Find a rectangular-coordinate equation for the curve by eliminating the parameter. x = cot(t) y = csc(t) 0 < t < pi

Q: 2.) Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the…

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Q: Find dy/dx and d2y/dx2 , and find the slope and concavity (if possible) at the given value of the…

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Q: For the plane curve, (a) graph the curve, and (b) find a rectangular equation for the curve. x- 2…

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Q: Given the parametric equations below, eliminate the parameter t to obtain an equation for y as a…

A: find t in terms of x and plugin to second parametric equation.

Q: For the parametric equations: x(t) = t^2 and y(t) = ln t (a) find a Cartesian equation  (b)…

A: Given thatx(t)=t2 and y(t)=lntFrom y(t)=ln(t) we get t=eyThen we plug it in x=t2So, x=ey2or, x=e2y

Q: For the plane curve, (a) graph the curve, and (b) find a rectangular equation for the curve x= 16…

A: Solve the following

Q: 18. The parametric equations of a curve are given by x= at", y= 2at, where a is a constant and t a…

A: To find the equation of tangent line

Q: 1) a) sketch the curve. b) eliminate the parameter and find the Cartesian equation for the curve. c)…

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Q: Given the parametric equations below, eliminate the parameter t to obtain an equation for y as a…

A: Here, we have to eliminate the parameter t.

Q: Find parametric equations for the curve with the given properties. The line passing through (4, 5)…

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Q: 15sin (t), y 8cos (t) 3. Eliminate the parameter to find a Cartesian equation of the curve: x =

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Q: x = e' – 1, y = e", 2t -0 <t < Eliminate the parameter to find a Cartesian equation of the curve.…

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Q: Given this pair of parametric equations and value of t, x = Vt, y = at t = 4 a) Find the point…

A: To solve this put t=u and then solve it Here we are going to use formula of differention of tn…

Q: find parametric equations for the given curve.  x 2 + y 2 = 49

A: Given: find parametric equations for the given curve.   x2 + y2 = 49=72The parametric equation for a…

Q: Find the slope of the parametric curve x = -6t²-1, y = 2t³, for -∞<t<∞, at the point corresponding…

A: We can find the slope at the indicated point in the following steps.

Q: Given the parametric equations below, eliminate the parameter t to obtain an equation for y as a…

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Q: Find and simplify dy/dx and d2y/dx2, and find the slope and concavity (if possible) at the given…

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Q: Find parametric equations for the line that is tangent to the given curve at the given parameter…

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Q: x = 4t − 3,    y = 2t,    t is greater than or equal to 0.  Find a rectangular-coordinate equation…

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Q: (iii) Given the curve with parametric equation x = e and y = In(2-r²) Find the equation of the…

A: Formula: The normal line of the parametric equation x=ft and y=gt at the point t=t0 is the line…

Q: Find Y and and find the slope and concavity (if possible) at the given value of the parameter. (If…

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Q: Eliminate the parameter to find a Cartesian equation of the curve. (b) Sketch the curve and indicate…

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Q: 73. x = ² – 1, y = t³ + t; t = 2

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Q: Find dy/dx and d²y/dx2, and find the slope and concavity (if possible) at the given value of the…

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Q: A curve's parametric equation is given by 3t 3t2 || Y = 1+ t3 ' 1+t3

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Q: Given the parametric equations for a plane curve: x= 5 cost y=2 sint 3n , use an arrow to indicate…

A: The parametric equations are used to denote the coordinates of a point which is used to form an…

Q: X= 4 cos(t) , y= 5 sin(t) find rectangular coordinates equation for the curve by eliminating the…

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Q: 74. x = sin t, y = cos t; t = T/4

A: Given; x=Sint, y= cost, t=π/4

Q: Let P be the point with Cartesian coordinates (6, 9), and C be the plane curve with parametric…

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Q: Find dy/dx and d'y/dx2, and find the slope and concavity (if possible) at the given value of the…

A: Using differentiation we have

Q: Find parametric equations for the line that is tangent to the given curve at the given parameter…

A: Let r(t) be a curve, the derivative r'(t) is a vector tangent to the curve. The equation of the line…

Q: Sketch the curve by using parametric equations to plot points. Indicate with an arrow the direction…

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Q: . Consider the curve given by the equation 2(x+y)=5siny. b)Determine the concavity of the curve for…

A: Apply second Derivative test

Q: ig. x = sin(t), y = csc(t), 0 < t < x/2 (a) Eliminate the parameter to find a Cartesian equation of…

A: solution is given below

Q: Given the parametric equations below, eliminate the parameter t to obtain an equation for y as a…

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Q: Find parametric equations for the line that is tangent to the given curve at the given parameter…

A: At t=0,x(0)=6cos(0)=6y(0)=04-6sin(0)=0z(0)=2e3(0)=2 The point on the the curve at t = 0 is (6,0,2).

Q: Find parametric equations for the line that is tangent to the given curve at the given parameter…

A: Given the curve r(t)=(4t2)i+(3t+1)j+(t3)k. We need to find parametric equations for the line that is…

Q: Find the parametric equations for the tangent line to the curve x = ? - 1, y = f + 1, z = f at the…

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Q: 3. The two curves r,-1-cose and razcose are intersecting at angles: A. (-5. B. (. c.).

A: Explanation of the answer is as follows

Q: Find dy and d?y and find the slope and concavity (if possible) at the given value of the parameter.…

A: Given, x = 1t y =t2 t = -3

Q: Finding the length of the curve with parametric equations  x(t) = 3t2,  y(t)=2t3,  0 ≤ t ≤ 2

A: Given: - The parametric equations are, x(t)=3t2, y(t)=2t3, 0≤t≤2 To find: - The length of the curve…

Q: A curve C is defined by the parametric equations x=t+e^t, y=1-e^t a) Find the equation of the…

A: We will find the equation of tangent and points where the tangent is horizontal and vertical as…

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

A: We have to find a rectangular coordinate equation for the given curve.

Q: Find a rectangular-coordinate equation for the curve by eliminating the parameter. x = t + 1  y =…

A: We have to find rectangular equation

Q: Find. and find the slope and concavity (if possible) at the given value of the parameter. (If an…

A: Question is solved.

Q: 5. Given the parametric curve x=r - 31 + 2, y=t-r a) Find the equation of the tangent line at the…

A: In this question we will use basic of calculus i.e application of differentiation. We will use the…

Q: Parametric equations of a curve are given by x = t sin t y = t cos t for 0 <t<1 (a) Plot the curve.…

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Q: I= 2 cos(t) lu-3 sin(t) Find the slope of the tangent line to the parametric curve at the point 3…

A: x=2cost,  y=3sint Differentiating with respect to t, we get dxdt=2-sint  &amp;…

Q: Find and simplify dy/dx and d'y/dx, and find the slope and concavity (if possible) at the given…

A: take the derivative with respect to t