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

Q: siny dy 2. 3 |- cosy

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Q: V2x-x² Write the integral 2 dz dy dx in cylindrical coordinates. DO NOT EVALUATE THE INTEGRAL!

A: We know that, the cylindrical coordinates in terms of the cartesian coordinates is given by,…

Q: (х+ siny)dx+ (хcosy— 2y)dy 3D0

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Q: 2-) Calcu late +he folloming integ rols by using the integration met hods a)| (hx" +8x²+ 15x) dx dx…

A: We are allow to solve one que at a time

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: 2. dx Ix Also, Prove that 22 %3D dxdj = dy dX

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Q: If flix.y)=XSin²(y)+y°Cos(x) prove that fn=2[Costy).Sin(y) ySin(x)]

A: First of all, we partially differentiate function f wrt. x and then we partially differentiate the…

Q: lim Y+ Y Cos y Yo 4 Siny cosy

A: Given limy→0y+ycosy4sinycosy

Q: et secydx + sinydy = 0

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Q: 1. S(2cos4y – 1)i - sin4ydy

A: As per our guidelines we are suppose to solve only first question if the multiple questions are…

Q: Find the center of mass and the moment of inertia about the​ y-axis for a thin rectangular plate cut…

A: Given that density = x + 2y + 4 and rectangular plate is bounded by the lines y =1 and x = 6

Q: 3. Find the area under one arch of the curve y = sin(2r).

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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: Evaluate the integral / (10x + 15y)dx + (18x – y)dy along the paraboli - arc y = x² from (0,0) to…

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Q: Evaluate the integrals

A: We’ll answer the 15th question since we answer only one question at a time. Please submit a new…

Q: Siny dy = Cas y (l-x Cosy) Cauy) %3D

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Q: determine the area of the curve r = v V3 cos e + sin 0 that is below the r-axis.

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Q: A particle moves along the x-axis with velocity dx/dt = ƒ(x). Show that the particle’s acceleration…

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Q: Calculate the double integral. 7x sin(x + y) da, R = [0, * [0, =]

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Q: sin³ y dy 2. S 1- siny

A: Solution Given   ∫sin3y1-sinydywe need to find the integral

Q: dy x(2 In x+1) 1. dx siny+y cos y

A: Since you have asked multiple question, as per our guidelines we are supposed to answer only one…

Q: Show that+ = 0, %3D ax dy? where f(x, y) = In(x² + y²) + tan¯'(²) %3D

A: The partial derivative of a two variable function fx,y with respect 'x' can be calculated by…

Q: Find the area of the surface generated by revolving the curve about the given axis. x = 6 cos(e), y…

A: Solution

Q: dy when t = 0: dx Find

A: dydx = ? at t=0.(a)Given equations - y = 2t-4-3               ..................(1)x = 3e-2t…

Q: Write the approximate change formula for a function z = ƒ(x, y) at the point (x, y) in terms of…

A: Consider the following function: z=fx,y

Q: I) Find the volume of the solid obtained by rotating the sine function between x -0 and x x about…

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Q: Sketch the motion of a particle with position as: x = 5 sint y = ²/-nstsn - St≤n as tvaries in the…

A: We need to plot the motion of the particle, whose position is defined as: x=5sint, y=t2 in the…

Q: Cos y dy 1-siny

A: The given integral is: I=∫cos2y1-sinydy   As we know that; The trigonometric identity: sin2x+cos2x=1…

Q: Find the Torsion along the curve: X = (t-sin t)ê +(1- cos t)ê, +tê,. %3D

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Q: Find equations for the a) tangent line and b) normal plane to the curve 1 x=t- cost, y = 3+ sin 2t,…

A: x=t-cost, y=3+sin2t, z=1+cos3t We know that rt=xt, yt, zt dxdt=1+sint, dydt=2cos2t, dzdt=-3sin3t At…

Q: sin y cos(cos y)dy

A: We have to evaluate the integral: ∫sin y coscos ydy In this case we will use substitution method. So…

Q: Find the arclength of r(1) - (cost Ar sin r)i+ (sint-t cost)j+3k for %3D

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Q: #2. Show that the line integral (sin y dx + (x cos y – sin y) dy)

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Q: integral y sinh y dy

A: Given:

Q: Compute the length of the curve where 0 ≤0 ≤ T. x = 2 cos² 0, y = 2 cos 0 sin 0,

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Q: Find the Moment of Inertia of the plate with respect to Y- axis and its Radius of Gyration. (Present…

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Q: Evaluate the integral / (4x + 12y)dx + (15x – y)dy along the parabolic arc y = x² from (0,0) to (1,…

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Q: (siny - ysinx) dx +(cosx +xcosy) dy =0

A: We will use the method of exact differential equations.

Q: Determine the speed (in meters per second) of a particle with a trajectory (2 sin (3t), 9 cos (3t)),…

A: Consider the given parametric equation of the trajectory of the particle, 2sin3t,9cos3t so we can…

Q: A Proton of mass (md is moving with un initial velecity (v) Collicling wwith ahelium atom of mass ()…

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Q: (a) If f(x.y) = e siny - e sinx then verify that fry fyz- %3D

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Q: Sketch the cardioid r = 3 cos 0 and find the coordinates of the points on the cardioid where the…

A: Given polar equation is r=3cosθ

Q: (sin y — y sin х)dx + (сosx + хcos y — у)dy %3D 0

A: Given differential equation is,  (siny-ysinx)dx +( cosx +xcosy -y)dy=0 comparing the given equation…

Q: A rod with density p(x)=4+sin(x) (in grams per cm) lies on the x-axis between x=0 and x=pi/3. Find…

A: Please see the explanation below

Q: dy +Hanx Siny = I Cos y die

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Q: Ssinx Losxdx X. a) vse u=coS X Esie to evalvale %3D b) Vre V=Sinx to e valvate %3D

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.