2a) Find the slope of the curve represented by the parametric equations, at 0 = T/6 %3D x = 5+ 3 sec 0 y = -3 + 4tano

Q: Find dy/dx and d²y/dx2, and find the slope and concavity (if possible) at the given value of the…

A: We are given the parametric equations: x=6cosθy=6sinθ We know that the derivative of  cosa=-sina and…

Q: Eliminate the parameter from the parametric equations to find the rectangular equation for the…

A:

Q: Find dy/dx and džy/dx2, and find the slope and concavity (if possible) at the given value of the…

A: The answer is found in step-2

Q: Find the exact length of the curve described by the parametric equations. x = 5 + 6t², y = 3 + 4t³,…

A: Find the length of the curve   x= 5+t2 ,y= 3+4t2 , 0<=t<=1 .

Q: 2. Determine the ry-coordinates of the points where the following parametric equations will have…

A: Given : Parametric equations : x = 2sin t,  y = 4 cos t,  0 ≤ t ≤ 2π To find : xy coordinates…

Q: Sketch the curve represented by the parametric equations x = 2 + sec θ, y = 3 + tan θ (indicate the…

A:

Q: find parametric equations for the given curve.  Line through (2, 5) perpendicular to y = 3x

A: Find parametric equations for the given curve.  Line through (2, 5) perpendicular to y = 3x

Q: Consider the curve given by the parametric equations = 3 cos 0 and y = 3 sin 6, 0<0<T. Which of the…

A:

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

A:

Q: By eliminating parameter t, sketch the parametric curve for the given parametric equations. Then,…

A:

Q: Sketch the curve represented by the parametric equations    x = et − 1,                    y = e3t…

A:

Q: 1. (a) Sketch a curve represented by the parametric equations x = 1 - t² and y = 1+t. Then find a…

A: As per company guidelines we are allowed to solve one question at a time so i am solving first one…

Q: Given this pair of parametric equations and interval for t, x=t+sint, y=cos(2t), 0 ≤t ≤2 (A) write…

A: The parametric equations are x=t+sint, y=cos2t and t∈0,2π.

Q: Sketch the parametric curve of the given parametric equations and indicate the orientation. 1. x=3t…

A:

Q: Sketch and identify the curve defined by the parametric equations x = sin²t, y = 2 cost

A: Given the parametric equations  x=sin2t y=2 cost To find : Sketch and identify the curve using given…

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

A:

Q: Sketch the plane curve represented by the parametric equations x = Vi and y = 2t – 1 by eliminating…

A: Sketch the plane curve represented by the parametric equations             x=t     and     y=2t-1 by…

Q: ELIMINATE THE PARAMETER IN THE PARAMETRIC EQUATIONS: x=t +1 Y = t t-1

A: Topic - equations

Q: Sketch the graph of the parametric equation. x=sec t , y=tan t

A: Square both the equations.

Q: 14. The curve represented by parametric equations x = 4cose and y 4sine is a

A:

Q: Eliminate the parameter t from the parametric equationsx = 3+1 2 sec t and y =2+  4 tan t.

A: Given parametric equations are x=3+12 sect and y=2+4 tant We have to eliminate the parameter t from…

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: Find dy/dx and d2 y/dx2 , and find the slope and concavity (if possible) at the given value of the…

A: Given, x = cos3 θ, y = sin3 θ Parameter θ = π/4

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

A:

Q: 8. x 2t2, y =t + 1 ||

A: We use substitution method to eliminate parameter

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

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: Find dy/dx and d-y/dx, and find the slope and concavity (if possible) at the given value of the…

A: Given: x=6 cosθ, y=6 sinθ a) dydx at the point θ=π4 can be calculated as, dydxθ=π4=dydθdxdθθ=π4…

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

A:

Q: Try to sketch by hand the curve of intersection of the circu- lar cylinder x + y² = 4 and the…

A: Given, Circular cylinder, x2+y2=4 Parabolic cylinder, z=x2

Q: Determine the xy-coordinates of the points where the following parametric equations will have…

A:

Q: Find the Cartesian equation of the parametric equations x = a cost y = b sint 0<t< and identify its…

A:

Q: Sketch the curve represented by the parametric equation and indicate the orientation of the curve.…

A:

Q: 2. Find the coordinates of the centre, vertices and foci of the curve with parametric equations: x =…

A:

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: 3t For the parametric equations: 39e2 and y = 16e %3D

A: We can find the answer as below.

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: 18. x = et, y = e2t - 1

A: Solution

Q: 12. Sketch the plane curve defined by the given parametric equations, and find an x-y equation for…

A: The given parametric equations are,

Q: Sketch the curve represented by the parametric equations x = e−t ,y = e2t − 1 (indicate the…

A: The given parametric equations of curves are: x = e^(-t) y = e^(2t) - 1 The graphs of these…

Q: 6. a. Find the length of the curve using the equation 12xy = 4x4 +3, from x = 1 to x = 3. b.…

A:

Q: d) Find the slope of the parametric equations x=2+3sin and y=0-cose at 0=

A: Given: x=2+3cosθ and y=θ-cosθ   As we know that; The slope of the tangent line to the given curve is…

Q: Find dy/dx and d²y/dx², and find the slope and concavity (if possible) at the given value of the…

A: The solution is given as follows:

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: Find two different sets of parametric equations for the rectangular equation  y = 4x + 1, t = −1 at…

A: Given equation is y=4x+1, t=-1 and the point is (-2,-7).

Q: a) A curve is given by the parametric equations 1 where 1 <t<3. t' I = 2 lnt and y = - i. If L is…

A: We need to find length of curve.

Q: Sketch the curve represented by the parametric equations x = √t, y = t − 5 (indicate the orientation…

A: Given parametric equation, x=t         ...(1)y=t-5       ...(2)

Q: Eliminate the parameter to find a Cartesian equation of the curve with parametric equations x = et –…

A:

Q: Sketch the curve represented by the parametric equations x = et , y = e3t + 1 (indicate the…

A: Sketch the curve represented by the parametric equations x = et , y = e3t + 1 (indicate the…