Consider the following. x2 + 2 sqaureroot of 3  xy − y2 + 8 = 0 (b) Use a rotation of axes to eliminate the xy-term. (Write an equation in XY-coordinates. Use a rotation angle that satisfies 0 ≤ ϕ ≤ π/2.)

Q: Q2) Verify v(x.y)-3x3y-y3+5x is harmonic in the entire complex plane then find the conjucte harmonic…

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Q: The second derivation of y = cos(2x)

A: Given  y = cos(2x)   ........ (1) We know that  d (cosx)dx= -sinx        ........ (a) and  d sinxdx…

Q: If x=sin@,y=0 ,y=cosp0,Prove that (1-x²)y,-xy,+p°y=0

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Q: Suppose z = f(x, y) = (x² + 3) sin(y) + xy² . By setting one variable equal to a constant (either x…

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Q: show that r = cos 2θ is symmetrical with respect to the horizontal axis.

A: show that r = cos 2θ is symmetrical with respect to the horizontal axis.

Q: The Imaginary part of the complex function f(z) is, v(x, y) = x³ – 3x²y + 2x + 1 + y³ – 3xy² Prove…

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Q: 9. Is AP' Q' R'a 270° rotation of APQR about the origin? Explain. Ay 6 R R' -6 -4 -2 2. 6.

A: Find the coordinates from the graph

Q: Is w = zī harmonic ? if so find its conjugate.

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Q: Prove that a rotation of θ, where cot 2θ = (a − c)/b, will eliminate the xy-term from the…

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Q: TE: Enter the exact answers in terms of i,j and k. Same direction as – 3i + 5j. u = Oppositely…

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Q: The classification of Laplace equation is O A. Parabolic B. Elliptic C. Hyperbolic D. Noneof these

A: To determine: The classification of Laplace equation is: a) Parabolic b) Elliptic c) Hyperbolic d)…

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A: we have to find parametrization of circle.

Q: Perform a rotation of axes to eliminate the xy-term. (Use x2 and y2 for the rotated co 3x² - 2√3xy +…

A: Given problem:- Perform a rotation of axes to eliminate the xy-term. (Use x2 and y2 for the rotated…

Q: Find all angles between 0 and 2T satisfying the condition COS X = 2 Separate your answers with…

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Q: 3.2 Given that A ABC lies on the horizontal plane and that, CB = b, ABD=a,CBD= B and BCD= 0 as shown…

A: Solution 3.2.1 In right angled triangle ∆BAD ADBD=hBD=sinα⇒h=BDsinα              … (1) In triangle…

Q: 2. a) Write a rotation R by an angle (counterclockwise) with the centre at the point (34, 1) in…

A: Answer:

Q: Find T, N, and k for the plane curve r(t) = - 7t i-7 In (cos t) j, -

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Q: Determine the appropriate rotation formulas to use so that the new equation contains no xy-term.

A: If x and y axis are rotated  through an angle θ , the coordinates (x, y) of a point P relative to…

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Q: Prove that the curve y:(-,) → R³ is regular with factor H and determine whether the image y (t) = (2…

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Q: b)A hanging chain has the b)F Shape y=3C0sh(3x), o 4X sIn2 calkulate the lengnt of the chain.

A: Length of chain is the same as length of curve

Q: Show that u(x, y) is harmonic in some domain and find a harmonic conjugate v(x, y) (7 Marks) When:…

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Q: In math land, there is a clock. The hour hand of this clock is 1 ft long. However, the clock is…

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Q: 3. Find the angle or rotation and new equation of curve 9x2 + 24xy + 16y2 + 90x – 130y = O such that…

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Q: QUESTION 5 Evaluate F dr, where F(x,y)=[2y-3cos(x)]i + [4x +6sin(y)]j and C goes counterclockwise…

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Q: Determine the equation of the directrix of r-. 26.4 4+4.4 cos e * x = -6 Oy- 6 X= 6

A: Find the directrix

Q: 4. Check whether u(x, y) = y³ – 3x²y is harmonic or not. If u(x, y) is harmonic, then find its…

A: Given u(x,y)=y3-3x2y

Q: Show that r = cos20 is symmetric about the y-axis.

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: The equation for the sinusoidal graph below is: f(x) = 4sin(2x) 3sion (2) 1 f(x) = 3sin f(x)=2sin…

A: Given is a sinusoidal graph.   To Choose: The correct equation for the sinusoidal graph

Q: Show that r = cos(2theta) is symmetric about the y-axis.

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Q: Find the general soultion of the follwoing equations dy cos x + y = cos²x, 15

A: According to our guidelines, In case of multiple questions we are supposed to answer the first…

Q: Determine whether the space curve given by r(t) = (sin(t), cos(), 8t) intersects the z-axis, and if…

A: Given curve , rt= < sin t , cos t2, 8t >The curve intersects z axis at the point where both…

Q: Find the set of points satisfying the equation in the complex variable z: |z|^2 +ℝ(z^2) = 4 where…

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Q: the Image tion of theT line 2x ty -1=0 under the rotation about wんat is equati the point (i,!) angle…

A: What is the image equation of the line 2x+y-1=0 under the rotation about the point (1,1) at an angle…

Q: Show that r = cos(2pi) is symmetric about the y-axis.

A: The solution of the problem is given in the next step.

Q: Identify the symmetries of the curves in. Then sketch the curves in the xy-plane. r = 1 + 2 sin θ

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Q: the solia generated Find the volumc af by revolving about the line X =3 the reg ion and y = x² + x…

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Q: 3. Find the length of the curve r = a (1 - cos 6) from 0 = 0° to 0 = n and also the total length of…

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Q: • Find a harmonic conjugate of u(r, y) = x² – 2x – y². Show that u(r, y) = e" cos y is harmonic.

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Q: Find the general solution to the hypergeometric ODE #(1 – 2)y" + (; - 2-) a - - 0. 3 ) y y = 0.

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Q: A weight suspended from a spring is pulled down a distance of 6 ft from its central position, then…

A: Given that a weight suspended from a spring is pulled down a distance of 6 ft from its central…

Q: (a) Suppose u(x, y) = 2x – x + 3xy? is harmonic, then find its conjugate harmonic v(x, y). -

A: The harmonic conjugate to a given function  is a function  such that is complex differentiable…

Q: Let f1 be reflection with respect to the y-axis and let f2 be counterclockwise rotation through π/2…

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Q: y = sin 0–. +2 4

A: To find the transformed graph.

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Q: Sketch the function of time z(t) = cos(t) eiwt in the complex plane, with w = +π .....

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Q: (a) Suppose u(x, y) = y³ – 3.x²y is harmonic, then find its conjugate harmonic v(x, y). %3D

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Q: Suppose z = f(x, y) = (x² + 4) sin(y) + xy². By setting one variable equal to a constant x = c, y =…

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