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

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: 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: Find equations of both the tangent lines to the ellipse x2 + 4y 36 that pass through the point (12,…

A: see below the calculation and answer

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: Sketch the curve by eliminating the parameter, and indicate the direction of increasing tat t-0. =…

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

A: The characterstics eqaution of the curve is

Q: find parametric equations for the given curve. y = x2, translated so that the minimum occurs at…

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Q: Find the points on the parametric curve c(t) (3t2 - 5t, t3 - 10t) where the tangent line has slope…

A: Given curve is Firstly, we find dy/dx

Q: Do the curves ri(t) = (t² + 3, t+1, t² – 5) and rž(s) = (4s, 2s – 2, s + 1) intersect? If so, at whi…

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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 the exact length of the curve. =글Vy (y-3), 16 <y< 25 X =

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Q: 1. Eliminate the parameter in the following and sketch the curve. Indicate the orientation. a) r…

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Q: dy 20 yx %3D

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Q: 7. Sketch the curve with parametric equations z =e, y =e', teR.

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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: Determine all points on the parametric curve {x= 2t^3−24t y=t3−6t^2+9t−4 where the tangent slope is…

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Q: Sketch the curve with parametric equationsx = 3t − 4, y = 3 + t^3

A: Here we have to sketch the curve with parametric equations.  x=3t-4; y=3+t3

Q: The cartesian equation of the curve x= vt ,y =1-t is : (a)y = 1– x², x 2 0 (b)y =1-x ,x20 (c) x = 1…

A: Eliminate t in given equation.

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 an equation for the tangent plane to the surface 2° – ay? = 0 at the point (27, 1, 3).

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Q: ) Eliminate the parameter t to find a Cartesian equation for: x = t² and y = 3 + 5t. and express…

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Q: ) Find the pdar eawation for the cartesian curve x²-y²= \x?+yz A)rsinz0=2 b)r=ュ )cos 20=1 Dr=cos2@…

A: In polar coordinates, substitute x =r sin(theta) and y= r cos(theta)

Q: y = e*, 0<z<1.

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Q: Compute the length of the curve given parametrically by x=1/3t^3 and y=1/2t^2 for 0 less or equal to…

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Q: Find the length of the parametric y = 2 , - V3sts V3. curve x = 1+

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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: Evaluate ∫C x ds, where C is the parabolic curve x = t, y = t2, from (0, 0) to (2, 4).

A: Given: Parabolic curve x=t, y=t2 from (0,0) to (2,4)

Q: Without eliminating the parameter t, find a Cartesian equation for the line tangent to the curve C,…

A: Let's find.

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: Find the slope of the parametric curve x = -2t3 + 1, y = 3t2, for - ∞ &lt; t &lt; ∞, at the point…

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Q: Find the exact length of the curve.42. x = et − t, y = 4et/2 , 0 ≤ t ≤ 2

A: Given eqn : x=et-t,  y=4et/2 ,  0≤t≤2 So, we use dxdt=et-1,  dydt=2et2   Length of the curve =…

Q: Consider the curve given by the equation y2+x3=0. Find its curvature at the point (−1,1).

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Q: Find the exact length of the curve. 1 Vy (v - 3), 4 < y< 16 3 X =

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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: Sketch the curves below by eliminating the parameter t. x = V3t + 4, y = 3t + 2

A: Given query is to sketch the curve by removing t.

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

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Q: Find the equation of the tangent plane at the point (-2,1 – 3) to the ellipsoid surface + y? + = 3.

A: Find the equations of the tangent plane and normal line at the point (-2, 1, -3) to the ellipsoid…

Q: ind the orthogonal trajectory of the curve y? = ax²(1- cx); with a held fixed.

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Q: (2) find the (x,y) coordinates of all points of intersection ot the curves.

A: b.(2) Given the polar equation of two cardioids r=1+sinθ,r=1-cosθ. To find the points of…

Q: 13. Eliminate the parameter and sketch a graph of the plane curve. Indicate the orientation. x = 3…

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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: Find the equation of the tangent plane to the surface z = +y? at the point (2, –2, 5)

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

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Q: Find the length of the curve given by the parametric equations z = 2t3/2 0 <t< 4 ' y = 3t + 1

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