1. Sketch the parametric curve and eliminate the parameter to find the Cartesian equation of the curve. x = 3 cos 0, y – 2 + sin 0, 0 <0 < n b. x = t2 - 2, y = 1 – t, -2

Q: Consider the parametric equations x = 4 cos(0) and y = 2 sin(0). (a) Create a table of x- and…

A: We know that   cos(-θ)=cosθ  and   sin(-θ)=-sinθ

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…

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: Suppose parametric equations for the line segment between (1,9) and (0, Sx(t) = a + bt ly(t) = c+ dt…

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Q: 18. The parametric equations of a curve are given by x= at", y= 2at, where a is a constant and t a…

A: To find the equation of tangent line

Q: 1) a) sketch the curve. b) eliminate the parameter and find the Cartesian equation for the curve. c)…

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Q: 7. Consider the curve C given by the parametric equations x = cos(0), y = sin(0) cos(0) (a) Sketch…

A: This is a problem of parametric curve trace and the application of calculus.

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

A: First we add x2 and z2

Q: 20. Sketch the curve defined by the parametric equations over the given interval. Include the…

A: By putting the different values of t in x and y.we can draw the graph

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

A: given parametric equations are x=1+12t , y=t3-t , z=t3+t

Q: 15) (10.) Sketch the parametric curve x = 2 + 3sin(t), y = -3+ 3cos(t) for <t<. Find the slope of…

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Q: 1.) Given the parametric equations: x=t'- 1 and y=f+t, find the 1ª and 2nd derivatives.

A: We will find the derivatives.

Q: Find a parametric equation for the path of a particle that moves halfway around the circle…

A: We have to find the parametric equation for the path of a particle.

Q: 20. Sketch the curve defined by the parametric equations over the given interval. Include the…

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Q: Suppose that a parametric curve C is given by the equations x = f(t), y = g(t)for 0 ≤ t ≤ 1. Find…

A: The parametric curve C is given by the equations x=ft,  y=gt  for  0≤t≤1.

Q: Suppose parametric equations for the line segment between (7, 3) and (3, 0) have the form: S z(t) =…

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Q: 3. Consider the parametric curve C given by * = te', y =t + cos t. (a) Find the equation of the…

A: Given: The parametric equation of the curve C is  x=tet, y=t+cost (a) To find: The equation of…

Q: Suppose parametric equations for the line segment between (2, a(t) 6) and (0, 0) have the form: = a…

A: Explanation of the solution is given below...

Q: Consider the parametric curves r(t) = - cos(t) y(t) = ; sin(t) in 7 <t < 2m (a) Eliminate the…

A: We need to use Trigonometry identities

Q: Find the graph of the parametric equations x = cos t, y = sin t. (0 ≤ t ≤ 2Π)

A: When angle increases from 0 to 2π we have increase in angle in the anticlockwise sense. Use the…

Q: 3. Consider the parametric equations x = 1+ cos(t), y = -2+ sin(t), 0S <2M. 3.1. Find an equation…

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Q: 1. For the parametric equations: x = 4t3, y= 2 +60t – 8t?, find: a) All values of t at which the…

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Q: Suppose parametric equations for the line segment between (3, – 4) and (0, 3) have the form: S ¤(t)…

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Q: 1) (a) Convert the following equations from parametric to rectangular. State the domain and range of…

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Q: (d) Given r(t) = (ln(t+1), t cos 2t, 2¹). (i) Find r'(t). (ii) Find parametric equations for the…

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Q: x = 3 sin t y =-4 cost 0<t< 2n

A: Given x=3sint, y=-4cost and 0≤t≤2π

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

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Q: 2 Make a graph of the parametric equations x(t) = t - 3 on the interval 0sts 4 y(t) = ) = t ³ - 5 t

A: Given parametric equations  X(t) = t2-3  Y(t) =t3-5t

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

A: Recall: sin2t+cos2t=1

Q: The astroid curve below is defined by the parametric equations x(t) = 2 cos' t, y(t) =2sin't.…

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Q: 5. Given a curve in the following parametric equation: x = 3- 2 sint, y = 4+ 2cos t, 0<ts Then: a.…

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Q: 1. By eliminating the parameter t from the following parametric equations, find an equa- tion in…

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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 an equation y = f(x) for the parametric curve c(0) = (cos(0), 3 cos(0) + 8 sin²(0)) and compute…

A: The objective is to find y(x) and it's it's derivative .

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

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Q: 9.1.2   Sketch the plane curve defined by the given parametric equations, and find an x-y equation…

A: Consider the equations x = 1+2cos(t) and y = -2+2sin(t).

Q: 1. Consider the graph of r(t) = 2t i+ tj +t° k Determine parametric equations of the tangent line to…

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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: 1. By eliminating the parameter t from the following parametric equations, find an equa- tion in…

A: As per the instruction, we will be answering the first one. For (a), Given: Now,…

Q: 7. Consider the curve C given by the parametric equations x = cos(0), y = sin(0) cos(0) (a) Sketch…

A: Let's sketch the graph and find tangent of given parametric equations.

Q: 1 '1+t²⁹ Given R'(t) = (4e²t, , 2cosh t), and R(0) = (1, -2,3).

A:

Q: 2. Find parametric equations for the tangent line to the curve r(t) = (t8,t³,t7) at (1,1,1).

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Q: 9.) a. Find the parametric equations for the tangent line to the Curve at' the Specific point. X =t°…

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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: 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: Consider the following parametric equation. x=7(cos(t) + tsin(t)) y=7(sin(t) - tcos(t)) what is…

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Q: 15) Find a set of parametric equations to represent the graph of y = 4x – 3 using the parameter t =…

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Q: 2. Given the parametric equation: x= 4 cos (t), y=9 sin (t), 0 <t< 2n, a) sketch the curve and…

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