1. Find and Y and simplify whenever possible. d²y dx dx2 Given parametric equations: x = t3 +1, y = t2 + 1

Q: For the parametric equations: x = 23e-4t and y 44e5t dx (?)

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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…

A: We are given the parametric equations: x=6cosθy=6sinθ We know that the derivative of  cosa=-sina and…

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

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Q: For the parametric equations: a = 12e2t and y = 23e3t %3D da (i) dt dy (ii) dt dy (iii) dx ||

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Q: You are given the parametric equations x=10−t^2 , y=t^3−12t List all of the points (x,y) where the…

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Q: Find a/dx? at t=1 by the given parametric equations. *=t2 and y=t³. d²y/dx² is! 2 is Blank 1. The…

A: Use double differentiation

Q: 2. For the parametric equation shown below, determine the value of (dy/dx) and (d²y/dx²). x = 3t? –…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: For the parametric equations: x = 12e2t and y = 36e3t dx (i) dt %3D dy (ii) dt %3D dy (iii) dx

A: Given x=12e2t and y=36e3t

Q: dy (a) Find as a function of t for the given parametric equations. dx = t- t4 -3 – 2t dy dx dy as a…

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Q: 2. For the parametric equation shown below, determine the value of (dy/dx) and (d²y/dx²). X = 3t? –…

A: Authoring guidelines: As per the authoring guidelines, we can solve only the first question. Please…

Q: d/dx(y(x)) if x and y are related by the parametric equations x = t+sint, y = t^t.

A: As we know that; The Power Law: ddxxn=nxn-1 The Product Rule: f·g'=f'·g+f·g' The Chain Rule:…

Q: For the parametric equations: x = 3e2t and y = 8et %3D dx (i) dt dy (ii) dt dy (iii) dx %3D ||

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Q: 2. For the parametric equation shown below, determine the value of (dyldx) and (d²y/dx?). x = 3t? –…

A: To find dydx& d2ydx2 using the given parametric equations.

Q: Consider the following parametric equations x=3+2t -t y=t+1 , -1<t<3 Sketch the graph of the…

A: Given query is to find the graph of the parametric equation.

Q: Find for the following parametric equations. dx2

A: First we find dy/dx  dy/dx = (dy/dt)/(dx/dt) Differentiate y with respect to t dy/dt = 2t…

Q: d'y and dx² dy 23 Find -in terms of t for each of the following parametric equations. dx a x= -3, y…

A: d. Given parametric equations: x=et  y=et-e-t To find - dydx  and d2ydx2 which  can be given as-…

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

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Q: Match the parametric equations with the correct graph. e0.9t t 0 cos(9t), y sin(9t), z e = ZA Z A 2…

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Q: find parametric equations for the given curve. . (x + 9) 2 + (y − 4) 2 = 49

A: To find the parametric equation of the given curve (x+9)2+(y-4)2=49 Given equation is in the form of…

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

A: Given: x=6 cosθ, y=6 sinθ a) dydx at the point θ=π4 can be calculated as, dydxθ=π4=dydθdxdθθ=π4…

Q: You are given the parametric equations x=10−t^2 , y=t^3−12t  List all of the points (x,y) where the…

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Q: Consider the parametric equations x t-Ssint and y = 1-cost. Which of the following represents dx…

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Q: For the parametric equations: = 41e2 and y = 27e* dx (i) dt dy (i) dt (tit) d

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

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Q: For questions 5-6 consider the parametric equations x t' and y=2-t. X = 5. When t=2, then dy %3D dx…

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Q: Find the rectangular equation for the following two parametric equations. x = 2t – 1 and y = t² + 6…

A: Given equation is  x = 2t-1            ..............(i) And y = t2+6          .............(ii) So,…

Q: dy Consider the parametric equations x = e' -1 and y=1-t. Which of the following represents dx 1-12…

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Q: s on the graph of parametric equations 2VE %3D tF (2,0), then |PF|= B. 5 C. 6 D. 7

A: Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: For the parametric equations: x= 39e and y = 16e dx (i) dt dy (ii) dt dy (iii) dx || ||

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Q: d/dx(y(x)) if x and y are related by the parametric equations x = t+sint, y = t^t

A: Given  equations x = t+sint, y = t^t

Q: Find in terms of t for each of the following parametric equations. and dx dx a x=r - 3, y =r'+1 1+3…

A: 23 b. Consider the parametric equation x=t+3t and y=t2-4t. Differentiate x=t+3t with respect to t…

Q: For the parametric equation shown below, determine the value of (dy/dx) and (d²y/dx²). X = 3t – 4t +…

A: a x = 3t2 -4t +2 y = t3 -2t2 + 2t -5  dy/dx and d2y/dx2 =? dx/dt  = 6t -4 d2x/dt2 = 6 dy/dt = 3t2…

Q: Consider the parametric equations below. x = t?, y = t3 X =

A: Given data:     The first parametric equation is: x=t2. The second parametric equation is: y=t3.…

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

A: Given query is to find derivative , double derivative and slope.

Q: Find the equation for the following parametric equation in rectangular coordinates. x = 2t + 1 y =…

A: The solution is :

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: For the parametric equations: * = 22e2t and y = 3e3* da (*) dt dy (é) dt dy (á) da

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Q: dx and 3. Given the following parametric equation: =3t^2, =t^3+4. Determine without eliminating…

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Q: If x(t) = 7 sint+ 9 and y(t) = 8 cos t + 3, eliminate the parameter to write the parametric…

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

A: To find dy/dx and d2y/dx2.   Slope is given as = dy/dx.

Q: dy d'y Find and given the parametric equations dr dr? x = t and y = 3t2 + 3t + 9. dy dz d'y dr?

A: Formula: If x and y are differentiable functions of t then dydx=dy/dtdx/dt and…

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

A: Givenx=t+1y=t2+3tt=−2

Q: Determine dæ dy and of the parametric equations dy dæ? 1. x (t) = t2 – 4t and y (t) = 2t³ – 6t - -

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Q: Given the parametric equations x = 20 + sin 20, y =1- cos 20, dy whereð is the parameter, dx

A: here option D is true

Q: d) A set of parametric equations is given as x =- cott and y=cost, 0<t<*. Find dy in terms of t, and…

A: Here a set of parametric equations is given x = 12cot t    ⋯(1)andy = cos t   ,  0&lt;t⩽ π2…

Q: Consider the parametric equations below. x = t2, y = t5

A: We have to find cartesian equation

Q: (b) Find the graph of the parametric equations: I = sin 0, y = 3 – 2 cos 20

A: Plugging values of θ, to find the corresponding values of x and y: When…

Q: Find ,Y, and of the given parametric equations dy d²y dx ' dx² d³y dx3 X = cost, y = 5 sin t in…

A: The given parametric equations,x=cost, y=5 sint

Q: For the parametric equation: x = 4t - 3 & y = t? +4, find dy/dx

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

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

A: slope is defined at dy/dxand concavity is defined at d2ydx2