x = et – 3, y = e2t (a) Eliminate the parameter to find a Cartesian equation of the curve.

Q: Eliminate the parameter to find a cartesian equation of the curve. x = et,  y = e-4t

A: A curve is a two dimensional object with equation of the form y=f(x). This equation can sometimes be…

Q: find parametric equations for the given curve. y = 9 − 4x

A: The given equation

Q: Find the Cartesian equation of a curve defined parametrically by 5t and y = 10t for all real values…

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

Q: Find the equation for the line tangent to the parametric curve: t3 – 4t 4t2 – t4 - at the points…

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Q: Consider the following. x = e', X = y = e-3t (a) Eliminate the parameter to find a Cartesian…

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Q: The cartesian equation of the curve x = vt ,y= 1– t is : (a)y = 1 – x², x 2 0 (b)y = 1 – x ,x 2 0…

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Q: - For what value(s) of t does the curve given by the parametric equations x= -² -1 and y=t* +2r² –…

A: As per our guidelines we are allowed to solve one question at a time . Kindly repost the rest…

Q: - Find dx2 for the curve defined by parametric equations x = t³ and y = e'.

A: Differentiate given parametric equation

Q: Find the equation of y, glven the derlvative and the Indicated polnt on the curve. dy = 2x- 1 xp

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Q: Consider the following. x = et - 4, y = e2t (a) Eliminate the parameter to find a Cartesian equation…

A: To find The cartesian equation of the curve by eliminating the parameter

Q: Eliminate the parameter to find a Cartesian equation of the curve: x = VE ,y = 1 – t and then sketch…

A: Given,x=t...............(1)andy=1-t...................(2)differentiating both the equation w.r.t.…

Q: The cartesian equation of the curve x = VE .y 1-t is :

A: The characterstics eqaution of the curve is

Q: Find the Cartesian equation of a curve defined parametrically by 5t and y =10t for all real values…

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Q: Consider the following. x = et − 4,    y = e2t   Eliminate the parameter to find a Cartesian…

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Q: Find parametric equations for the given curve. y = 4x2 - x

A: The given curve is y = 4x2 - x

Q: Consider the parametric equations x(t) = 1 + 3t2, y(t) = 4 + 21³, -1 <t <1. • What is the length of…

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Q: (b) Eliminate the parameter to find a Cartesian equation of the curve.   for  −5 ≤ y ≤ −1

A: The parametric equation of curve are x=1-t2 y=t-3

Q: I Discuss the properties of the curve and sketch fully: a) y = x² e-x 1+lnx b) y = -

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Q: Find a rectangular-coordinate equation for the curve x = 2cos(t) and y = 3sin(t), 0 <t < 2n.

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Q: 7. Eliminate the parameter to find a Cartesian equation of the curve: x = Vt, y = 5 – 3t

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Q: y =(+ + +)* x = 4t + 1, 4

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Q: 8. Eliminate the parameter to find a Cartesian equation of the curve: x(t) = t, and y(t) = 3t+4, t≥…

A: To eliminate the pararmeter to find a Cartesian equation of the curve: xt=t, and yt=3t+4, t≥0.To…

Q: Find the exact length of the curve described by the parametric equations. x = 7 + 6t², y = 9+ 4t³,…

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

A: Given parametric equation is

Q: Consider the following.x = et - 6y = e2t(a) Eliminate the parameter to find a Cartesian equation of…

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

Q: Eliminate the parameter to find a cartesian equation of the curve x = t4, y = ln(t)

A: A function is a relation which maps each value in its domain to exactly one value in its range. A…

Q: The cartesian equation of the curve x= vt ,y 1-t is: (a)y = 1– x2, x2 0 (b)y = 1-x,x N0 %3D (c) x =…

A: Eliminate t then solve

Q: -Obtain the Cartesian equation of the curve by eliminating the parameter. 14) x = t - 3, y = t2 + 5…

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

Q: I Discuss the properties of the curve and sketch fully: a) y = x² e-x 1+lnx %3D

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Q: x = et – 1, y = e2t a) Eliminate the parameter to find a Cartesian equation of the curve.

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Q: Eliminate the parameter to find a Cartesian equation of the curve. x=2 sint, y=3cost, 0st<27

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Q: x = Vt, y = 4 - t (a) Sketch the curve by using the

A: (a) Put t=0. x=0=0y=4-t=4-0=4 So at t=0, the point on the graph is (0,4). Put t=4 x=4=2y=4-4=0 So at…

Q: Find the equation of the curve at any point  P(x,y) of a curve the subtangent equals -1/x

A: Given that the subtangent equals -1x. Then we get, tan θ2=-1x⇒tan θ=2 tan θ21-tan2 θ2⇒tan…

Q: Find the exact length of the curve described by the parametric equations. • x = 7+3t², y = 1 + 2t³,…

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Q: Consider the curve defined by the equation x(^2)+2xy+y^(3)=4. Part a: Find the local linearization…

A: Given informationDefine curved equation

Q: The cartesian equation of the curve x= f ,y = 1-t is : (a)y = 1– x², x 20 (b)y =1-x ,x 2 0 (c) x = 1…

A: The given curve is in paramatric form as following- x=√t y=1-t Where t is a parameter. To find the…

Q: Eliminate the parameter t to find a Cartesian equation of a curve. x = 1 + 3t,  y = 2-t^2

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Q: Eliminate the parameter to find a Cartesian equation of the curve for −2 ≤ y ≤ 4. x = t2 − 3,…

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Q: Eliminate the parameter to find a Cartesian equation of the curve. x = t2,    y = t5

A: A curve is a two-dimensional object with equation of the form y=f(x). Curves can be parameterized to…

Q: Eliminate the parameter to find Cartesian equation of the curve: x=2 sint, y = 5 cost, -n <t<n 6. a

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Q: 1. Find the equation of the tangent lines to the ellipse x² + 4y = 8 perpendicular to the line x +…

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Q: The cartesian equation of the curve x = vE .y 1-t is: (a)y = 1- x2, x 2 0 (b)y = 1-x ,x 20 (c) x =…

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Q: The cartesian equation of the curve x = 1-t.y vt is: (a)y = 1-x, x2 0 (b)y = 1-x .x 20 (c) x=1-…

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Q: Eliminate the parameter to find a Cartesian equation of the curve. x= cos 21, y=3 sint, 0sts2n

A: To find the Cartesian Equation from the given parametric equations. x = Cos2t  , y = 3Sint , 0 ≤ t ≤…

Q: Find a rectangular-coordinate equation for the curve by eliminating the parameter. x = et, y = e-t

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Q: Discuss the properties of the curve (w/ solution) and sketch fully: y = x?e-*

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Q: Consider the following equations. x = 1 − t2,    y = t − 2,    −2 ≤ t ≤ 2   Eliminate the parameter…

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Q: Sketch the curve r = 3 sin 20. a b Show that its Cartesian equation is (x² + y² )° =36x²y²,«

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Q: 7 Find the stationary point on the curve e + ye = 2e'. %3D

A: In the given question, the concept of the stationary point is applied. Stationary Point The critical…

Q: 1 Find the stationary points and state the nature of the curve y=xe.

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.