A) Find B and t for the space curve r(t): = (3 sin t)i + (3 cos t)j + (t)k.

Q: A curve is defined by the parametric equations x = sint, y = 1– cos t, 0 <t< 27.

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Q: Determine A so that the curve y = 4x+ 16 can be written in parametric form as x(t) = t – 5, y(t) At…

A: Put value in given equation and simplify

Q: Determine whether the space curve given by r(t)=⟨sin(t), cos(t2), 8t⟩intersects the z-z-axis, and if…

A: We have given the space curve r(t)=⟨sin(t), cos(t/2), 8t⟩ Point of intersection of space curve and…

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

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Q: Show that the curve with parametric equations x = tcost, y = tsent, z = t is z cone z2 = x2 + y2 and…

A: We have to show that the curve with the given parametric equations is a cone with the equation…

Q: If z =t cost, y =tsint, z=t, then x² + y² = t² cos²t+t² sin² t = t² = z², so the curve lies on the…

A: Given x=tcost, y=tsint and z=t and z2=x2+y2 Substitute x=tcost, y=tsint and z=t in z2=x2+y2…

Q: Use the given graphs to sketch the parametric curve x=f(t), y= g (t). x=f(t) y =g(t) 2 2 -1 2 -2 -1…

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Q: Consider a spatial curve in three-dimensional space given in parametric form by x(t) = cos t, y(t)…

A: Introduction :

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: Convert the following parametric curve into Cartesian form: x = 3 sin t, y = 4sin t

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Q: Let C be the curve given by r(t) = (t cos 1, 1 sin 1, 1). (a) Show that C lies on the cone x² + y² =…

A: GivenParametric equation is r(t)=&lt;tcost,tsint,t&gt;To show C lies on cone x2+y2=z2.

Q: Eliminate the parameter f in the parametric equations z(t)=√t+1, y(t) = Sketch the graph of the…

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

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Q: A curve is defined by the parametric equations z (t) = e-* and y (t) = e*. What is in terms of t ? A…

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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: Let C be the parametric curve defined by tan-1t y = } In(1+ t²) where t > 0. dy (a) Find and dx dx2…

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Q: Let C be the parametric curve defined by z= tan" 120 a. Find and . Do NOT eliminate the parameter.…

A: From the given problem: x=tan-1ty=12ln1+t2,t≥0 We know that, the chain rule: dydx=dydt×dtdx

Q: The unit circle x² + y=1 can be wrriten in parametric form as x = cos(0) and y : = sino. dy and…

A: Follow the procedure given below

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

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Q: Denote that G is a parametric curve x(z) = z2-z-2 y(z) = z²-=2+z Calculate whether if G is concaving…

A: Given parametric curve G: xz=z2-z-2yz=z3-12z2+z We have to calculate whether if G is concave up or…

Q: Find the length of the parametric curve C = {(x(t),y(t)) : t E I} x(t) = cos (t) , y(t) = sin³ (t),…

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Q: Consider the curve C in R³ defined by the parametric equation c(t) V2 v2 T = (cos(t), sin(t), t).…

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Q: TRUE OR FALSE. A plane curve C defined by the parametric equations x = f(t) and y = g(t), where t is…

A: check the given statement is true or not.

Q: 3) Sketch a graph of the helix r(t) = (− cos(2ñt), 4 sin(2πt), 3t), listing the rotation direction,…

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Q: Let R(t) = (²,1-t², t) and r(t): = cost. Determine the parametric equations of the line tangent to…

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Q: Find the length of the parametric curve defined over the given interval. A) B) 3 3 2 C) D) 1

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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: 2) Draw a plane curve of the parametric function below, then prove algebraically that it has an…

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Q: Consider the space curve r(t) = (cost cos 2t, cost sin 2t, sin t). (a) Find r(t).

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Q: Find the length of the parametric curve x = e^t + e^-t, y = 5-2t on the interval [0,3]

A: Find the length of the parametric curve x = e^t + e^-t, y = 5-2t on the interval [0,3].

Q: r(4)=DTsin(i+ 34 j+ t°K 2. POINT: (1,2,1)

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Q: CHOOSE ONE. Find the length of the curve x = 4- y (a) using the parametric equations r = 2 cos t and…

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: Find T(t) and then find a set of parametric equations for the tangent line to the helix given by…

A: Consider the equation of helix given by r(t). Find the value for t , derivative at t and modulus of…

Q: Sketch the plane curve represented by the parametric equations x = 6 cos t, y = 4 sin t, π ≤ t ≤ 2π…

A: Given  x = 6 cos t, y = 4 sin t, π ≤ t ≤ 2π

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: Find the length of the curve C defined parametrically by C: r(t) = e' cos t, y(t) = e sin t, 0<t< T

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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 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: - (2e'cos t) i+ (2e'sin t)j 7K Find T, N, and k for the space curve 7k.

A: Given,           The space curve is rt=2etcosti+2etsintj+7k.To find : Find, T, N and k for the given…

Q: Find the length of the curve C defined parametrically by C: x(1) = e' cos t, y(t) = e' sin t, 0 <t <…

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Q: Find T, N, and k for the plane curve r(t) = ti+ In (cos t) j. -5<t<5. T(t) = i+Oi %3D

A: Given: r(t)=t i+lncos tj,  -π2&lt;t&lt;π2 Formulas to obtain T, N and k are given as:…

Q: Sketch the cardioid curve r = 1 + cos θ.

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Q: Find the length of the following​ three-dimensional curve. r(t)=cos t, sin t, 3t​, for 0≤t≤2

A: Given that rt =cost,sint,3t  for 0≤t≤2 find the length

Q: 1. Sketch the parametric curve x = (cos t) (1+ cos t), y= (sin t) (1 + cos t) , 0 < t < 27 .

A: we have been given the parametric curve x=(cos t)(1+cos t) and y=(sin t)(1+cos t) where 0≤t≤2π

Q: Find the length of the parametric curve defined by x=r°, y=t- for 0st<1 7.

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Q: 1. Let C be the parametric curve defined by Determine if C is concave up or concave down at…

A: Given parametric curve isx(t)=t2-t-2,y(t)=t3-12t2+tThe concavity of the curve C at the point -2, 32…

Q: Consider the parametric curve C defined by x = x (t) and %3D y = y (t). (a) How do you find the…

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

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