The Cartesian equation for the curve y=3 sint, z =2 cost is Select one: O z? y? 1. O None of these answers. 1. = 1.

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: 48. x = e' – t, y= 4e"², 0<t<2

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Q: Q/ Find the angle between two curves: 3 y = ==- x? , y = x? 2

A: The angle between the two curve is                                         tan θ =m1-m21+m1m2…

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

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Q: At what point do the curves r (t) = (t, 2 – t, 24 + t²) and r2(s) = (6 – s, s – 4, s?) intersect?…

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Q: Find the coordinates of the point(s) on the curve y = Va + 3 that are closest to the point (8, 0). O…

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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: Find the length of the curve described by y = V sec* t – 1 dt, - sI 4 4 (a) 4 (b) (c) (d) 2/2 (e) 1

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Q: 1. Find the equation of the tangent line to x? + y? = 9, at the point (2, v5). %3D

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Q: The x coordinate of the point of intersection between the two curves Y e14a and y = 1 is = x =

A: Given: y=e14xy=1

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

A:

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

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Q: 4) Consider the curve y 1 2x2 3 dy a) Find and simnplify dr b) Find an equation, in simplified form,…

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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: Express the curve by an equation in a and y given #(t) = e' and y(t) = 7 – e2. II %3D a) O -a? + y =…

A: Consider the curve  xt=et,yt=7−e2t

Q: 1) Given the curve 2x? + y3 = x3 + y? find the x-intercept of the tangent line at the point (2,1)

A: We find dy/dx using the implicit differentiation and we plug x=2 and y=1

Q: An equation of the line tangent to a curve at the point (1, 3) is y = x+2. If at any point (x, y) on…

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Q: y = 1/2 (e² + e^¹), − 1 ≤ x ≤1

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Q: a)Find the exact length L of the curve 3y? = (4x – 3)°, 1 0. Answer: b) Evaluate Sxe*dx Answer: 1 c)…

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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: Find the equation of the tangent line to the curve (a lemniscate) 2 2(a? + y?) = 25(æ² – y²) at the…

A: Topic:- application of derivatives

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

A:

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: a)Find the exact length L of the curve 3y = (4x – 3), 1 0. Answer: b) Evaluate xe*dx Answer: .3 c)…

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Q: I Discuss the properties of the curve and sketch fully: a) y = x? e-x

A: (a) Given- y=x2e-x To Find- The properties of the curve and sketch the curve.

Q: The equation y? (y² – 4) = x² (x ² – 5) is known as the devil's curve. Give an equation for the…

A: Given  :

Q: The Cartesian equation for the curve z = sect, y= tant, -<t< is Select one: O y=z. O none of these…

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

A:

Q: The curve assumed by a heavy chain or cable is: y = C cosh %3D If C = 50 Calculate; The value of…

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Q: Find the equation of tangent to the circle x + y = 25 at the point (3, –4) %3D 25 ix + O b. y = 7 O…

A:

Q: 19. For what values of the constants a and b is (1, 3) a point of inflection of the curve y = ax³ +…

A: Consider the value of y and solve:

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

A:

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

A:

Q: Express the curve by an equation in a and y given #(t) = t² and y(t) = 2 t4 + 6. а) x = 4 y? + 5, y…

A: To convert the parametric equation into cartesian we must have to eliminate parameter t from both…

Q: Find parametric equations for the tangent line to the curve of intersection of the cylinders x? +² =…

A: Here finds the parametric equation for the tangent line to the curve of intersection.   where the…

Q: Find the exact length of the curve (a) x = 1+ 3t2, y = 4+ 2t³, 0<t<1 (b) x = e' cost, y = e' sin t,…

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

Q: At the point (a, b) the curve æ = t2 – 4t, y = t2 + 2t, teR has a tangent line having slope 2. What…

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

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Q: The point on the curve x? + 2y = 0 that is nearest to the point (0,-;) occurs where y'is A) 0 B)…

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Q: Find the equation of the lines tangent to the curve x2 + y2 = 4 and parallel to the y-axis ? O A. X…

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Q: At what point do the curves r₁(t) = (t, 5 − t, 35 + t²) and r₂(s) = (7 — s, s − 2, s²) intersect?…

A:

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

A:

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

A:

Q: The curve has an equation of x = y^3, find the radius of gyration with respect to the x-axis. * O…

A: The curve has an equation x=y3 K=IxA K= Radius of gyrationIx=Moment of inertia/Secon moment of…

Q: Find the equation of the line through the origin auel normal to the line x=y-S,2:2y-3?

A: Let ,     L1 : x-01=y-51    L2 : y-321=z-02L be the required line which passes through 0,0,0 &amp;…

Q: a) y = x? e-X

A: We have to discuss properties of the graph

Q: ² fx ds, where C is с t a. the straight line segment x = t. y = from (0,0) to (16,4) b. the…

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Q: At what point do the curves r;(t) = (t, 4 – t, 24 + t2) and r2(s) = (6 – s, s – 2, s2) intersect?…

A: The curves are r1(t)=t, 4-t, 24+t2 and r2(s)=6-s, s-2, s2

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.