12. Given: x = 2t - 1 and y = 3t + 1, a) Construct a table of values, showing t, x, and y. b) Sketch the graph and indicate with an arrow the direction in which the curve is traced ast increases. Find dy/d c) Eliminate the parameter to find a Cartesian equation of the curve.

Q: Find the exact length of the curve. x = et - 4t, y = 8et/2, 0≤t≤2

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Q: A Curve a with aca) = (2,4,4), 2e2) = (0 ,2 54). %3D %3D Find Kea), B)

A: We will find out the required value for given curve.

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: 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: Evaluate x ds, where C is a. the straight line segment x =t, y =. from (0,0) to (6,2) b. the…

A: We need to evaluate ∫Cx ds

Q: Sketch the curve by eliminating the parameter, and indicate the direction of increasing tat t-0. =…

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Q: The cartesian equation of the curve x = VE .y 1-t is :

A: The characterstics eqaution of the curve is

Q: sketch the given curves together in the appropriatecoordinate plane, and label each curve with its…

A: Draw graphs of y=ex and y=1ex

Q: Consider the following. x = In(t), y = Vt, t2 81 (a) Eliminate the parameter to find a Cartesian…

A: Given parametric equation is  x=lnt, y=t,       t≥81

Q: Do the curves ri(t) = (t² + 3, t+1, t² – 5) and rž(s) = (4s, 2s – 2, s + 1) intersect? If so, at whi…

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Q: Find the distance between the point (p, 4p) and the parabola y? = 2px, where p is a fixed positive…

A: let the point on parabola be A= (x, y)  B = (p, 4p) Thus,  AB = x-p2+y-4p2 but parabola is y2=2px…

Q: Find the exact length of the curve. x = et – t, y = 4et/2, 0st < 5

A: Find the length of curve:

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

A:

Q: 1) The maximum distance from the origin of the xy plane to the circle described by (x – 12)? + (y –…

A: given equation of circlex-122+y-62=16 As per our guideline we supposed to answer only first question…

Q: Find the length of the curve x = 5-t, for 1 < t < 2. length = y = 3-t, z = 3t 5,

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Q: Find all hyperbolic lines that passes through i +1 and parallel to the y-axis.

A: Find all hyperbolic lines that passes through i+1 and parallelto the y-axis.

Q: Sketch the curve represented by the equations x = 1/ √(t + 1) and y = t/(t+1) , t &gt; −1 by…

A: The given parametric equations are: The given equations are in the form of a parameter t, whose…

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: Evaluate x ds, where Cis с a. the straight line segment x = t, y = = 737₁1 3' b. the parabolic curve…

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Q: Find the exact length of the curve. 23/2, Osxs 6

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Q: If a curve C is given by r(t) = ⟨t, t2⟩ , what is | r'(t) | ?

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Q: X bn t-1),y=2t-1for tin [.0ol,10]; windowi I-5-S]° by E2,20]

A: We graph the curve as

Q: 7. Eliminate the parameter to find a Cartesian equation of the curve: x = Vt, y = 5 – 3t

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

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Q: Explain the steps required to find the length of a curve x = g1y2 between y = c and y = d.

A: It is given that x=gx for c≤y≤d.

Q: Sketch the curve r = 1/2 θ (the spiral of Archimedes) for θ between 0 and 2π by plotting the points…

A: The curve is  r=12θ ;0,2π The table with the values  θ 0 π4 π2 π 3π2 7π4 2π r 0 0.392 0.785…

Q: Find the 0lar eauatiDo for the curve represented by the given Cartesian euation.

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Q: O1- The straight-line AB of true length 12 cms, is inclined 20 ° to H.P., and having the following…

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Q: I have taken the integral of A, and I'm towards the end of finding B but I'm confused on how I use…

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Q: Find the exact length of the curve. x = et − t,    y = 4et/2,    0 ≤ t ≤ 5

A: We will use arc length formula to solve this questions

Q: Find the exact length of the curve.42. x = et − t, y = 4et/2 , 0 ≤ t ≤ 2

A: Given eqn : x=et-t,  y=4et/2 ,  0≤t≤2 So, we use dxdt=et-1,  dydt=2et2   Length of the curve =…

Q: Prove that the curve given by the equations x=R(cost+tsint),y=R(sint−tcost) is the involute of the…

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Q: Draw a diagram showing two perpendicular lines that intersecton the -axis and are both tangent to…

A: The given parabola equation , y=x2. To draw two perpendicular lines that intersect on the axis and…

Q: Find the exact length of the curve. x = et - 4t, y = 8et/2, 0 sts 4

A: We find dx/dt and dy/dt

Q: Eliminate the parameter t to find a Cartesian equation of a curve. x = 1 + 3t,  y = 2-t^2

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

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Q: Consider the implicitly defined curve xy? +3x2 = 4. %3D Verify that the point (1, 1) is on the…

A: Consider the following curve: xy2+3x2=4 Substitute x=1 and y=1 in the above curve:…

Q: 2. Sketch the plane curve by plotting points then indicate the orientation of the curve. x = t2 – 4…

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Q: The siope of a line tangere to the curve y=fx)at(3 4) 0f iz cists) equais

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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: Explain how to find the length of the curve                         r(t) = ⟨ƒ(t), g(t), h(t)⟩, for a…

A: To Determine: Explain how to find the length of the curve Given: we have rt=&lt;f(t),g(t),h(t)&gt;…

Q: Evaluate S,lz| dz for the curves C1 and C2, both of which begin at a = 1 and end at b = -1. The…

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Q: Find the polar eauation for the curve represented by the given Cartesian eavation. Dy=-4x² 1.

A: We need to find polar equation.

Q: Find the exact length of the curve. y = (1 + x*,3/2, OSxS 5

A: The curve is y=231+x232 , 0≤x≤5

Q: The orthogonal trajectory of the 1-parameter family of curves, y = cr will be given by: r² + y? = c…

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Q: Sketch the curve r = 3 sin 20. a b Show that its Cartesian equation is (x² + y² )° =36x²y²,«

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Q: (2) find the (x,y) coordinates of all points of intersection ot the curves.

A: b.(2) Given the polar equation of two cardioids r=1+sinθ,r=1-cosθ. To find the points of…

Q: Find T, N, and B for the curve r(t) = (14t, 14t, e') at (0,0, 1). Hint: After finding T', plug in…

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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