24. Match the graphs of the parametric equations x = f(f) and y= g(t) in (a)-(d) with the parametric curves labeled I-IV. Give reasons for your choices. (a) 2+ (b) II 24 (c) III (d) IV

Q: List all of the points (x, y) on the parametric curve t° + 4t, y = 6t? where the tangent line is…

A: Given that, Parametric equation of the curve are following, x = t3 + 4t,      y = 6t2 and the…

Q: Find parametric equations and a parameter interval for the motion of a particle in the xy-plane that…

A:

Q: 1) Find the parametric equations of the line that is tangent to circle x² + y2 = 25 %3D at point (3,…

A: Given: Equation of circle: x2+y2=25 and tangent at point 3, -4

Q: Find parametric equations for the tangent line to the curve of intersection of the paraboloid z =x²…

A: Tangent line to ellipse will be perpendicular to normals of both the surfaces Therefore,  The…

Q: Find parametric equations of the tangent line to the curve of intersection of paraboloid z = x² + y²…

A: We know that tangent line to ellipse will be perpendicular to normal of both the surface. Therefore,…

Q: Find the First and Second Derivate of y with respect to x from parametric equations. x=3-t5;y=7t-5

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Q: Suppose a curve is given by the parametric equations x = f (t), y = g (t), where the range of f is…

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Q: find parametric equations for the given curve. y = x2, translated so that the minimum occurs at…

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Q: 2. Given the parametric equations: x = t + sin t,y = t- cost, findand

A: Solution...

Q: Find parametric equations of the tangent line to the curve of intersectic paraboloid z = x² +y? and…

A:

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

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Q: 2. Find the parametric equations of the tangent line to the curve as result of the intersection of…

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Q: 15. Find the radius of curvature at 0 = ÷n of the parametric equations x = 3(0 + cos 0), y = 3(1 —…

A: Given two parametric equations, x=3(θ+cosθ),y=3(1-cosθ) To find the radius of curvature at θ=π3

Q: Find parametric equations for the tangent line to the curve of intersection of the paraboloid   z =…

A: The given curve is the intersection of paraboloid z = x2+y2 and ellipsoid 3x2+2y2+6z2 = 29.

Q: 27. Show that the curve with parametric equations x = t cos t, y =t sin t, z = t lies on the cone z²…

A: To Show: i. Show that the curve with the parametric equationx=tcost, y=tsint, z=t  lies on the…

Q: 7. Sketch the curve with parametric equations z =e, y =e', teR.

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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: Find parametric equations for the line tangent to the curve of intersection of the surfaces at the…

A: Here we have to find the equation of the tangent line.

Q: Find a set of parametric equations for the curve of intersection of the cylinder (x − 1)² +: 4 the…

A: We will use trigonometric identity  sin2t+cos2t=1 and parametric form of standard ellipse to find…

Q: find a parametric equation for the line that is perpendicularto the graph of the given equation at…

A: We have to find parametric equation for the line that is perpendicular to the graph of the given…

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: Find parametric equations and a parameter interval for the motionof a particle that starts at (a, 0)…

A: The given equation of circle at (a,0) is The general parametric equation of circle is where x,y…

Q: ) (i) Find the parametric equations for a smooth curve, C: x= 4z, y = -3z that joins two points,…

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

A: Recall: sin2t+cos2t=1

Q: 6. Find a set of parametric equations for the line tangent to the space curve at the given point. 2…

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Q: 1. Evaluate the length of the curve defined by the parametric equations x = cost, y=sint, z…

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Q: Determine the relative maximum, relative minimum, and point of inflection without eliminating the…

A: The parametric equations are, x=1t3 y=t2-t   Differentiate x=1t3 with respect to t. dxdt=ddx1t3=-3t4…

Q: 10. Find the value of 2 for the parametric curve xx= y = 2t2 -6 at the point (1.-6).

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Q: Try to sketch by hand the curve of intersection of the parabolic cylinder y = x² and the top half of…

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Q: Find an equation of the line through (0,0,0) that is parallel to the e parametric equations x(t) = 2…

A: To find out equation of any line we need one point on the line and a vector which is parallel to the…

Q: Find the parametric equations of the tangent line to the curve of intersection of the surfaces x² -…

A: The equation of the tangent plane to the surface f(x, y, z)=0 at x0, y0, z0 is defined as: fxx0, y0,…

Q: Find a parametric description for the curve x=y^2-9 from (0, 3) to (-5, -2) such that t=0…

A: We need to parametrize the curve x=y2-9 from 0,3 to -5,2 We need to put either x=t or y=t and see a…

Q: Find the parametric equation of the line tangent to the curve of intersection of the cylinder…

A:

Q: What does the graph of the parametric equations x(t)=3−t and y(t)=(t+1)2, where t is on the interval…

A: Given data÷

Q: Find parametric equations and a parameter interval for the motionof a particle that starts at (a, 0)…

A:

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: 10. Find the equations of the two tangent lines at the (-1,0) for the parametric curve x = 12- 2, y…

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

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

A: Topic = Functions

Q: Find parametric equations and a parameter interval for the motionof a particle that starts at (a, 0)…

A:

Q: Try to sketch by hand the curve of intersection of the parabolic cylinder y = x2 and the top half of…

A: Given that the curve of intersection of the parabolic cylindery=x2 and the top half of the ellipsoid…

Q: List all of the points (x,y) on the parametric curve x=t^3+4t,  y=6t^2 where the tangent line is…

A:

Q: 1. Sketch the graph of the curve represented by the parametric equations x = 4cost, y = 4sint 0sts…

A: We have to sketch the graph of the curve and find all points where the curve has a slope of 12.

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: find parametric equations for the line tangent tothe curve of intersection of the surfaces at the…

A: Given surfaces, x2+2y+2z=4     and   y=1f(x,y,z)=x2+2y+2z-4          and   f(x,y,z)=y-1  And point…

Q: 30. Find parametric equations for the tangent line to the curve of intersection of the cone z = x +…

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Q: 1) Find the parametric equations of the line that is tangent to circle x² + y² = 25 at point (3, -4)

A: Given, Equation of circle: x2 +y2=25 at a point (3,-4). now, parametric equation of the line is…

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

A: