2û - j +² R…

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Q: 4. Consider the additive group Z. Z Prove that nZ Zn for any neZ+.

A: We know that a group G is said to a cyclic group if there exists an element x of the group G such…

Q: [s]y(x) = g₂e²k + g₂e² Q11) L(y") = a) s Ly(x)) + sy(0) - y'(0) s) s (y(x))-sy(0)-y'(0) b) s (y(x))+…

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Q: (a) Define a metric space (X, p). (b) Let p: R+ → R+ be a function defined by ln (2). Prove that p…

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Q: Show that the function Lan f(x) = x³ +e³x has exactly one real root. First of all, by the…

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Q: ¹t-In(t² + 1) te [-3

A: Given that C be x=t(t2+1)-12y=2t-2tan-1t-lnt2+1, t∈[-3,3] therefore, dxdt=1t2+1-122t2(t2+1)-32…

Q: The Denham Motel in Leduc has 90 rooms. If $300 per room is charged the owner will rent 40 rooms per…

A: Given that The Denham Motel in Leduc has 90 rooms. If $300 per room is charged the owner will rent…

Q: Q11) The general solution of y" - 4y' +9y = 0, is: a) y(t) = c₂e2t cos(5 t) + c₂e2t sin (5 t)…

A: Solution :-

Q: Let k> 0. SET UP an iterated double integral that will give the volume of the solid formed in the…

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Q: Evaluate f(x) = sin(√) from to using 6-segment Simpson's rule. Round off all computed values to…

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Q: A. Given the set of equations below, 17x+6y+4z+5t=17 8x+22y+2z+4t=20 6x+3y+17z+7t=11 3x+4y+7z+19t=22…

A: Since you have posted a multiple question according to guildlines I will solve first (Q1)question…

Q: The Ferris Wheel Al and Betty have gone to the amusement park to ride on a Ferris wheel. The wheel…

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Q: Let E be the region bounded below by the cone z 7- (2²+ y²) and above by the sphere 2² = 10²-2² -…

A: Given- Let E be the region bounded below by the cone z = -7·x2 + y2 and above by the sphere z2 = 102…

Q: Let f(u, v) = (u - v, 1,u + v) and g(x, y, z) = xyz. Find the entry a12(i.e. the entry in the first…

A: As per our guidelines we are answer submit of only first three sub parts question of multiple sub…

Q: 7. Which word best describes the solution to this system of equations? (x, y, z)=(4,-2,3)+ s(5,-3,2)…

A: Consistent

Q: Q3) For the following function: 1 U= zlog(x² + y²) 1. Determine whether it is harmonic (satisfy…

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