2y )dx - (x +3 cos y)dy around the parallelogram havi - 6

Q: Plot along with its tangent r = -6ecos0 + 8 cos 40 in %3D 4

A: We knowx = rcosθy = rsinθGiven: r = -6ecosθ+8cos4θ                     Where θ∈0,2π     Hence, x =…

Q: Find the solutiTon of followina ordfnarg differentral equation -2x

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Q: Use Green's theorem to calculate §. -y² dx + xy dy where C is the vertex triangle (1,3), (4,0) and…

A: Consider the given integral. I=∮c-y2dx+xydy The green theorem is defined as, ∮cPdx+Qdy=∬R∂Q∂y−∂P∂x…

Q: . The eight curve x = (1/2) sin 2t, y = sin t, 0 stsa (one loop) y -1

A: Given, xt=12sin(2t)y(t)=sin(t) , 0≤t≤π    The area of R is given by A=12∫xdy-ydxNow on…

Q: Find a parametrization of the right branch (x > 0) of the hyperbola(x/a)2−*(y/b)2= 1 using cosh…

A: Given that. xa2-yb2=1     ...(1) Need to evaluate parametrize form of (1).

Q: 6) Find the equation of the osculating plane of the helix x = sin 3t, y = 2t, z = cos 3t at the…

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Q: 2. Find the coordinate of the points on the cardioid r=1- cose at which there is a horizontal…

A: We are given the polar curve: r = 1- cosθ use formula:         x=r cosθy=r sinθ then,  dxdθ=-sinθ+2…

Q: Q3// B Verify that dv3p'sin Ddpd@d owhen using spherical coordinate

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Q: A cantilever beam of length L is embedded at its left end. Find the deflection of the beam when w(x)…

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Q: Show that the cylindrical equationr 2(1 − 2 sin2 θ ) + z 2= 1is a hyperboloid of one sheet.

A: The cylindrical co-ordinates is converted into rectangular co-ordinate as x=rcosθ         ⋯⋯1y=rsinθ…

Q: Find parametric equations of the tangent line to the curve of intersectic paraboloid z = x² +y? and…

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Q: Transform (4, 7/3, ) from spherical into cylindrical form (here o is any angle).

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Q: 2. Find the equation of the plane tangent to the elliptic paraboloid z = point (1, 1,3). 2.a2 +y, at…

A: To find out the equation of the plane tangent to the elliptic paraboloid.

Q: A particle is moving in space with position function R(t) = (cos(4t), sin(4t),5 - 3t) %3D Find the…

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Q: Find the tangent plane to the equation 3y cos(4x – 2y) at the point (2,4,12) Z =

A: Z=3ycos(4x-2y)  Point= (2,4,12)

Q: Use spherical coordinates to find phi. Z=3sqrt(x^+y^2)

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Q: 8. Describe the motion of a particle with position (x, y): x = 3sin (t),y 4cos (t)

A: To describe the motion of a particle for below curve. x=3sint, y=4cost

Q: The value of cosh(3z+1)dz, where C is the line segment from z=1 C to z= 2i. O a. (-sinh(6i+1)+sinh…

A: We have to find the value of integral,  I = ∮Ccosh(3z+1)dz  ;  where C is the line segment from z=1…

Q: Q1/ plot x2-y2=z (Elliptic paraboloid) in 3D.

A: Topic:- plot in 3-D

Q: Consider the curve C parametrized byx = −1 + 6 sin t and y =(1/2)− 6 cos t for −π ≤ t ≤ 7π. What is…

A: First of all, consider the given parametrized equation of curve C. Rearrange the equations to write…

Q: Find the tangent plane to the equation z = 6y cos(4x – 2y) at the point (2,4,24) Z =

A: It is given that z=6ycos4x-2y and the point is 2,4,24. Recall the fact that if the equation of the…

Q: B.2. Express to its standard form, determine the center, radius ar 10. x² + y? + 10x – 14y + 58 = 0…

A: # We are entitled to solve one question at a time , please resubmit the other question if you wish…

Q: In spherical coordinates equation for the paraboloid z = 2- x - y is p(cos o- psin? $) = 2 Select…

A: We have to find out  spherical coordinate

Q: z = tan (VZn + Ze

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Q: Compute sin (z) dz over the counterclockwise circle (traversed once) with radius 7 centered at Zo =…

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Q: An equation for the tangent plane to the surface z + 3 = xy cos (2) at the point (3, 1, 0) is:

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Q: 4-22-y2 Compute y? Vx2 +y? + z² dz dx dy by converting to spherical 4-x2- coordinates.

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Q: Verify that dV = p² sin y dp de dp when using spherical coordinates. %3D

A: You have posted multiple questions. As per the instruction, we will be answering only the first…

Q: c. Based on the orientation of your rectangle would we integrate with respect to x or y? С.

A: Follow the procedure given below.

Q: x2-y는 군.Give the spherical coordingtes.

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Q: 5. Discuss the bifurcations of the system ŕ = r(µ – sin r), 0 = 1 as µ varies.

A: Given that: This system has no fixed points, but r can take on zero values where μ≤0. Where equality…

Q: Find an equation of the tangent(s) to the curve with paramnetric equations ¤ = 1+ VE, y = e" at the…

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Q: au +20 dy 10 www ax dy dy?

A:

Q: Describe the motion of a particle with posi- tion P(x, y) when x = 5 sin t, Y = 2 cost

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Q: 4. Find an equation for the tangent plane to the surface z = 3x + 5y + arctan in the point (0, 1,…

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Q: (a) Obtain the equation of the tangent plane and the condition for tangency to the conicoid Ar? +…

A: Conicoid given is- Ax2+By2+cz2=1 at the point (α,β,γ) We have to obtain the equation of the tangent…

Q: 13. Find the point on the curve 7(t) = (2 sin t, 2 cos t, t), 0<ts 7, where the tangent line is…

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Q: By about how much will ƒ(x, y, z) = ex cos yz change as the point P(x, y, z) moves from the origin a…

A: Given function is Firstly, we will find gradient f at (0,0,0) Now, we will find unit vector along…

Q: - I he symmetrie equidton of alne quation of alme Find the paramedic equation

A: Since you have asked multiple question, we will solve the first question for you. If you  want any…

Q: 6) Find the equation of the osculating plane of the helix x = sin 3t, y = 2t, at the point (-1,л,0).…

A: Given :x=sin3ty=2tz=cos3tpoint -1, π, 0

Q: What kind of conic section is given by the quadratic form ? -11x,? + 84x,x2 + 24x2? = 156 Transform…

A: Given quadratic form is-11x12+84x1x2+24x22=156The above conic is determined and transformed to…

Q: Use Green's Theorem to evaluate 5x*dx +xydy where C is the triangle with vertices (0,0), (1,0),…

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Q: What is the integrating foc tor of the equation %3B

A: Topic:- differential equations

Q: Show that the arclength of the graph of y = sin x on the interval [0, 27] is equal to the circum-…

A: The length of the smooth curve ζ : [ 0 , 2π] →ℝ2  is given by I(ξ) = ∫02π ξ'(t)  dt

Q: polar Co-ovdina 4x²= y²-44+8

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Q: Consider the given curve: R(f) = (2 cos f, 12f +3,-2 sin f) Reparametrize the curve using arclength…

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Q: The length of the path describe by the parametric equations, x=(1/3)t^3 and y=(1/2)t^2, where 0≤t≤1,…

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Q: The arc length of the curve r= cos 30 with 0<0 ST is I V-9(sin 30)² + (cos 30)² d0 0. I V(sin 30)² +…

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Q: TQand TR are secants from Point T to Cirlce A as shown below: s. If mQR = 70° and mSP 34°, what is…

A: Given: To explain the correct of the given statement as follows,