Find a parametric description for the circle x2+y2-6y=0, oriented clockwise and where t begins at 0. Restrict the domain of t such that one full revolution occurs.

Q: Evaluate the arc length of the curve generated by the parametric equations below for t (-1,1) x(t)=…

A: The expression for the arc length of the parametric curve is; L=∫abx't2+y't2dt   Given: xt=3+3t2 ;…

Q: Which of the following is the surface area of the solid body created by rotating the given…

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Q: Which of this is a parametric representation of the unit circle? * O x=sin t, y=cos t O x=3sin t,…

A: The solution of the problem is given in the next step.

Q: use the given graphs of x = ƒ(t) and y = g(t) to sketch the corresponding parametric curve in the…

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Q: Show that the curve with parametric equations x = tcost, y = tsent, z = t is z cone z2 = x2 + y2 and…

A: We have to show that the curve with the given parametric equations is a cone with the equation…

Q: osen y

A: Is it sen y =x

Q: Find the length of the following parametric curve. x = 6 + 916, y = 5 + 6t°, 0<t < 2.

A: solution is given below

Q: The curve C is the circle of radius 5 contained in the plane z 5 and centered around the z-axis,…

A: Solution:-

Q: Use the given graphs to sketch the parametric curve x=f(t), y= g (t). x=f(t) y =g(t) 2 2 -1 2 -2 -1…

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Q: Find a parametric description r(t) for the following curve. The quarter-circle from (1, 0) to (0, 1)…

A: A circle at origin and radius = 1 is given by r=1  At (1,0) , r=1 and θ=0  At (0,1), r=1 and θ= π/2…

Q: Use the graphs of x = f(t) and y = g(t) to sketch the parametric curve x = f(t), y = g(t). Indicate…

A: We can solve this problem by plotting some points on the curve of y vs x by taking some specific…

Q: Show that the Curve X()=let, et, 5t) Lies on hyperbola

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Q: The parametric curve X= 2sin(t) + 2, y=3cos(t) – 2 describes a clockwise traveling vertical ellipse…

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Q: Evaluate where C is the portion of the circle centered at the origin with radius 2 in the 1st…

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Q: A curve is defined by the parametric equations z (t) = e-* and y (t) = e*. What is in terms of t ? A…

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Q: Use the parametric equations of an ellipse x = acos(theta), y = bsin(theta) on the interval[0,2pi]…

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Q: Eliminate the parameter on t to write the parametric function as a Cartesian equation in y = form.…

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Q: use the given graphs of x = ƒ(t) and y = g(t) to sketch the corresponding parametric curve in the…

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Q: Denote that G is a parametric curve x(z) = z2-z-2 y(z) = z²-=2+z Calculate whether if G is concaving…

A: Given parametric curve G: xz=z2-z-2yz=z3-12z2+z We have to calculate whether if G is concave up or…

Q: 3) Sketch a graph of the helix r(t) = (− cos(2ñt), 4 sin(2πt), 3t), listing the rotation direction,…

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Q: Consider the parametric curve defned by r=3+5t and y=1+ Over which values of y does t curve has a…

A: Given problem:- Consider the parametric curve defect by   x = 3 + 5t and y = 1 + 3t   Over which…

Q: Find the length of the parametric y = 2 , - V3sts V3. curve x = 1+

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Q: . Find a parametrization for the circle (x – 2)² + y² = 1 starting at (1, 0) and moving clockwise…

A: Consider the equation of circle

Q: In each part, find an equation of the sphere with center (−3, 5,−4) and satisfying the given…

A: Consider the given: a) Tangent to the xy−plane:x−−32+y−52+z−−42=−42x+32+y−52+z+42=16

Q: x = \t +1 y = 1 t> -1 t +1

A: the given parametric equations arex=t+1,   y=1t+1,     t&gt;-1

Q: The circle of radius 1 centered at (-3, 4,1) and lying in a plane parallel to the yz-axis is a)…

A: The circle of radius 1 centered at (-3, 4,1) and lying in a plane parallel to the yz-axis is Then x…

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 the exact length of the given parametric curve. X = = 8t³, y = 12t², 0 <t< 2

A: Consider the parametric equations

Q: Prove that the curve given by the equations x=R(cost+tsint),y=R(sint−tcost) is the involute of the…

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Q: Sketch the graph of the following parametric (a) x = 1+t , y= 2t – 3, 2<t< 5 1 (b) x = 2t , y = 1+…

A: Here we have to draw the parametric equations:- a) x=1+t,    y=2t-3,   2≤t≤5b) x=2t,    y=11+t2c)…

Q: A curve called the folium of Descartes is defined by the parametric equations 3t 3t2 x(t) = y(t) 1+…

A: solution is given below...

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: In each part, find an equation of the sphere with center (2, −1, −3) and satisfying the given…

A: Given that: Centre of sphere = (2, -1, -3)

Q: 9) Sketch x = indieate the onientatiba of the 2t°, y = 3t, -4sts4 aud with %3D Curve an arow,

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Q: Show that the curve with parametric equations x = t cos t, y = t sin t, z =t lies on the cone z? =…

A: We have to check if x,y,z parametric equations lies on the given cone.

Q: Find the asymptotes of the curve defined by the parametric equationsx=φ(t)=1t−2,y=ψ(t)=tt−1.

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Q: Eliminate the parameter in x = -t +2t and y =t-4 and then identify the parametric curve and sketch…

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Q: Verify Green's Theorem in the plane for F = -3y³i+ (3x3 + cos y)j where C is the circle x2 + y? =…

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Q: Evaluate integral and use parameter t to show parametric equations for circle ∫c x6y d s where C…

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Q: Use the parametric equations of an ellipse x= 9 cos e = 14 sin 0 0<0 < 2T to find the area that it…

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Q: Find the polar eauation for the curve represented by the given Cartesian eavation. Dy=-4x² 1.

A: We need to find polar equation.

Q: Let YR be the circle of radius R with counter clockwise orientation. Prove that 1 -dz = 0. lim z3 +…

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Q: Use the parametric equations of an ellipse, x = a cos(e), y = b sin(e), 0 se s 27, to find the area…

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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…

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Q: Find the length of the parametric curve defined by x=r°, y=t- for 0st<1 7.

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Q: Prove that any polar curve r= f θ with the propertythat the angle ψ between the radial line and the…

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Q: Find the polar eauation for Hhe curve Cartesianm eavation. represented by the given 2.

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Q: Use the parametric equations of an ellipse, x a cos(0), y = b sin(0), 0 seS 2n, to find the area…

A: Given that the parametric equation of an ellipse is  x= a cos(θ) , y=b sin(θ) , 0≤ θ ≤ 2π . Here we…