Q.3 (a) Express j = 3yî + x²j – x²k in terms of cylindrical coordinates. %3D (b) Transform g = ½f from spherical polar coordinates to cartesian. %3D

Q: How to solve this equation y''' - 8y" + 4y' +48= 4x2+1 using Laplace Transformation.

A: Converting the equation in Laplace transform:…

Q: When 9-x-y (x²+ y² +z²)% dzdydx the t 2n n 3 to spherical coordinates becomes the form !! p…

A: Solve the triple integral.

Q: Find the general solution of the DE s

A: Given: - The differential equation is, dydx=2yx+x3y+xtanyx2 To find: - The general solution of the…

Q: 4–x2 Sở SY dy dx using polar Evaluate 2x-x2 Coordinates.

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Q: D Eolm the secend order diffefential equation using the parametric delinitien of y=asine X-a Cos e…

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Q: Q1) Evaluate the integral S S dy dx using polar coordinate

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Q: Solve for Y(s), the Laplace transform of the solution y(t) to the initial value problem below. y" -…

A:

Q: 4. Find the length of the curve having a parametric equation of x = a cos 3 6, y = a sin 2 0 from e…

A:

Q: 4. Find the length of the curve having a parametric equation of x = a cos 3 0, y = a sin 20 from 8 =…

A: We are asked to find the length of the curve whose parametric equations are as follows:…

Q: 5. Eliminate the parameter to find the equation of the ellips Sx(t) = 4 cos(t) + 1 ly(t) = 3 sin(t)…

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Q: 4. (i) Use the parametric equations of an ellipse, x = a cos (t) , y = b sin (t), 0 < t 2m, to find…

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Q: 3 Evaluate the integral cos(x² + y²)dydx by converting to polar coordinates 0 0

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Q: 2. Given that cos pv o v+B? 2B (a) Find the Fourier transform of x+b? (b) Use the result from (a) to…

A: Sol

Q: 9/Find Parametric equations for the Line that is tangent to the curve r(t) = eti + (Sint); + In…

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Q: 3 1 [fe dydx a) By using the change of order evaluate the integral 0 Jx /3 3 2 b) Use the polar…

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Q: find the Laplace transforms A preliminary in- of the functions in Problem. tegration by parts may be…

A:

Q: find the Laplace transforms A preliminary in- of the functions in Problem. tegration by parts may be…

A:

Q: 9/Find Parametric equations for the Line that is tangent to the curve r(t) = eti + (Sint)j + In…

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Q: Example 14. Use polar coordinates to evaluate the double integral 16-z2 dy dx (9 + x2 + y²)³/2 ° I

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Q: Q1) Evaluate the integral N 4-y2 dx dy using polar coordinate

A:

Q: 8. Find the positive constant a(> 0) so that the parametric x = at, y = -t? is a solution to y =…

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Q: 3. Consider the parametric equations x = 1+ cos(t), y = -2+ sin(t), 0S <2M. 3.1. Find an equation…

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Q: -K Owhich methodisused to make U CHA) =\+C 픈 TIX Sin a Solution to the Problem initial and boundary…

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Q: Q5. If y = C,e* + C2e²x Prove that: ỹ - 3y + 2y = 0 Help f(x) = +2 (a, cos+ b, sin) Fourier series…

A: (Q5) Now we will prove the differential equation.    To prove,  we will differentiate the y with…

Q: Given the IVP: y" - y'-6y = 60, y(0) = 0, y'(0) = 5. %3D Use the Laplace transform to find Y(s).…

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Q: -2 Find the projection of v = 1 onto the line l of R³ given by the parametric equation l = tủ, where…

A: We will find out the required projection.

Q: TY 7. Compute dy dx by converting to polar coordinates. V4-2 x2 + y2

A: 7. Given integral is ∫02∫-4-x20xyx2+y2dydx The objective is to solve the integral using polar…

Q: -7. х 3D sin?t, у— cos t yA

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Q: Solve for Y(s), the Laplace transform of the solution y(t) to the initial value problem below.…

A:

Q: *+ xx + x = 0 has a centre at the origin. %3D

A: Given: x.. +xx.+x3=0

Q: find the Laplace transforms A preliminary in- of the functions in Problem. tegration by parts may be…

A: Given:

Q: 1. Evaluate the integral: VI-x² (b) e-a²-y° dy dx (Hint: Use polar coordinates)

A: Given:

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

A:

Q: (d) Use the conditions Y(0) = Y(b) = 0 to determine the value of the constant k and show that the…

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Q: 8. Solve for the critical points of the parametric equations x = t3 – 1,y = t² +t %3D

A: The answer is found in step-2.

Q: of the functions in Problem. tegration by parts may be necessary. find the Laplace transforms A…

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Q: Given that x(t) = log (3t) and y(t) = t² + 3, which of the following gives a Cartesian form of the…

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Q: 1. Consider the graph of r(t) = 2t i+ tj +t° k Determine parametric equations of the tangent line to…

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Q: Solve for Y(s), the Laplace transform of the solution y(t) to the initial value problem below. y'' -…

A:

Q: Q2: a) Use the polar coordinate to find the integral (x+y') dxdy ! -y 1/16 1/2 b) By using the…

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Q: 3) Le-- y" + 3y - 4y = 20, Given the IVP: y(0) = 0, y(0) = -5. %3D %3D A) Use the Laplace transform…

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Q: Q#4: a) Evaluate f (x +2y)dx+ (y – 2x)dy along the ellipse C defined by x = 4 cos 0, y = 3 sin 0…

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Q: 7. Evaluate the integral I | sin(9.r² + 4y²)dA by hand, using an appropriate change of variables,…

A: The given question can be solved as shown in step2

Q: 11. C is the curve F(t) = (In (2 – t), V+3). Find parametric equations for the tangent line to C at…

A: According to question,Given Curve C,Ft = ln2-t, 1t-2, t+3

Q: The parametric equations x = 4 - 5 sin 3t and y = 3 + 5 cos 3t for  0 ≤ t ≤ π/2  represent a curve…

A:

Q: Q2: Find parametric equations of the line tangent to the graph of r(1) at the point where t= to.…

A:

Q: 1. Find parametrizations of the curve of intersection of x² + 4x + z² = 0 and x- – 2y + z = 3.

A: Given curve is x2 + 4x + z2 = 0 .  This can be written as (x+2)2 + z2  = 4  So the curve is a circle…

Q: V2 Evaluate x² dy dx by changing /4- to polar coordinates. Select one: O a. T A – а. л — 2 О. 2л — 6…

A: Given: ∫02 ∫-4-x2-x  x2  dy dx Evaluate the given integral by changing

Q: Solve for Y(s), the Laplace transform of the solution y(t) to the initial value problem below. y" -…

A: Given that y''-6y'+9y=cos 6t - sin 6ty0= 2; y'0 = 6 Using laplace and inverse laplace, solve the…

Cylindrical Coordinate System

The distance from a selected reference axis, the direction from the axis relative to a selected reference direction, and also the distance from a selected reference plane perpendicular to the axis area unit, all accustom outline purpose positions in a cylindrical reference frame. Counting that the aspect of the reference plane faces the purpose, the latter distance is expressed as a positive or negative variety.