The following are the parametric equations for the motion of an object: x(t) = t cos(5t^2 + 2);  y(t) = t^2 ln (-5t): Find the slope of the curve followed by the object as a function of t.

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

A: Explanation :  Given that x= 3cost + sint y = e^2t

Q: Find the equation of the tangent line to the curve defined by the parametric equations x(t) = 2t3 -…

A: Topic- application of derivatives and tangent equation

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…

A:

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

A:

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

A: It is given that x=3-sint, y=3+cost. we have to find the graph of the parametric curve

Q: Find the derivative dydx of the polar function r=1+sinθ at θ=π4.

A:

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

A:

Q: Consider the parametric equations x = 2t – 5, y = 6. dy Use the derivative formula from Section 10.2…

A:

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

A:

Q: Find two different sets of parametric equations for y = x2 + 6.

A: Our Aim is to find the two different sets of parametric equations for y=x2+6

Q: Find the parametric equation of the line that passes through P(-2, 0, 3) and is parallel to the line…

A: Given that: Equation of line is:     x=-1+3t, y=2-2t, z=3+t  and the point is : P(-2, 0, 3)

Q: find y'' for the curve cosx-siny=4

A:

Q: Find the cartesian equation of the curve x = 2 sin (2t) and y = 3sin (t). Graph.

A: To find the Cartesian equation of the given curve.

Q: Find the slope of the tangent line to polar curve r = 6 – 9 sin 0 at the point (6-

A:

Q: Find a Cartesian equation of the curves. 1) r= 2 sin 0 2) r = 5 csc e

A: 1) r=2sinθ2) r=5cosecθwe have to convert these curves into cartesian equations

Q: Given the curve with parametric equations, find the slope and the equation of the tangent line at…

A: Here we have to find the Slope of tangent line at indicated points . We are given parametric…

Q: Find the second derivative in terms of t for the parametric equations below- x=t² -t+2 y =t -3t

A: Given that, the parametric equations are x=t2-t+2 and y=t3-3t Find the first derivative in terms of…

Q: The parametric equation of the motion of a particle on a plane is given by 3/2. x = te + 2t12; y=t'…

A:

Q: what points does the curve described by the parametric equations x = 2a cos t – a cos 2t d y = 2a…

A:

Q: By eliminating the parameter, determine the rectangular equation equivalent to the parametric…

A: This is the problem of the application of differential calculus and parametric to cartesian…

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

A:

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

A:

Q: Find the exact slope of the tangent line to the parametric curve at the point where y = 2 sin(t) t =…

A: x=8 cos (t) y=2 sin (t)

Q: The derivative I of the parametric equations and y=5vt is

A:

Q: Match the given parametric equations with one of the parametric curves. x= 2- sint, y= 2 + cost

A: To determine the parametric curve for given equation.

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 The slope of the tangent is given by…

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 a rectangular-coordinate equation for the curve by eliminating the parameter. x = sin2(t), y =…

A: Given parametric equation is

Q: Find the derivative of the following parametric equations as indicated. Express the final answer in…

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 equations of the tangent and normal to the curve expressed in parametric form at the point…

A:

Q: Find the parametric equations for the tangent line to the curve x =t* _ 1,y=t* +1,z=t* - at the…

A:

Q: Find the equation of the tangent line(s) to the following set of parametric equations at the given…

A:

Q: Write an equation for the line tangent to the graph created by the parametric 3 cos 0 and y(0) = 3…

A: To find the equation of tangent line.

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

A:

Q: Find the slope of the tangent line to polar curve V3 T r = 4 – 6 sin 0 at the point 4 – 6 Preview

A:

Q: Find the equation of the tangent line to the curve defined by the parametric equations x(t) = t3 +…

A:

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: Eliminate the parameter to find a cartesian equation of the curve. x = sin(1/2θ),  y = cos(1/2θ),…

A: x=sin12θ,  y=cos12θ

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: Plot the cissoidr 2 sin 0 tan 0 and show that its equation in rectangular coordinates is x3 y2 2 - x

A:

Q: Find the second derivative of y with respect to x from the parametric equations given. x = 3 + 4…

A:

Q: find parametric equations for the given curve. 4x − y2 = 5

A: Given curve is:

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…