Curvature k and torsion of a helix C are in a constant ratio to the curvature k, of the plane curve C, obtained by projecting C on a plane perpendicular to the axis of helix i.e. they are connected by the relation t = k₁ sin a cos a k = k₁ sin² a where is the constant angle at which the helix cut the generators. and

Q: A point moves along a right-circular helix C, which is the curve of the path 7 :R → R³ given by,…

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Q: Match each parametrization with the corresponding surface. (i) (ii) (iii) (iv) (v) Answer Bank (u,…

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Q: (a) A filament is formed into a circle of radius a, centered at the origin in the plane z = 0.…

A: For Biot-Savart law dH=μ04πIdl×rr3=μ0Idlsinθ4πr2 gives the magnetic field produces at a point due to…

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A: step 1 :           Conditions to find the length of the curver = f(θ) , ∝ ≤ θ ≤ B* The curve r =f(θ)…

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A: The parametric equations of a curve in two variables are obtained when both the variables of the…

Q: For which values of t is the parametric curve x=8t, y=t+t, -0c0s ts 00 concave up? (Enter your…

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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: Question 3 (4+4pts) Let r(t) = a) Find parametric equations of the line tangent to the graph of r(t)…

A: Here I am attaching image so that you understand each and every step.

Q: Question 5. (a) Find a vector function that describes the curve of intersection of the cylinder x² +…

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Q: Graph the curve with parametric equations x = sin(t), y = 2 sin(2t), z = sin(3t). And Find the…

A: The parametric equation of the curve is: x=sint, y=2sin2t, z=sin3t. To Do:We have to graph the given…

Q: Solve: b,c and d part  (b) Give parametric equations for the tangent line to the curve C at the…

A: Given curve is r→(t)=t, t, t2 we can write the above r→(t)=ti+tj+t2k Here x(t)=t, y(t)=t, z(t)=t2…

Q: TRC Prove that CoshZ =Goshx Cosytrisinh X Siny

A: The given problem is to prove the following complex hyperbolic trigonometric identity.

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Q: Find the length of the curve T=e* 30 T<0<T given in polar coordinates. a) V10 sinh(37) b)2/10…

A: Power rule ddnxn=nxn-1 Length of a curve with equation r=fθ , a≤θ≤b is given by  L=∫abr2+[drdθ]2dθ

Q: Consider the Lissajous figure given by the set of parametric equations cos(5t), y = sin(3t). Select…

A: Topic = Derivative