Let z = 3t, y = - 2 + 18t. dy as a function of t, then find the slope of the parametric curve at t = 6. da Determine W. dz 业 d'y as a function of t, then find the concavity of the parametric curve at t = 6. Determine dz? 3D

Q: Given the the parametric curve Į æ(t) = ecost y(t) = t³ – 243t

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Q: Consider the parametric curve C: x 1+cost, y= -3+2sint, 0stS (1) Sketch the curve and indicate the…

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Q: Consider the parametric curve given by the equations x(t) = t + 30t – 8 y(t) = t2 + 30t + 20 How…

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Q: Given the parametric equation x = t+ lnt and y = t - Int %3D dy d²y Find and dx da? Find the point C…

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Q: Use the graphs of x = f(t) and y = g(t) to sketch the parametric curve x = f(t), y = g(t). Indicate…

A: We can solve this problem by plotting some points on the curve of y vs x by taking some specific…

Q: Let x = 9t?, y = 7t° – 8t?. d²y as a function of t, then find the concavity to the parametric curve…

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Q: 2. Consider the parametric curve r = t + 1, y = t - t. dy (a) Find d.r dy (b) Find da?

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Q: Use the given graphs of x = f(t) and y = g(t) to sketch the corresponding parametric curve in the…

A: It is a line joining (0,1) and (1,0) So the equation of the line is:

Q: Find the equation for the line tangent to the parametric curve: x = t^3 - 9t y = 9t^2 - t^4   at…

A: Find slope and then use equation of tangent line

Q: Consider the parametric equations x(t) = 1 + 3t2, y(t) = 4 + 21³, -1 <t <1. • What is the length of…

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Q: Consider the parametric curve given by the equations x(t) = t + 2t – 34 y(t) = t2 + 2t – 25 How many…

A: And: 8√2

Q: Find the exact length of the parametric curve x =1+3t², y = 4+2r°, 0<t<2.

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Q: Find the equation for the line tangent to the parametric curve: t3 – 25t 25t2 – 14 at the points…

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Q: Consider the following parametric curve. Answer parts a and b. x = 4t, y = t°; t= - 1 dy in terms of…

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Q: Sketch the curve x = 3sin?t, y = 4cos?t (0<t <÷) by eliminating the parameter, %3D and indicate the…

A: Introduction: When a function y=fx can be expressed as x≡xt,y≡yt by introducing a new variable t,…

Q: : Find the length of the following parametric curve. x = 6 + 1", y = 1 + 7t21/2, 0 st s 2.

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Q: Consider the parametric curve C that is defined by C: x=t^3, y=t^2+t, −1≤t≤3. (a). Find the…

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Q: Find of the parametric curve x = sect, y = tant, at t = dx? Select one: -3V3 -1 3V3 3y3 1 3v3 O none

A: Here we find the double derivatives value at t=π/3

Q: Consider the parametric curve defined by 1 a(t) %3D y(t) = t² || What is the slope of the line…

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Q: Given the parametric curve and value of t x(t) = Vf, y(t) = 2t + 4 dy at t = 4 dx Find dy help…

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Q: Find the length of the curve defined by the parametric equations t, y = 5 In((t/6)? – 1) I = from t…

A: Given, x = 56t , y = 5lnt62-1 = 5lnt2-36-5ln(36)and 7≤t≤10

Q: x²y³z ds, where C is the curve with parametric equations x = e -t cos(4t), y = e-t sin(4t), z = et,…

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Q: Assuming that the curve traces out exactly once, determine the length of the curve given by the…

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Q: consider the parametric curve x=t2 , y=9t-t3 . find dy/dx at t=2.

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Q: Let x = 2t, y = - 4t° + 36t?. y = dy as a function of t, then find the slope of the parametric curve…

A: Please refer to the image below.

Q: Find the equation for the line tangent to the parametric curve: t3 – 25t 25t² – t4 at the points…

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Q: Consider the parametric curve C that is defined by C: x=t^3, y=t^2+t, −1≤t≤3. (b) Is the curve…

A: Consider the parametric curve C that is defined byC: x=t^3, y=t^2+t, −1≤t≤3. (b) Is the curve…

Q: Find an equation y = f (x) for the parametric curveand compute dy/dx by differentiating f (x). c(t)…

A: To find the equation for the parametric curve

Q: Find the exact length of the given parametric curve. X = = 8t³, y = 12t², 0 <t< 2

A: Consider the parametric equations

Q: Find the length of the parametric curve: x = 2t + 1; y = t? – 3,0 <t < 5

A: Given that: x=2t+1,  y=t2-3,0≤t≤5To  calculate   dxdt  and   dydt,dxdt=ddt2t+1=2dydt=ddtt2-3=2t

Q: Consider the plane curve given by the parametric equations x = t + 22t – 23 y = t2 + 22t – 5 -- What…

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Q: (ь) Find the value of a for which the tangent to the parametric curve = 4t° +t? + at, y = t – 6 at t…

A: Given the two parametric curves x=4t3+t2+αt   and y=t4-6. We need to  find the value of α for which…

Q: dy at t = of the parametric curve: x = csct, y cot. dx 7C Find Select one: V3 21 -V3 none 2.

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Q: Consider the curve described parametrically by X = 3cos(t) , y = 3sin(t) , 0<t< 57/4 tch the curve,…

A: Given parametric Curve x= 3cos(t), y=3 sin(t), 0≤t≤5π4

Q: Let C1 be the curve with parametric equations x = cost, y = sint – t, where t e [0, 5]. (a) Find the…

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Q: a) Find the are length of the parametric curve x = B(t. sint), y = B(1+ cost), in the range 0 sts,…

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Q: To calculate the derivative dy/dx of the parametric equations x(t)= 3cost and y(t)=3sin t for…

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Q: Find the length of the parametric curve I = cos(t) y = 1 + sin(t) from t = 0 to t =

A: Given- x=cost and y=1+sint To Find- The length of the parametric curve from t=0 to t=π. Identity…

Q: Find length of the curve described by the parametric equations x = T sin t, y = r cost, e <t< T. А.…

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Q: Find the length of the parametric curve x = 2t + 1, y = 3 + 2tž, 0 < t <%.

A: Find the Length of the curve

Q: Find the length of the parametric curve C {(x(t), y(t)) : t E 1} x(t) 4cos(t), y(t) = 4sin(t), with…

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Q: Find the equation for the line tangent to the parametric curve: at the points where t = 5 and t =…

A: Solution is given below:

Q: Find an equation of the tangent line of the parametric curve, I = 1+÷, y=t³ –t² +3,

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Q: Find the length of the parametric curve defined over the given interval. A) B) 64 37 z=t+V = 6. C)…

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Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

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Q: The curve C have the parametric equation: x(t) = t² + 1 and y(t) = t³ – 1 a) Make a sketch of curve…

A: In the Cartesian coordinate system, the parametric equations use a third variable(usually "t") to…

Q: A curve is defined by the parametric equations: x(t) = e' cost, y(t) = e' sint dy d²y Determine and…

A: The tangent line to the curve in parametric form is given as follows

Q: Consider the parametric curve given by equations:  x(t)= t2 + 30t - 21 y(t)= t2 + 30t - 37  How…

A: At t = 0, determine x(t) and y(t). x0=02+300-21=0+0-21=-21   y0=02+300-37=0+0-37=-37   Thus, the…

Q: and y =- for tz 0. A curve C is defined by the parametric equations x= Vi +1 t + 1 dy (a) Find dx in…

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Q: Given the parametric curve x(t) = 3t + In(t), y(t) = 3t – In(t)

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