Eliminate the parameter in the parametric equations x(t) = e³t and y(t) = 3e' to a Cartesian form of the equations. Select the correct answer below: O x= O y = O y = O x =

Q: The parametric equations for the paths of two objects are given. At what rateis the distance between…

A: Given: The parametric equations for the paths of two objects are given. At what rateis the distance…

Q: Find parametric equations for line that is tangent to the curve x=cost, y=sint, z=t at the point…

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Q: Eliminate the parameter t from the parametric equations x = 3 cos t, y = 5 sin t and then sketch the…

A: In eliminating parameter t from the given parametric equations we do establish the relationship…

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Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

A: The given curve is rt=t2+1,4t12,et2-t. Notice that the given curve satisfies t=1(If t=1 is plugged…

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Q: Find the radius of curvature at 0 = t of the parametric equations x = 3(0 + cos 0), y = 3(1 – cos…

A: To find the radius of curvature, first find out dxdθ and d2xdθ2. x=3θ+cos θdxdθ=31-sin θd2xdθ2=-3cos…

Q: For the parametric equations: = 26e4 and y = 46et dx () dt %3D dy (ii) dt dy (ii) %3D dx

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Q: 5. Eliminate the parameter to find a Cartesian equation of the following curves. et (a) x = vt+1, y…

A: Eliminate parameter t.

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Q: 2. Find a set of parametric equations for a particle that oscillates on the line y = 6x - 5 between…

A: formula:

Q: The equation of the tangent line to the parametric equations, x =t +sint, y 4t-cost att 0 is y = -1…

A: As we know that; The slope of the tangent line to the given curve is equal to the first derivative…

Q: Write the parametric equations x = = 5 sin² 0, y = 3 cos² 0 e given Cartesian form. 3sqrt(1-x^2/25)…

A: Given query is to find the Cartesian equation.

Q: Find parametric equations of the line through (-1, –1, 6) that is parallel to 2i – 4j+k. x(t) = y(t)…

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Q: In three dimensions, the cylinder x? + z2 – 10x – 6z – 2 = 0 has radius k i +tj+ and the axis line…

A: Radius =6  r(t)= (5+6cos(thetha))i+tj+(3+6sin(thetha)k

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

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A: Given:

Q: Given parametric equations x = 2 cos 0 and y = sin 0. d²y Then dx2 in the point (V2,) is

A: Given parametric equation is  x=2cosθ and y=sinθ

Q: 5. Given the parameter 7, constants a and c, show that the parametric equations: X(+) = (cosh () –…

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Q: A particle is moving along the curve given by the parametric equations x=1+t, y=1−t. Determine the…

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Q: Match the given parametric equations with one of the parametric curves. x-3- sint, y = 5+ cost O A.

A: To sketch the given parametric equation :- x = 3 -sin t  and  y = 5+cos t

Q: 2) Use polar coordinate dydx (1+ x² + y° )'?

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Q: 1. Eliminate the parameter to find a Cartesian equation of the curve with parametric equations z =…

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Q: Find the distance from the point (3, 2, 5)to the line with parametric equations x=t,y =l +t ,z = 2 +…

A: The equation of the line in matrix form:                                                xyz = 012 +…

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: 1. Eliminate the parameter to find a Cartesian equation of the curve given parametrically by (x(t),…

A: Recall: sin2t+cos2t=1

Q: Find a parametric equation for the line that is perpendicular to the graph of the equation 2x + 4y +…

A: Equation of line normal to graph of functions f(x) is :  r<t> = <x0,y0,z0> +…

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Q: Translate the spherical equation below into a cylindrical equation! tan2(Φ) = 1

A: We have to find the transformation

Q: Find parametric equations of the line through (–3, 0, 3) that is parallel to 5i – 8j+ k. x(t) y(t)…

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Q: Find the parametric equations for the line through the point (0, 1, 2) that is perpendicular to the…

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Q: Find the length of the curve whose parametric equations are x = 3t^2 and 3t^3, from t = 0 andt = y =…

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Q: Find the points (x, y) on the curve with the parametric equations (x3Dt3- 4t at ly=t +2 which the…

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Q: Eliminate the parameter, t, in the parametric equations, x = 6cost and y = 3sint. 2 x2 + y2 = 36 x2…

A: We have to eliminate the parameter, t, in the parametric equations, x = 6cost and y = 3sint.

Q: Eliminate the parameter t from the parametric equation x = 3 sint y = 3 cost 0 ≤t≤ 2π.

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Q: Find an equation of the tangent(s) to the curve with parametric equations x = 1+ vt, y = e at the…

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Q: Find the 1st and 2nd derivatives of y with respect to x from parametric equations. a). x=3 (t + 2)…

A: First differentiate x and y wrt t then divide

Q: 8. Solve for the critical points of the parametric equations x = t3 – 1,y = t² +t %3D

A: The answer is found in step-2.

Q: 4) Find the critical points of the parametric equations x = 5 – In t y = t + Int

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Q: Eliminate the parameter to find a Cartesian equation of the curve with parametric equations x = e^t…

A: Just put the exponential term value from one equation into the other and easily eliminate the…

Q: 7. Sketch the curve with parametric equations x = e-t , y = e', teR.

A: Topic = Functions

Q: Find the corresponding Cartesian equation of the parametric equation       x=3cosθx=3cosθ.…

A: Given:           x=3 cos θ,   y=4 sin θ            0≤θ≤2π From: x= 3 cos θ            cos θ=x3 From:…

Q: 8. Solve for the critical points of the parametric equations x = t - 1,y = t² +t

A: To find the critical points of parametric curve x(t)=t2-1, y(t)=t2+t

Q: Eliminate the parameter in the parametric equations x(t) = –7t – 2 and y(t) = Vt – 8 to find a…

A: givenx(t)=-7t-2..................(i)y(t)=t-8..................(ii)we can rewrite 2nd equation…

Q: x = 3 ln(t), y = 4t1/2, z = t3; (0, 4, 1)

A: Given Data: x=3lnt ......1y=4t1/2  ......2z=t3      ......3 x0, y0, z0=0, 4, 1   For the specified…

Q: If I have a pair of parametric equations  x=20cos(t) and y=10sin(t)  How can I increase the speed…

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Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

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