What is the length of the latus rectum for the curve, (x + 3)2 + 4(y – 1)² = 4 а. 2 O b. 1 О с. 4 O d. 3

Q: Determine the length of the curve r(1) = t*i+ t°j – 5k, 4 <1 < 1. %3D Give your answer correct to…

A: Given curve is  r(t)=t4i+t6j-5k,    1≤t≤4

Q: Calculate the length of the curve č: [0; 1] → Rgiven by ( 글2 + 2t st2 + 2t + 5 (t):: HIN

A: The length of the given curve is given by using the formula of arc length in parametric equation as…

Q: Find the length of the curve. Vzti + e'j + e-tk, 0 <ts 3

A: Given the curve

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: x = 12t°, y = 18t², 0 sts v8 X= The length of the curve x = 12t°, y = 18t on 0sts V8 is

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Q: Find the length of the curve. r(t) = ( 8t, t², ), 0 <t< 1 %3D 12

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Q: Find the length of the curve y = V4t2 – 1 dt, 1<x<2 O 3 O 8 O 104 3. O 15

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

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Q: Find the length of the curve 4t2 -1 dt, y = %3D 1<x<3 8. 15 104 3 3.

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Q: Find the curvature K of the curve. r(t) = 5ti + 2tj %3D

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Q: Find, correct to four decimal places, the length of the curve of intersection of the cylinder 25x2 +…

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Q: Find the length of the curve given by ř () = (6t, 12/T, 3Int) for 1<tse. O 8e-4 O 2e-1 O 4e - 2 O…

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Q: Find the length of the curve. Vzti + e'j + e-tk, 0 sts 3

A: Given data:     The given expression is: r(t)=&lt;21/2ti+etj+e-tk&gt;. The given limits of t are:…

Q: The radius of curvature of the curve r = 4cos 20 at 0 = is %3D 4

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Q: Find the curvature of the curve r(t) = 2ti + 12t2j + t2k

A: Given vector is rt=2ti+12t2j+t2k. Compute the derivatives.…

Q: Find the length of the curve. y = 2 – 4x, 1<a< 3 O 54 3V17 O 17 O 2y17

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Q: 2tź from t = 0 tot = 1. 3 t°, y = 9. Find the length of the curve defined by x = %3D %|

A: Length ‘L’ for the curves in parametric form can be given by the formula mentioned below as. Then…

Q: r(t) = 6ti + 3/2ťj+2¢k, 0<t<1

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Q: Find the length of the curve. 2,3/2,0 st s9 x= 4t, y 3 61 242 2 3 O 2. seçenek 4. seçenek 122 61 3 3…

A: We can find the arc length as below

Q: Find, correct to four decimal places, the length of the curve of intersection of the cylinder 9x2 +…

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Q: C3. Find the length of the of the curve x= 1 from y = 1 to y = 2 %3D 4 8y?

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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: Evaluate ∫C x ds, where C is the parabolic curve x = t, y = t2, from (0, 0) to (2, 4).

A: Given: Parabolic curve x=t, y=t2 from (0,0) to (2,4)

Q: Find the length of the curve. x=(y - 1) 3/2 from y = 1 to y = 4 O 7 O 10 21 2 O 1

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

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Q: The length of the curve that results from the intersection of r = 1,0 <0 < T,0 < ¢ < 0.5n, with 0 =…

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Q: Find the cylinder surface determined by Curve 4x?+9g? -36=0 and d= ( 1, -1. 32 line.

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Q: A satellite (S) in orbit around the Earth is sending two signals that are tangent to Earth at points…

A: Given that , mACB⏜=208° mAB⏜=152° ∠S=?

Q: Find the curvature of the plane curve y=2t^4 at the point t=2 κ(2)=

A: The given curve y=2t4

Q: Find the length of the curve. Vzti + etj + e-tk, Osts 3

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Q: The length of the curve y = (2+ 2x )3/2 between x=0 and x=2 is O 41/3 O 45/2 O 43/2 O 47/3 49/6 ООО…

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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: 1 1-Зу?, /1 – 3y, x = 0.05 < у < 0.2 L = %3D

A: As per the guidelines in case of multiple questions I am.supposed to do the first problem. Kindly…

Q: Find the length of the indicated portion of the curve. r(t) = (1 + 4t)i + (1 + 8t)j + (2 – 2t)k, -…

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Q: Find the length of the curve. x = (v - 1) 3/2 from y = 16 to y = 25 O 4 61 O IK

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Q: Find the length of the curve r(t) (1,t²,), 0sts1 %3D «3 Ost<1

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Q: Find the length of the curve y- v2- 2,0 <z<1 O a. b. V dz O. So Vi 2-2z od. fo dz 2+2 2-2z

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Find the length of the curve 24xy = y + 48, Select one: 85/85-8 243 80/10-13/T3 27 O None of these

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Q: What is the length of the curve I=1+32, y = 4+2t, (0 <t<1) ?

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Q: Evaluate + 5x)dx + (ye* – 3y²)dy where C is the boundary of the curve given below. -2

A: Detailed explanation mentioned below

Q: Find the torsion for the curve r= (3sin t i + 3costj+ 4tk)

A: To find the torsion for the curve r=3sint i+3cost j+4tk

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

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Q: The value of f. ydx + zdy + xdz where C is the curve x = y = z = 2t? from t = 0 to t = 1 is

A: Here we have to find the value of ∫cydx+zdy+xdz where C is the curve x=y=z=2t2 from t=0 to t=1.

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

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Q: s to the curve y = x* at the %3D

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Q: Determine the length of the curve r(t) = 4sin(3t)i + 3tj + 4cos(3t)k, 0 <t < -. 2 Give your answer…

A: Arclegth of the position vector

Q: ² fx ds, where C is с t a. the straight line segment x = t. y = from (0,0) to (16,4) b. the…

A: