Calculate the curvature of the curve defined by r(t)=9cos(4t)i+9sin(4t)j. Give the answer with 4 decimal places of precision.

Q: Find the curvature k of the curve C : 16 =1 at the point (0, 3)

A: 1. convert the equation into parametric form 2. use formula for curvature written below

Q: Find the curvature of the plane curve Y = 4t* at the point t = 1. K(1) =

A: que: Curvature of a plane curve y = f(x) is given by K = y||(x)|(1+(y1(x))2)32 Here y = 4t4

Q: Find the curvature and radius of curvature of the plane curve at the given value of x . y = x −4/ x,…

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Q: Find the curvature of the plane curve at the pointindicated. y = e^t , t = 3

A: y=et,  t=3 Differentiating with respect to t, we get dydt=et Again differentiating with respect to…

Q: Find the curvature and radius of curvature of the plane curve at the given value of x.

A: We have,   It is known that radius of curvature is given as, Here K is curvature of the curve.…

Q: Find the radius of curvature of the parabola y² = 4px at (0, 0).

A: Given that the parabola y² = 4px  To Find the radius of curvature of the given parabola at (0,0).…

Q: What is the curvature of the path of the motion at t=1

A: Since velocity is given we need to calculate  r''(t) only at t=1

Q: Find the curvature of the curve r(t) =

A: This question can be solved by applying the formula for curvature.

Q: Find the curvature of the plane curve at the point indicated. y = t^n, t = 1

A: First find the first and second derivative of the given curve…

Q: Find the curvature K of the curve at the point P. r(t) = 4ti + 3tj, P(-4, 3)

A: Given,          rt=4t i+3t2 j , P-4,3We know that,           The curvature K of the curve is given…

Q: Find the curvature of the curve given by r(t) = (2 cos t, t, 2 sint)

A: The given curve is rt=2cost, t, 2sint. In order to find the curvature of this curve, first find its…

Q: Find the curvature of the curve r(t) = 4ti + 3 cos tj + 3 sin tk .

A: curve r(t) = 4ti + 3 cos tj + 3 sin tk . We need to find the curvature of the given curve.

Q: Find the curvature K of the curve at the point P. r(t) = 2ti + 5t´j, P(-2, 5) K =

A:

Q: Find the curvature of the curve defined by F (+) = (5 cos(t), 6 sin(t)) at t = 2

A: κ=  r'(t)→× r"(t)→r'(t)→3 We have to just evaluate for given r(t)

Q: Find the curvature of the curve given by r(t) = 2ti + t2j −( 1/ 3) t3k.

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Q: Find the curvature and radius of curvature of the plane curve at the given value of x. y = x - 32 ,…

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Q: Find the curvature of the curve r(t) = eti + 4tj at the point P (1, 0) .

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Q: Find the curvature of the curve r(t) = (2 + 5t, 5 – t, 4 – 2t) at the point t = - 3. Give your…

A: We have to find the curvature of the curve r→(t)=2+5t, 5-t, 4-2t at the point t=-3 .

Q: Find the curvature of the curve r (t) = (4 cos(3t), 4 sin(3t), 4t) at the point t = 0 %3D Give your…

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Q: Find the curvature of he curve :  at y = (x^3)/3 at x=1 a. 1/sqrt(2)                       b.…

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Q: Find the curvature of the curve r (t) (2 cos(5t), 2 sin(5t), 4t) at the point t = 0 CoS Give your…

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Q: Find the curvature and radius of curvature of the plane curve at the given value of x. y = 9x 4…

A: Given curve is, y=9x-4x Differentiating this with respect to x we get,  dydx=9-4ddx(1x)⇒dydx=9+4x2…

Q: Find the curvature K of the curve at the point . r(t) = 2ti + 4tj, P(-2, 4) K =

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Q: Let C be the curve represented by Ŕ(t) = (cos 2t, 2√3t, 5 — sin 2t). - ㅠ Determine the curvature of…

A: To find out the curvature of C.

Q: Pind the curvature x of the curve given by 7(()- (V2)i+ (e)j+(e)k, at the point P(0, 1, 1),

A: Curvature K = |r' x r"|/|r'|^3

Q: 2. Find the radius of curvature for the curve r*cos20 %3D 1.

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Q: Find the curvature of the curve 7(t) = (3 cos(4t), 3 sin(4t), 4t) at the pointt = 0 Give your answer…

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Q: Find the curvature of the curve r(t) = et cos ti + et sin tj + etk at the point P(1, 0, 1) .

A: Given curve is rt=etcosti+etsintj+etk.…

Q: Find the curvature of the plane curve at the pointindicated. y = t^4, t = 2

A: By Curvature we mean that to which extent any plane or graphical function is curved along onto a…

Q: Find the curvature of the curve r (t) = (- 5+ 4t, 1+ 3t, 5t) at the point t - 7.

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Q: find the curvature of the plane curve at the point indicated.  y = tn, t = 1

A: Given y=tn

Q: Find the curvature of the curve r(t) = 3ti + 2t2j at the point P(−3, 2) .

A: rt=3ti+2t2j Comparing with rt=xi+yj, we get x=3t & y=2t2 Now put x=-3 & y=2, we get -3=3t…

Q: Find the curvature of the curver(t) = (4 cos(t), 4 sin(t), 5t) at the point t = 0 %3D Give your…

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Q: Find the curvature k of the curve given by r(t) = (2t²,t, ¿ť²)

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Q: Consider the curve given by the equation y2+x3=0. Find its curvature at the point (−1,1).

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Q: Find the curvature of the curve given by r(t)=(4sint, 4, 4cost)

A: Given that : r(t)=4sint, 4, 4cost Therefore, r'(t)⇀=4cost, 0, -4sint. Therefore,…

Q: Find the curvature of the curve. r(t) =<2t, - 3sin t, 3cost)

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Q: Find the curvature of the curve r(t) = 2ti + 5 cos tj + 5 sin tk

A: The given curve is rt=2ti+5cost j +5 sint k. This implies that, r't=2 i-5sint j +5 cost kr''t=0…

Q: Find the curvature and radius of curvature of the plane curve at the given value of x. 32 y = 9x, x…

A: Given that Y= 9x - 32/x ; x= 4. And we find curvature and curvature of the plane at give x value.…

Q: Find the curvature and radius of curvature of the plane curve at the given value of x. y = x3, x = 2

A: Consider the following equation of curve: y=x3 Differentiate y with respect to x: dydx=ddxx3y'=3x2…

Q: Find the curvature of the curve r(t) = 3ti + 2tj

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Q: Find the curvature k of the curve C: 16 + =1 at the point (0, 3)

A: To find the curvature of the curve at the point (0,3).

Q: Find the curvature of the plane curve y = 4t³ at the point t = 2.

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Q: Find the curvature of the curve 7(t) = (3 cos(4t), 3 sin(4t), 4t) at the point t %3D Give your…

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Q: At what point does the curve have maximum curvature? y = 7 In(x) (x, y) = What happens to the…

A: Given,              y = 7 ln(x)