The path r(t)= (t- sin t) i + (1- cos t) j describes motion on the cycloid x =t- sin t, y =1- cos t. Find the particle's velocity and acceleration vectors at t = and sketch them as vectors on the curve. The velocity vector at t = is (O i+ j. %3D 2 (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)

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A: Given:

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

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Q: Find a Cartesian equation of the curves. 1) r= 2 sin 0 2) r = 5 csc e

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A: The solution is given below :

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A: we are given the curve r(t)=3ti+e4tj+6e-tk we have to find the velocity vector , acceleration vector…

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Q: Let z x = 2 cos u, and y 3 sin v. Find dz in terms of u and v. %3D Provide your answer below:

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Q: Q1: Find the length of the cardioid r= 1 + cos 0 0 < 0 <T

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Q: -8. AB is tangent to to OC at point B. E 6. MZCDA - 8. MZDBA = 32

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

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Q: Q3) the position vector of a point is given by: R(t) = cos³t i+ sin³ t j, Find: 1. Coordinates of…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: Find the length of the curve: r = /1+ cos(20),0ses 2n

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Q: Q3- i) Prove that cos-u dx 1 du V1-u? dx ii) Find the angle of inclination of the line y + 2x-4 = 0.

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A: Given that integrate counterclockwise  ∮Cz2z2-9dz by Cauchy's formula where  C : |z-3-3i|=32π.…

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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.