(i) Find a Cartesian equation of the curve C. Hint: square the equation for y and replace the expressions in t in terms of r. Discuss how difficult it would be to answer parts (f)-(h) without the given parametrization of the curve C.

Q: Consider the parametric equations y = e' +t te [1, 10] Briefly explain how you know that the curve…

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Q: 3 Find the distance of the point Q from the line L with the following parametric equations. x = -1+…

A: The given line is: x=-1+4ty=1+3tz=7-3t  To find the distance of the point Q 36-5 from the given line…

Q: For the parametric equations: a = 12e2t and y = 23e3t %3D da (i) dt dy (ii) dt dy (iii) dx ||

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Q: A lizard moves through the plane with its position at t seconds given by the parametric equations…

A: →cos(nπ) = (-1)n  →First find the inital co-ordinates at t = 0. Now, we have to find the time at…

Q: find a parametrization for the curve. the left half of the parabola y = x^2 + 2x

A: First, we will find the symmetric line of the given parabola y=x2+2x. We know that the symmetric…

Q: You are given the parametric equations x=10−t^2 , y=t^3−12t List all of the points (x,y) where the…

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Q: Eliminate the parameter to write the parametric equations as a Cartesian equation. If x(t) = 3t – 2,…

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Q: Consider the parametric equations below. x = 4 + 5t,    y = 1 − t2   Eliminate the parameter to…

A: Calculation:Compute the Cartesian equation as follows.Rewrite x = 4 + 5t as follows t = (x – 4)/5.

Q: 1. Graph the line using parametric equations from t = 2 tot = 6. x = 10 – 2t, y = 3 – ÷t

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Q: The curve graphed below has the parametrization C = {(v 4 %3|

A: Introduction: A parametric equation is one in which the dependent variables are defined as…

Q: Question 3 Find the tangent plane to the equation z 3r - 5y + 5y at the point (- 5, 2, 65). Submit…

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Q: Sketch the curve represented by the parametric equations x = t + 1, y = t2 (indicate the orientation…

A: Given: x=t+1, y=t2. first we eliminate t and find equation of curve in x and y x=t+1…

Q: Exn=9sin+2 and v(r)-8 cost+ 2, eliminate the parameter to write the parametric equations as a…

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Q: 1. (a) Parametrize the curve of intersection of the sphere a? + y? + 22 22 + 222 = 1, Try your best…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: For the parametric equations: a = 12e and y = 29e3t dr (i) dt dy (ii) dt dy (iii) dr || ||

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Q: The parametric equations x = 16+ ² + St. Y= 4+³+3+² ned come correspond to the Do Not make…

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Q: 2. Find the point(s) of intersection of the following two parametric curves, by first eliminating…

A: From x=t+5 we get t=x-5 Then we plug this in the y=t2 So, the equation is: y=(x-5)2   We can plug…

Q: What is the Cartesian form of the parametric equations.x(1) =t+ 4 and y(t) = t² + 31 + 1? Provide…

A: To eliminate the parameter.

Q: Saved Match the parametric equations with the corresponding plane curve displayed. x=t-75 ly=? 130…

A: Given : Parametric equations x = t - 75y = t3   To find : Correct graph of the given parametric…

Q: Q2:- Find the parametric equations for the following Cartesian equations. 1) x=(/y² + 4 + 2) 2) 4x2…

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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: Consider the parametric equations below.x = 5 + 2ty = 1 - t2 (b) Eliminate the parameter to find a…

A: From the equation for x, write t in terms of x.

Q: A lizard moves through the plane with its position at t seconds given by the parametric equations…

A: parametric equations x=3cos(2pi t)+2, y= -6cos(2pi t)+1.

Q: find parametric equations for the given curve. . (x + 9) 2 + (y − 4) 2 = 49

A: To find the parametric equation of the given curve (x+9)2+(y-4)2=49 Given equation is in the form of…

Q: Consider the following parametric equation. a. Eliminate the parameter to obtain an equation in x…

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Q: You are given the parametric equations x=10−t^2 , y=t^3−12t  List all of the points (x,y) where the…

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Q: Sa(t) = t2 – 3 lu(t) = 2t +1' Consider the parametric curve -2 <t< 3. At which time(s) does the…

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Q: Eliminate the parameter to find a Cartesian equation of the curve.

A: We have to eliminate t between x &amp; y.

Q: Eliminate the parameter in the parametric equations #(t) = 2t + 5 and y(t) = 8t equations. Provide…

A: In this question we will simply eliminate parameter t and get an equation between x and y. Solution…

Q: Find the length of the parametric curve: x = 2t + 1; y = t? – 3,0 <t < 5

A: Given that: x=2t+1,  y=t2-3,0≤t≤5To  calculate   dxdt  and   dydt,dxdt=ddt2t+1=2dydt=ddtt2-3=2t

Q: Consider the parametric equations below. x = t2,    y = t5   Eliminate the parameter to find a…

A: We will solve for t from y = t5

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

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

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Q: Can you help me Graph the curve parametrized by r(t) =⟨1−3t^2,t⟩, −∞<t<∞

A: The given parametric equation is rt=1-3t2, t. Note that one of the coordinate having degree 2 and…

Q: Consider the parametric equations x = √t − 2 and y = (1/ 2)t + 1, t ≥ 2. What is implied about the…

A: Consider the given parametric equation as x=t-2 and y=12t+1

Q: x = 1 + 4t,    y = 3 − t2

A: Here we extract t from the 1st equation then put this into second equation.

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

A: We can find the answer as below.

Q: find a parametrization for the curve. the lower half of the parabola x - 1 = y2

A: Consider the given equation x - 1 = y2 By adding 1 from both sides, ⇒ x = 1 + y2 Let, substitute y =…

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: Sketch the curve represented by the parametric equations x = 2t/2, y = t4+ 1 (indicate the…

A: Given parametric equation, x=2t2 and y=t4+1we have to write the corresponding rectangular equation…

Q: Consider the parametric equations: x = 2t2, y =43t3. Find d2ydx2at the point t=18 without…

A: Given parametric equations are x=2t2 and y=43t3. To find d2ydx2 at the point t=18 without…

Q: For the parametric equations: a = 16et and y 18e %3D da (i) dt 32*e^(2t) %3D dy (ii) dt 54*e^(3t)…

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Q: Consider the following parametric equations  x(t)=et , y(t)=e-5t a) eliminate the parameters to…

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Q: Consider the parametric equations x(1) = 1 + 3r², y(1) = 4 + 2r°, 0sts1. a. What is the length of…

A: If the parametric equations of a curve are x(t) and y(t), then the length of the curve over the…

Q: Plot the parametric curve x=t^3 ; y= sin(t^3); for (t, -2, 2). a) what familiar curve is produced?…

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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: The parametric equations of a curve are given by = 4t – 7t2 and y = t – 12t a) dy dzr Find in terms…

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Q: The position in feet, of a baseball t seconds after being thrown from third base to first base is…

A: A)                                t                        x=80 t             y=-16t2+24t+5 0…

Q: What is the Cartesian form of the parametric equations æ(t) = 4cost – 1 and y(t) = 5sint + 2?…

A: Here I am attaching image so that you understand each and every step.

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…