A bumblebee is flying so that its position is given by~r(t) = cos(2t), cos(3t),sin(5t) for the osculating circle at t = π/6, find either the equation, or a set of parametricequations describing this osculating circle.

Q: Find the length of one arc of the curve whose parametric equation are x=2θ-2sinθ and y=2-2cosθ.

A: We have to find length of arc whose parametric equations are : x=2θ-2sinθ and y=2-2cosθ Suppose 0 ≤…

Q: Identify the length of the arc having parametric equations x = t3 and y = 2t2 from t = -2 to t = 0

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Q: The parametric curve x= 414 + 412 + 1, y= 5t 3 – 5t has two tangent lines at the point (9, 0). Find…

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Q: Find the equation of the tangent plane to the following surface at the given point. 4y cos (3ar 2)…

A: Given equation of surface and point is

Q: Consider the curve parametrized by a = e-sin(0) and y = ecos(8) for 0 ≤ 0 < 2π. At what points (x,…

A: The parametrized curve x=e-sinθ and y=ecosθ for 0≤θ&lt;2π.

Q: The graph of the curve described by the parametric equations x = 2t2 and y =t³ – 3t has a point…

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Q: 2) Graph the x, y-curve described by the parametric equation by eliminating t from the equation. x =…

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Q: Suppose a curve is traced by the parametric equations x= 6.08 sin(t) and y = 22 -…

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Q: Find the equation of the tangent line of the parametric equations x = 2 – 3 cos 0, y = 3+2 sin 6 at…

A: Given that: x=2-3cosθ and y=3+2sinθ

Q: Eliminate the parameter to find the cartesian equation of the curve: x = 2 sin 0, y = cos² 0, sos…

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Q: Find the slope of the tangent line to polar curve r=9sinθ at the point (9/√2,π/4)

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Q: find parametric equation (cartesian) for tagent line to r=cos(2theta) at theta=2

A: The equation of the tangent line is

Q: The unit circle x² + y=1 can be wrriten in parametric form as x = cos(0) and y : = sino. dy and…

A: Follow the procedure given below

Q: Consider the parametric curve defined by x = 2020 cos t y = 2020 sin t π Find the slope of this…

A: Slope of a curve at some point is the value of the derivative at that point.

Q: Eliminate the parameter in the parametric equations x = 7+ sint, y = 2+ sint, for 0sts, and describe…

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Q: Find the slope of the tangent to the parametric curve c(t) = (cos t, sin t) at the point (-1/2,-V3).

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Q: Find parametric equations for the tangent line to the curve a-tcost, y-t, z- tsint at the

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Q: Sketch the parametric curve at R* whose parameterization is given by a (t) = (cos (t), sin (1), t),…

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Q: Find the equations of the lines tangent and normal to the curve given by the parametric equations…

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Q: Consider the curves:r = 4sin 0 and r = 2 sin(0) + 2cos (0).

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Q: Consider the following parametric equation. #20(cos 0+0 sin 0) y- 20(sin 0-0 cos 0) What is the…

A: Given: x=20cosθ+θsinθy=20sinθ-θcosθ we know length of curveL on interval a,b is given by…

Q: Which of the following is the equation of tangent line of the curve that is g by parametric…

A: We have been given the parametric equation  x=e2t, y=2cost+6sint at a point (1, 2).

Q: Without using a calculator, sketch the parametric equations by eliminating the parameter. Indicate…

A: The given parametric equation x=4+2cosθ and y=-1+sinθ

Q: of the points where the parametric equation y = 2 cost 0≤t≤ 2π will have vertical tangent. Determine…

A: Given is the parametric equation x=5sin2t , y=2cost   0≤t≤2π We have to find the point where the…

Q: The curve with parametric equationsx = (1 + 2 sin θ) cos θ, y = (1 + 2 sin θ) sin θis called a…

A: Equations of the curve in the given question is: Slope of tangent line is given by dy/dx, hence…

Q: Eliminate the parameter t from the parametric equationsx =3 +sin t and y = cos t - 2.

A: Given: x=3+sint and y=cost-2 We have to eliminate the parameter t from the parametric equations.…

Q: The curve with parametric equationsx = (1 + 2 sin θ) cos θ, y = (1 + 2 sin θ) sin θis called a…

A:

Q: 9. Show that the curve with parametric equations x = sin t and y = sin(t + sin t) for 0st s 2n has…

A: Given that the curve with parametric equations are x=sint,y=sint+sint. First find the slope that is…

Q: Find the length of the arc of the curve having the parametric equations x = t³ and y = 2t2 from t =…

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Q: The unit circle x² + y = 1 can be wrriten in parametric form as x = cos(0) and y = sin0. dy Find and…

A: The unit circle can be written in parametric form as x=cosθ and y=sinθ We have to find dydx and the…

Q: Find an equation of the tangent(s) to the curve with parametric equations x = t cost, y = tsin t…

A: Given- x=tcost , y=tsint To find - To find the equation of tangent to the curve with given…

Q: Two parametric equations are given by: x = cos (1), y sin (t) u- sin(t) v - cos(t) In one figure,…

A: Any point in the cartesian coordinate system is defined as x,y. The parametric functions are defined…

Q: Find parametric equations for the arc of a circle of radius 7 from (0,0) to Q = (14,0). æ(t) y(t)…

A: Given that  Radius of circle is 7  P(0,0)to Q(14,0) To find the parametric equations of the circle

Q: The unit circle a + y: =1 can be wrriten in parametric form as x = cos(0) and y= sin0. Find and…

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Q: The derivative Z of the parametric equations z= 7 sin 3t and y= cos 3t is.

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Q: Find the arc length of the curve on the given interval. Parametric Equations x = 5t + 5, y = 7- 2t…

A: The parametric equations of the given curves are   x=5t+5,  y=7-2t and the given interval is -1≤t≤3…

Q: Find the length of the arc of the curve having the parametric equations x = from t = 0 to t = 1. t…

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Q: Can the parametric curve (t, sin t) be represented as a graph y = f (x)? What about (sin t, t)?

A: Parametric curve is (t, sint) i.e x = t and y = sint

Q: 5. Determine the slope of the tangent line, the the equation of the tangent line, and the concavity…

A: this is the equation of tangent line.

Q: A curve has parametric equations x = 2 sin t ,y = cos (2t) + 2 sin t for −π/2≤ t ≤−π/2 . Find out…

A: Given : parametric equations x = 2 sin t , y = cos (2t) + 2 sin t for −π/2 ≤ t ≤ π/2     Note :…

Q: Find parametric equations for the tangent line to the curve of intersection of the following two…

A: We have to find parametric equations for the tangent line to the curve of intersection of the given…

Q: Sketch the curve by using the parametric equation to plot points. Then, eliminate the parameter 0,…

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Q: The length of the curve determined by equations x = 8 cos t + 8t sin t and y = 8 sin t – 8t cos t…

A: Given: x=8cost+8tsinty=8sint-8tcost0≤t≤π2

Q: {; 4 cos(t) 2 sin(t) at the point 4 Find the slope of the tangent line to the parametric curve

A: We have the parametric equation of curve as x=4cost⇒cost=x4        ⋯⋯1y=2sint⇒sint=y2          ⋯⋯2…

Q: Find parametric equations for the arc of a circle of radius 3 from P = (0,0) to Q = (6,0). x(t) =…

A: Given :-   A circle of radius 3 from P=(0,0) to Q=(6,0)  To find:-  Find parametric equations for…

Q: The unit circle x² + y=1 can be wrriten in parametric form as x = cos(0) and y = sin0. dy Find and…

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Q: The parametric equations of a curve are given by 2 x = In and y = cosh-(2t). when t = 1. dx Find

A: Given,            The parametric equations of a curve are given by              x=ln2t  and…

Q: The velocity of a particle moving in the xy plane is given by the parametric equations dx/dt=…

A: The given parametric equations of the particle is dxdt=-2t sin2t and dydt=2t cos2t. Evaluate the…

Q: The curve with parametric equationsx = (1 + 2 sin θ) cos θ, y = (1 + 2 sin θ) sin θis called a…

A: Given: