3.1 A particle has a velocity of =cos ( 21)i +sin( 21)j. 3.1.1 Show that the objects' moves with a constant speed. 3.1.2 Find the acceleration of the particle at t = 0 s. 3.1.2 Describe the motion of this particle.

Q: Q 5: (a) Assume that after w months, butterflies' populace in 1000 is calculated as: f (w) = 12w…

A: Assume that after w months, butterflies populace in 1000 is calculated as                      f(w)…

Q: 2. a) Using Laplace transforms, solve the following first order ordinary differential equation - 2y…

A: Solution:-Step1:-   The given differential equation is                    y'-2y=e2t+sin 3t…

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A: Given differential equation is  md2xdt2-Bdxdt-kx=1    , m=1, B=1, k=6, x0=0, x'0=0⇒d2xdt2-dxdt-6x=1…

Q: 20.03 6. Use differentials (that is, linear approximation) to approximate: V3.9

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Q: Question3: Solve the differential equation using the Laplace transform y" + 3y' – 4y = cos(2t); y(0)…

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Q: Find L[e2t+2 + e-2t cos 3t + e2t t sin(2t)] A)+ 4s-8 s+2 s-2 ((s-2)2 +4)2 (s+2)2 +9 e2 B)- s+2 s-4…

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Q: Find L[e2t t sin(2t)+ e2t+1 + e²t cos 2t] 2s-4 s+2 A)+ A) s+2 * (s-1)² +4)² (s+2)² +4 45-4 S-2 B) +…

A: Given below an detailed solution

Q: 1. Find a linear differential operator (of lowest order) that annihilates the given function: flr) -…

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Q: 3. Given that 7 sin(5t)â + cos(5t)ŷ represents the position of a particle at time t, find î. and…

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Q: у" — 5у" + 7у' — Зу %3D 20 sin(t) , У (0) — у'(0) — 0, у"(0) %3D —2

A: Consider the provided question, We have the find the solution of the given D.E by using the Laplace…

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Q: Q1 (A): Find the deflection equation of simply supported beam which shown in figure by using the…

A: Given: B) The given ordinary differential equation is y''-y=sinhx+coshx

Q: 9. The velocity constant k of a given chemical reaction is given by: kt = [ ( 1 |(3–0,4x)(2–0.6x)…

A: Here I am attaching image so that you understand each and every step.

Q: 2. A particle of unit mass moves so that displacement after t seconds is given by x = 2 cos (t - 2).…

A: Given that a particle of unit mass moves so that displacement after t second is given by…

Q: Q 5: (a) Assume that after w months, butterflies' populace in 1000 is calculated as: f(w): = 12w +…

A: Assume that after w months, butterflies populace in 1000 is calculated as follows:…

Q: 11. An object moves along the x-axis so that at any time t 2 0, its velocity is given by v(t) = 4 –…

A: Given Data: The velocity of the object is: v(t)=4-3.8cos(0.7t) The time of observation of…

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A: We have to find the following conditions according to the given information

Q: The differential operator D2 +12D+ 40 has the form D -2aD+a? + B2 where a = - and B= 2 Therefore D2…

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Q: 11. An object moves along the x-axis so that at any time t2 0, its velocity is given by v(t) = 4 –…

A: Find your answer below

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Q: 7. A particle is moving along the x-axis with a velocity of v(t) = 8 cos (-). The particle is at x =…

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Q: 2. A particle moves along the x-axis so that at any time t > 0, its acceldration is a(t) t = 0, the…

A: Given,           at=32cos2t

Q: Solve the following differential equation by Laplace transforms. The function is subject to the…

A: Here we have to solve given differential equation using Laplace transform method.

Q: 2. f(t)=t cos 8t +2 3. f(t)=1** +a cosh /2t +bsinh 2t 4. -cos' (21)+e f(1) = %3D e 5. f(t)=-3t'e St…

A: Laplace Transformation: Given a function ft defined for all real t≥0, the Laplace transform of ft is…

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A: We solve the given ODE  (sec(y))2y'-3tan(y)=-1 ......(1)

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Q: Laplace Evaluate the following. Differential Equation 1. L{e* + cos 6t – est cos 6t} ,3t -

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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: 28. (a) Suppose that a body is dropped (vo = 0) from a dis- tance ro > R from the earth's center, so…

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A: Please check step 2 for the solution.!

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Q: Suppose the velocity of a particle at time t is given by 3/19 (t+1)2 + V+1 1 7(t) (tan(t). 1+12 1.…

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Q: 7. A particle is moving along the x-axis with a velocity of v(t) = 8 cos (). The particle is at x =…

A: The velocity of the particle is given by: v(t)=8 cost2

Q: 11) A particle moves along a line so that at time t its position is s(t) = -4 sin 5t, where s(t) is…

A: We will use second derivative test to find time at which maximum veolcity achieved

Q: (h) Starting from (19), show that a sin 8- ;(sin ) + =-j(j+1)Gsin? (0) (24) [4 Now, note that the…

A: Given-  To find- Starting from (19), show that Now, note that the angular differential equation in…

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Q: 5. Which of the equations given below is the auxiliary function (characteristic equation) of the…

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Q: 5. (4.9) A particle is moving with the given data. Find the position function of the particle:…

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Q: (a) L{t + sin 4t – e2t cosh rt} (b) L{e' + cos 4t U(t – 1/2)} - (c) L-!{ s + 1 (s +2)(s² + 2s + 5)…

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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: QUESTION 4 Given f(x) = 8x³ + 2x. Estimate the value of ƒ(2.01) using differential. %3D

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Q: 11. An object moves along the x-axis so that at any time t > 0, its velocity is given by v(t) = 4 –…

A: Given,               Velocity V (t) = 4 – 3.8 cos (0.7t)

Q: 1/10 1.A) e* cos(5x) dx integration by parts

A: Here we have to do integration by parts:   Apply integration by parts u as e3x and v = cos5x

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A: NOTE:- By Bartleby rules, only part (a) is answered A 1-kilogram mass is attached to a spring whose…

Q: 1. Solve the hyperbolic function of the following. i Prove that coshx – coshy = 2sinh (*) sinh ().…

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