A particle is moving with the given data. Find the position of the particle. cos(t)sin(t), s(0) 1, a(t) v(0) 3 s(t) X

Q: A particle is moving with the given data. Find theposition of the particle.  v (t ) = sin t - cos t…

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Q: Q.5/ A) Find dx for the following equation y = In(x2 + 4) – x tan-() %3D

A: Given equation is y=lnx2+4−xtan−1x2 We have to find dydx. Used Formula:- ddxlnx=1x ddxtan−1x=11+x2…

Q: r(t) =(sin 3t, cos 31, V7t), 1. Let a) Find T(t) and N(t)

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Q: Find the coordinates at t = 0, π/4 , π of a particle moving along the path c(t) = (cos 2t,sin2 t).

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Q: Find the position function of a particle given the following information: a (t) = 3 cos(t) – 2…

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Q: N(t) at the given point. cos(t)i+ 6 sin(t)j+ tk; t = 2

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Q: Eliminate the parameter t in the following. x = cos 2t, y = sin t

A: Given that x = cos 2t; y = sin t To eliminate: the variable t Needed formulae: cos 2t = cos2t -…

Q: Suppose the position function of a particle is given r(t) = (√3 cos (t), t-4, √3 sin(t)). If the…

A: Given : r(t)=3cos(t), t-4, 3sin(t) is the position function of a particle. To find : If the particle…

Q: The equation C = | 0.40 cos 1.20d0 and S= -0.40 sin1.20d0 are involved in the %3D %3D e study of…

A: Use the following formula: ∫θ1θ2eaθcosbθdθ=1a2+b2eaθ(acosbθ+bsinbθ)θ1θ2   Consider the equation for…

Q: Given the acceleration, initial velocity, and initial position of a body moving along a coordinate…

A: We have given Acceleration a = 18 cos 4t Initial velocity v(0) = -7 Initial position s(0) = -13

Q: find the speed at the given value of t. r(t) = (sin 3t, cos 4t, cos 5t), t =

A: Given: rt=sin3t, cos4t, cos5t To find the speed at the given value of t=π2. Solution: Speed is the…

Q: A heat-seeking particle has the property that at any point (x, y) in the plane it moves in the…

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Q: Given x2 + 11x + 30 dx 1 + cos?(x) At what value of t does the local max of f(t) occur? f(t) :

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Q: Find the velocity, acceleration, and speed of a particle with the given position function. r(t) = (4…

A: Given position function isrt=4 cos t , 6t , 4 sin tWe have to find velocity , speed &…

Q: Describe the motion of a particle with position (x, y) as t varies in the given interval. x = 4 + 3…

A: The solution is given below :

Q: Find the z-values of cos i = e²

A: Given

Q: 8. Find the length of the given curve over the indicated interval. r(t)= (r', 3 cos(t), 3t) [] 0, 2

A: Given r¯(t)=t2,3cost,3t in the interval [0,π2]

Q: x = e' sint,y = e² cos t at t = 0

A: We need to find radius of curvature.

Q: a. The velocity of a car in meters per seconds travelled from its origin is given by v(t) = In (t2 +…

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Q: x = a(0 – sin 0), y = a(1 – cos 0). %3D %3D urve followed by the particle as a function of 0.

A: The given parametric equations are, x=a(θ-sinθ)...............(1) y=a(1-cosθ) .............(2)

Q: A yoyo bounces up and down in the vertical direction with its acceleration after tt seconds given by…

A: d^2y/dt^2 = a(t)

Q: - A particle is moving along the x-axis with a velocity of v(t) 8 cos ( x=2 when t=0. Find the…

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Q: The acceleration ā of a particle at any time t is given by à = e-2 î + 3t ĵ+cos t k , then the…

A: The acceleration of a particle is given by a→=e-2t i^ + 3t j^ +cost k^  v(t) = ∫a(t) dt = ∫(e-2t i^…

Q: Suppose A(t) = [ e^t 0 0 0 cos t sin t 0 −sin t cos t]…

A: Given: At=et000cos tsin t0-sin tcos t To Find: To show that At-1 exists and then to find it.

Q: T For y 10 cos ( 10x 4 - its amplitude is its period is its phase shift is

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Q: Eliminate the parameter t from the following. S x(t) = sin t - 5 Ly(t) cos t + 2

A: Given

Q: Given x = sin3t, y = -cos3t, then find at t =. %3D dx а. 1 b. 3 с. О d. 2

A: We need to find dy/dx.

Q: Describe the motion of a particle with position (x, y) as t varies in the given interval. x = 3…

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Q: Find the velocity, acceleration, and speed of a particle with the given position function. r(t) = (5…

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Q: T=V3 + cos 0 is given by:

A: Trrr

Q: Describe the motion of a particle with position (x, y) as t varies in the given interval. x = 3…

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Q: A particle moves along the x-axis with velocity given by v(t) = 8 cos (4t) for time t > 0. If the…

A: Given, A particle moves along x-axis with velocity v(t)=8cos(4t), t≥0. Particle at position x=-6 at…

Q: dx = x[4 + 3xsin(ay)cos(ay)] dy

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Q: The general solution of the DE dx = cos?y is A y= sec?x В y=tanx + C y=tan-1(x) + c y= cos os-(x) +…

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Q: A particle moves according to the position function s (t) = e2t sin (3t). %3D

A: Definition used -                        v(t)= dsdt                       a(t)=dvdt=d2sdt2…

Q: a) Find dy/dx and d²y/dx² at the given point without eliminating the parameter x= 0+ cos 0, y=1+ sin…

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Q: Question 9

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Q: Eliminate the parameter t from the following. S¤(t) = sin t – 4 ly(t) = cos t – 2

A: Separate sin and cos one side then square and add

Q: A. Bernoulli 's Equation e-2x 3 1. yl =y- xy°c %3D | 2. ( 3 tan X 2 cos y) sto xdx t tan xsin ydy -…

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Q: f(8,t) = cos os(0e*) + cos( + e*) = COS + cos (s+

A: Find partial derivative.

Q: A particle moves along a circular path in such a way that its x- and y-coordinates at time t are x =…

A: Given Data: The coordinates of the circular path at time t is: x, y=2cost, 2sint The speed of the…

Q: The solution of the following Bernoulli's equation xy' + 2y = x¹(cos x) y² is

A: The correct answer is not given in options.The solution with the correct answer is given as

Q: e* cos e* dx J 4 + sin²e* A 1 tan-1 2 sin e* + C sin? e* + C 2 2 tan-1 B sin e* tan- 2 1 tan-1 2…

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Q: A particle is moving with the given data. Find theposition of the particle.  v (t ) = 10 sin t +3…

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Q: 3. A particle moving in a straight line has acceleration, a(t) = 10 sin t + 3 cos t, with initial…

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Q: Find the distance traveled by a particle with position (х, у); Cos t, y = (cos t)², 0 < t < 4TT X =

A: To solve this we have to use two point distance formula

Q: 7π| A d) S_T/A (sin x + cos x) dx

A: We will evaluate the given integral in the following step.

Q: 2. The speed of a particle at an arbitrary time t is given by || V(4t - 1) +sin? rt. Then V.d at t =…

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Q: Find the solution to the following Bernoulli's equations. 1. y3 sec x dx - y tan x dx = dy

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Q: Find the general solution to the following equations: dy 2+ tan y dx

A: The given is the differential equation which can be solved as shown in step 2.