(b) Given that cos (t) Vos(21) sin' (t) Jos(2)" |cos(2t) dy Find for the parametric equation given above. dx

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A: Given parametric equations, x= 3sint ,   y=3cost,     0≤t≤π3

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A:

Q: The x- intercept of the tangent line to the polar curve r=(1+sin 0) at 0=" is

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Q: The parametric equations for the paths of two objects are given. At what rateis the distance between…

A: Given: The parametric equations for the paths of two objects are given. At what rateis the distance…

Q: Consider the following parametric curve. x = sin(8t) + cos(t), y = cos(8t) - sin(t) Find dy dx dy dx…

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Q: 18. Find the second derivative of y with respect to x of the following parametric equations. x = 1 +…

A: Using derivatives of parametric equations.

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Q: Find ď²y dx² x = 3 sin t in the parametric equation y = 3 cost 0≤t≤ 2π.

A:

Q: Find an equation in rectangular coordinates for the curve r^2 = cos 2θ.

A: We know that, the relationship between polar and rectangular co-ordinates are given as r2=x2+y2…

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A:

Q: I the slope of the tangent line to the parametric curve X = 3 cos (t) y = 2 sin(t) ㅠ R 4 at the…

A: Given query is to find the slope of the tangent.

Q: Consider the parametric equations x = 2t – 5, y = 6. dy Use the derivative formula from Section 10.2…

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Q: 4. Find the length of the curve having a parametric equation of x = a cos 3 6, y = a sin 2 0 from e…

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Q: 1 cos(t) Find the slope of the tangent line to the parametric curve at the point y = 2 sin(t)

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Q: Write the parametric equations x = = 5 sin² 0, y = 3 cos² 0 e given Cartesian form. 3sqrt(1-x^2/25)…

A: Given query is to find the Cartesian equation.

Q: dy = cos 20. de dx Given that r= cos 0 ; = - sin 20 and de The slope of the tangent line to the…

A: Given that: r=cosθdxdθ=-sin2θdydθ=cos2θ

Q: Eliminate the parameter to find the cartesian equation of the curve: x = 2 sin 0, y = cos² 0, sos…

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Q: Find the equation of the tangent line to the parametric curve x = θ+cosθ, y=1+sinθ; θ = π/6

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Q: :2 cos(t) y = 3 sin(t) T = Find the slope of the tangent line to the parametric curve at the point 4

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Q: Given parametric equations x = 2 cos 0 and y = sin 0. d²y Then dx2 in the point (V2,) is

A: Given parametric equation is  x=2cosθ and y=sinθ

Q: Find the slope of the line tangent to the polar curve at the given point. 3 7n 2' 6 r= 3 sin 0; dy…

A: Compute the slope of the line tangent to the polar curve as follows.

Q: Consider the parametric curve defined by x = 2020 cos t y = 2020 sin t π Find the slope of this…

A: Slope of a curve at some point is the value of the derivative at that point.

Q: 7. Find the first derivative of y with respect to x of the following parametric equations. x = 1 +…

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Q: Eliminate the parameter in the parametric equations x = 7+ sint, y = 2+ sint, for 0sts, and describe…

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Q: Find the equation of the tangent line(s) to the following set of parametric equations at the given…

A: We have to find the equation of tangent from the parametric curve

Q: Graph the pair of parametric equations with the aid of a graphing calculator x = 4 sin t - sin 4t, y…

A: Given x=4sint-sin4ty=4cost-cos4t0≤t≤2π

Q: = = 2 cos (t) lu =1 sin(t) T Find the slope of the tangent line to the parametric curve at the point…

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Q: 1. x (0) = 0 + cos 0 y (0) = 1+ sin 0 given that

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Q: 2.) Given the parametric equations x=cos3t and y=sin3t. Find the equation of the normal line at the…

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Q: 7. Find the slope of the tangent to the parametric curve x = t - lnt, y = t + lnt at the point (e +…

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Q: •5 25-x2 Evaluate (x² + y? )° dy dx by converting to polar coordinates.

A: To evaluate the integral using polar coordinates

Q: Suppose a curve is traced by the parametric equations 3(sin(t) + cos(t)) = x у 3 18 — 6 соs"(€) — 12…

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Q: The derivative Z of the parametric equations z= 7 sin 3t and y= cos 3t is.

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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: The x- intercept of the tangent line to the polar curve r=3(1+sin 0) at 0=" 프 is

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Q: A curve has parametric equations x = 2 sin t ,y = cos (2t) + 2 sin t for −π/2≤ t ≤−π/2 . Find out…

A: Given : parametric equations x = 2 sin t , y = cos (2t) + 2 sin t for −π/2 ≤ t ≤ π/2     Note :…

Q: Find the slope of the line tangent to the following polar curve at the given point. 3x r= 3-3 sin 0;…

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Q: Consider the parametric curve x = sint + cos t, = cos² t 0 <t < 2n п Find an equation for the…

A: We find dx/dt and dy/dt from the given equations

Q: d) Find the slope of the parametric equations x=2+3sin and y=0-cose at 0=

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Q: If y = x2 is expressed with parametric equations such that = 6 when x = 1, what is ? dt dx %3D dt

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Q: {; 4 cos(t) 2 sin(t) at the point 4 Find the slope of the tangent line to the parametric curve

A: We have the parametric equation of curve as x=4cost⇒cost=x4        ⋯⋯1y=2sint⇒sint=y2          ⋯⋯2…

Q: 1 cos(t) ly = 3 sin(t) Find the slope of the tangent line to the parametric curve at the point

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Q: What is the equation for the line tangent to the parametric curve I = 4 sin(2t) y = 4 sin(t) at t=…

A: Explanation: Given that: x=4sin2ty=4sintt=π6or 30° Concept used: The standard equation of line…

Q: The parametric equations of a curve are given by 2 x = In and y = cosh-(2t). when t = 1. dx Find

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A: The given parametric equations of the particle is dxdt=-2t sin2t and dydt=2t cos2t. Evaluate the…

Q: 4 cos(t) { Find the slope of the tangent line to the parametric curve at the point 1 sin(t) 6 Y =

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Q: 1) Find the parametric equations of the line that is tangent to circle x² + y² = 25 at point (3, -4)

A: Given, Equation of circle: x2 +y2=25 at a point (3,-4). now, parametric equation of the line is…

Q: The position of a particle in the xy-plane at time t is given by r(t) = (cos 2t) i+ (2 sin 2t) j…

A: Given: rt=cos2ti+2sin2tj For finding equation in x and y whose graph is the path of the particle, we…

Q: 9. Find the slope of the tangent line to polar curve r = 9 cos 0 at the point 2' 3

A: