. Find a cartesian equation for the given parametric equations: a) x = t2 – 4 and y =t+1 b) x = 2 cos t and y= 2sin t , 0

Q: What is the surface area of the three dimensional solid formed by rotating the following parametric…

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Q: A set of parametric equations is given as x = t+2 cos t and y =t+sin t. Find dy in terms of t. i. dx…

A: Given parametric equations arex=t+2cost and y=t+sintfindi) dydx interms of t.ii) d2ydx2 when t=π3

Q: Convert the following parametric curve into Cartesian form: * = 3 sin t, y = 4 sin t None of these.…

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Q: Determine the number of cusps for the hypocycloid described by the parametric equations æ(t) = (2 –…

A: The standard form of hypocycloid parametric equations are x(t)=rk-1cos(t)+r cos((k-1)t),…

Q: osen y

A: Is it sen y =x

Q: Use the parametric equations of an ellipse, x = a cos 0, y = b sin 0, 0 < 0 < 2m, to find the area…

A: Given Parametric Equation of ellipse  x=acosθ and y=bsinθ ,0≤θ≤2π To find the area of the Ellipse

Q: Find the length of the curve r = 2 sin^3 (u/3), 0 … u … 3pi , in the polar coordinate plane.

A: Given:        r=2sin3u3,  0≤u≤3π

Q: Convert the following parametric curve into Cartesian form: x = 3 sin t, y = 4sin t

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Q: Determine the number of cusps for the hypocycloid described by the parametric equations x(t) =…

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Q: Find the length of the curve r = 2 sin^3 (u/3), 0&lt;=u&lt;=3pai, in the polar coordinate plane.

A: To determine the length of the polar curve.

Q: 17. Find the cartesian equation of the parametric curvex =1+e²*, y= e'. (a) z² = y? – 1 (b) 7 = x² –…

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Q: Find a rectangular equation for the plane curve defined by the parametric equations. x = t + 4, y =…

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Q: Sketch the plane curve r(t) = a cos3 ti + a sin3 tj and find its length over the given interval [0,…

A: The curve is r(t)=a cos3ti + a sin3tj   Interval is 0, 2π

Q: 19. Find y' in the parametric equations x =, t-1 t+1 A) (f – 1) 7-1 B) (1+ 1)? 2 +1 C) (1+1)? t +1…

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Q: Find the length of the parametric curve C = {(x(t),y(t)) : t E I} x(t) = cos (t) , y(t) = sin³ (t),…

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Q: Find the length of the parametric curve defined over the given interval. A) B) 3 3 2 C) D) 1

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Q: Select the following sets of parametric equations that describe the parabola y = x² x=t, y=t² □ y =…

A: To select the follwing sets of parametric equations that describe the parabola y=x2.1 x=t, y=t22…

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

A: Given: Use the parametric equations of an ellipse, x = a cos θ, y = b sin θ, 0 ≤ θ ≤ 2π,  to find…

Q: -2 Find the projection of v = 1 onto the line l of R³ given by the parametric equation l = tủ, where…

A: We will find out the required projection.

Q: Show that the graph of the parametric equations x = a + (c − a)t, y = b+(d−b)t, t ∈ [0, 1] is a line…

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Q: Match the parametric equations with the correct graph. x = t cos(t), y = t, z = t sin(t), t2 0 ZA ZA…

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Q: Find a set of parametric equations for the curve of intersection of the given paraboloid and plane:…

A: Solution:-

Q: Q1:- Draw the graph of the following parametric equations, and find the Cartesia 1) x = 6t + 2 y =…

A: Hello. Since your question has multiple parts, we will solve the first three part for you. If you…

Q: 4. Determine the length of the parametric curve given by the following parametric equations. (a) x =…

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Q: consider the following set of parametric equations: x = 6tanhθ ; y = 3sechθ Calculate d^2y/dx^2

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

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Q: Determine the length of the parametric curve given by the following parametric equations. (a) x =…

A: We will proceed as follows

Q: r(4)=DTsin(i+ 34 j+ t°K 2. POINT: (1,2,1)

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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: Given that x (t) = 3 sin t, y(t) = 2 cos² t, convert the parametric equations into the Cartesian…

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Q: Determine the length of the parametric curve given by the following parametric equations cos t y =…

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Q: 17. Consider the following parametric equations. x = Vt + 4, y = 3VE, , 0st < 16 a. Eliminate the…

A: The given data is: x=t+4       ....1y=3t          .....2 0≤t≤16

Q: 1. Use the parametric equations of an ellipse, x = a cos 0, y = b sin 0, 0 < 0< 27, to find the area…

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Q: Show that the parametric equations x a cosh u cos v, y b cosh u sin v c sinh u represent a…

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Q: Convert the following parametric curve into Cartesian form: x=2 sint, y = 3 sin t O 3x² + 2y² = 1 O²…

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Q: Which of the following are parametric equations for the ellilpse glven by 9. + y? = 1? Choose all…

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Q: 3. Convert the following parametric equations to rectangular equation (a) x = cosh t, y= sinh t (b)…

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Q: Find the length of the parametric curve C {(x(t), y(t)) : t E 1} x(t) 4cos(t), y(t) = 4sin(t), with…

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Q: consider the following set of parametric equations: x=6tanhθ ; y=3sechθ Calculate dy/dx

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Q: Sketch the parametric curve for the following set of parametric equations x = 5 cos t + 2 , y = 2…

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Q: Determine the length of the parametric curve given by the following parametric equations. (a) r= t -…

A: In order to determine the length of parametric curve  formula is ∫cd dxdt2 +dydt2 dt  Hence for a…

Q: Show that the acceleration of a point particle in polar coordinates (d²r dr de +2 d0 |Ô0 is…

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Q: 1. Sketch the parametric curve x = (cos t) (1+ cos t), y= (sin t) (1 + cos t) , 0 < t < 27 .

A: we have been given the parametric curve x=(cos t)(1+cos t) and y=(sin t)(1+cos t) where 0≤t≤2π

Q: 1 If the parametric equatioms are: x= sin-t and y= cos,t, 1 %3D - nstSn 2 then the Cartesian…

A: Given x=sint2, y=cost2, -π⩽t⩽π

Q: Graph the parametric curves x = cos t, y = sin t, 0 ≤ t ≤ 2π.

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Q: Sketch the graph of the following parametric equations: x(t) = cos(t); y(t) = sin?(t); t in [-7,0]

A: xt=cost,   y=sin2t ;   t in -π, 0

Q: Convert the following parametric curve into Cartesian form: x = 4 sin t, y = 5 sin t O 2² + y? = 20…

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Q: Given the parametric curve x(t) = 3t + In(t), y(t) = 3t – In(t)

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