For the following problem, a point is rotating with uniform circular motion on a circle of radius r. Give your answer in exact form. Find ω if r = 12 cm and v = 4 cm/sec.

Q: Consider the following. x = sin(t),    y = csc(t),    0 < t < π/2 (a) Eliminate the…

A: x(t) = sin(t)y(t) =csc(t)

Q: Consider the following. tan2(0), y = sec(0), -n/2 < 0 < t/2 X = (a) Eliminate the parameter to find…

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Q: Suppose an object moves in an elliptical orbit parametrized byx = 4 cos t and y = 7 sin t, where t ≥…

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Q: Find the exact length of the curve (b) x = e' cos t, y= e' sint, 0<t<T

A: Length of the curve for parametric equation is given by:

Q: Find the moving trihedral of the curve 7(t) at the indicated value: 7(t) = cos? t î + sin? t ĵ + 1…

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Q: 3. Deduce from the orbit equation (1 + e)ro 1 + e cos 0 that a planet is closest to its sun when 0 =…

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Q: Find the speed at t = π/4 of a particle whose position at time tseconds is c(t) = (sin 4t, cos 3t)

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Q: Find the arc length of the curve given in parametric form by c(t) = (t^3, t^2) for 0 ≤ t ≤ 1.

A: Let f(t)=x(t), y(t) be a curve expressed in the parametric form on [a,b]. The  length of the curve…

Q: Q1:- Find T(t) and N(t) for the curve helix x = a cos t, y = a sint and z = ct, and then find B(t),…

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Q: Given the following parametric equations on the interval 0<1<3: x = f(1) : 3 2 2/2 y = g(1)= 5 Graph…

A: Given : x=f(t) =t33-t22y=g(t)=225t5-2

Q: Find the length of the given curve: r(t) = (-3t, -3 sint,-3 cos t) where-3 sts 5.

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Q: Consider the parametric equations x(t) = 1 + 3t2, y(t) = 4 + 21³, -1 <t <1. • What is the length of…

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Q: Find the equation of the tangent line to right branch of the hyperbola π π ㅠ x = sect, y = tant, st≤…

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Q: •x= 5+4 sin 0 and y = -3 + 2 cos 0

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Q: A curve is described parametrically by x(t)=1/(t+1), y(t) =1/(t-1). Find the equation of the line…

A: Consider the curve Find the equation of the line tangent to the curve at t=2

Q: See the circular helix with equation D(t)= (-15 cost,15 sin t,8t). 1. Look for the value of t such…

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Q: For problems 3 & 4 find the arc length function for the given vector function. 3. i (t) = (t² , 2r°,…

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Q: Find the length of the hypocycloid defined by the equations x = a cos° (0), y = a sin° (0), 0 < 0 <…

A: Here we have to find the length of the hypocycloid defined by the equation x=acos3(θ) , y=asin3(θ)

Q: b. -2åx + 3d, - åz 2. If E = -xả, + yåy V/m, find the work involved in moving a unit positive charge…

A: We can solve using given information and calculate the work done

Q: Find the length of the spiral c(t) = (t cos t, t sin t) for 0 <t < 2n to three decimal places. Hint:…

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Q: For each of the following problems, a point is rotating with uniform circular motion on acircle of…

A: Given: r = 6 cm, v = 3 cm/sec

Q: 6. Find the angle above the horizon of the airplane as seen by the observer. Problem 5. Two traffic…

A: Given:

Q: Find the speed of the cycloid c(t) = (4t −4 sin t, 4−4 cos t) at points where the tangent line is…

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Q: Find the length of the curve. r(t) : cos(8t) i + sin(8t)j + 8 In(cos(t)) k, 0 stS T/4

A: Solution is given as below:

Q: Consider the following parametric equation. x = 7(cos 0 + 0 sin 0) y = 7(sin 0 – 0 cos 0) 11 What is…

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Q: Find the exact length of the curve. 43. x = t sin t , y = t cos t , 0 ≤ t ≤ 1

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Q: r = 2 cos 0,0 <o <n. 2 L = S°. dr r2 + de de.

A: Use the formula given to find length of curve.

Q: Find the length of the curve 7(t) = (cos(4t), sin(4t), 5t) for – 8 <t< 1 Give your answer to two…

A: use the arc length formula for finding length.

Q: Find an equation of the plane tangent to the following surface at the given point. V3 A,1, sin (xyz)…

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Q: Find the length of the curve x=cos^2t, y=sin^2t, 0≤t≤Pi.

A: In this question,we find the arc length of the curve using x=cos^2(t),y=sin^2(t),0&lt;=t&lt;=pi Arc…

Q: Let C be the curve parameterized by Y: [0, b] R³, y(s) = (12 cos(s²), 12 sin(s), 9 s²). Find b>0…

A: The given problem is to find the value of b for which the given length of curve of the given…

Q: Consider the following. x = sinh(t), y = cosh(t) (a) Eliminate the parameter to find a Cartesian…

A: Solution: The objective is to eliminate the parameter to find a Cartesian equation of the curve

Q: Find an equation of the tangent to the curve at the point corresponding to the given value of the…

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Q: Find the length of the curve. r(t) = cos(4t) i + sin(4t)j + 4 In(cos(t)) k, 0 <t< t/4

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Q: For each of the following problems, a point is rotating with uniform circular motion on acircle of…

A: Angular speed, w=linear speed,v/Radius,r

Q: Find parametric equations for the tangent line at t=3 for the motion of a particle given by…

A: To work out the equation of the tangent in terms of t

Q: Find the exact length of the curve. y = In(cos(x)), TC 0 < x<.

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Q: Question 2 Express the curve by an equation in z and y given z(t) = cos(t) and y(t) = 3 sin(t). a)…

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Q: Question 10. Find the angle between the curve r(t) = (t, sint, cos t), and the curve y + z2 = 1, x =…

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Q: Consider the following. x = sin(t), y = csc(t), 0 <t< n/2 (a) Eliminate the parameter to find a…

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Q: Consider the following. x = sin(6t),  y = −cos(6t),  z = 24t;    (0, 1, 4?) (a) Find the equation…

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Q: Find the moving trihedral and the curvature at any point of R(t) = (t²,– cos 8t, sin 8t). -

A: Given is : R→(t)=t2,-cos(8t),sin(8t) In order to find the curvature use the formula . Formula for…

Q: Find the length of the following two-dimensional curve. r(t) = (5 cos t, 5 sin ), for 0sts

A: Recall: Length of the Parametric form :L=∫t=at=bx'(t)2+y'(t)2 dt

Q: Consider the following. X = sin y = = COS (a) Eliminate the parameter to find a Cartesian equation…

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Q: Find the length of the following​ three-dimensional curve. r(t)=cos t, sin t, 3t​, for 0≤t≤2

A: Given that rt =cost,sint,3t  for 0≤t≤2 find the length

Q: Find the length of the curve r(t) = (e* cos t, et sin t , et), – In 4 <t<0.

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Q: Which of the following equations shows the best way to solve the length of the arc of the parabola…

A: We know, Length L of curve over an interval,from x=a to x=b is given by: L=∫ab(1+(dydx)2dx…

Q: Consider the following. x = tan?(0), y = sec(e), -1/2 < e < n/2 (a) Eliminate the parameter to find…

A: x=tan2(θ) and y=sec(θ) knowing that tan2(θ)=(tan(θ))2=sin2θcos2θ and that…

Q: For each of the following problems, a point is rotating with uniform circular motion on acircle of…

A: Given : if r = 10 ft and the point rotates at 20 rpm.   v = 2 × π × r × RPM   v = 2 × 3.14 × 10 × 20…

Q: Find the length of the curve r(t) = (cos(3t), sin(3t), 4t) for -6 ≤ t ≤ 5 Give your answer to two…

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