Find the length of the curve. r(t) = cos(6t) i + sin(6t)j + 6In(cos(t)) k, 0stsa/4

Q: Find the arclength of the curve z 9 cos(9t), y = 9 sin(9t) with 0 <t< 36

A:

Q: 4) Consider the curve given by: cos(xy) = x(y – 7) – 1 a) dy Find y' xp dy dx b) Find an equation of…

A:

Q: Find the length L of the curve R(t) = e* cos(3t) i + e* sin(3t) j + 3e*k over the interval [1, 5]. L…

A: given: Rt=etcos3ti+etsin3tj+3etk interval 1,5

Q: 2. Let y be the curve in R° given by t (t, 2 cos t, 2 sin t) for 0 < t< 47. Compute y? ds

A:

Q: = V4 cos" : – 1, y = 10 < x < 30

A:

Q: Find the exact length of the curve. 1x2 - In(x), 1< x s 8 у3

A: Hello! Thank you for the question. We will answer the first question since the exact one wasn’t…

Q: 2. Find the length of the curve 0<t< 2n. r(t) e'i + e' sin 2tj + e' cos 2tk,

A: From the given problem :   rt=eti+etsin2tj+etcos2tk   So,   x=et, y=etsin2t , z=etcos2t .   As we…

Q: Find the speed at t = π/4 of a particle whose position at time tseconds is c(t) = (sin 4t, cos 3t)

A:

Q: Plot the curve c(t) = (cos t, esin t ) for 0 ≤ t ≤ 2π

A: The plot of the curve for t within 0 to 2pi is shown in figure below.

Q: Compute sin z dz , where a is the piece of the parabola with equation y= a?, which lies between the…

A:

Q: Find the lengths of the curves r(t) = (2 cos t)i + (2 sin t)j + t2k, 0 ≤ t ≤ π&gt;4

A: Given r(t)=2costi+2sintj+2tk We need to find the length of the curvature . The length of the curve…

Q: Find the length of the given curve: r(t) = (-3t, -3 sint,-3 cos t) where-3 sts 5.

A:

Q: Find the lengths of the curves x = cos t, y = t + sin t, 0 … t … pi

A: Solution:Given   x= cos t,      y= t+sin t,   0≤t≤πFormula:Lenght=∫dxdx2+dydt2dt1+cos 2x=2 cos2…

Q: Find T, Ñ and B for the curve 7 (t) = (5 cos(4t), 5 sin(4t), 2t) at the point t = 0 Give your…

A: the given curve is  r→(t)=5cos(4t),5sin(4t),2twe have to find a) T→(t)=unit tangent vector at t=0b)…

Q: For the implicitly defined curve: cos(7y) 5y sin(x) dy (e.g., find y' ). dx a. Find a formula for dy…

A:

Q: 2. Find the arc length of the curve y= from x-2 to xD3 16 2x2

A: The solution is given as

Q: Find a path c(t) that traces the parabolic arc y = x2 from (0, 0) to (3, 9) for 0 ≤ t ≤ 1.

A: Given parabolic arc y=x2 from 0,0 to 3,9 for 0≤t≤1. The path ct that traces the parabolic arc has to…

Q: Find the exact length of the curve. 43. x = t sin t , y = t cos t , 0 ≤ t ≤ 1

A:

Q: r = 2 cos 0,0 <o <n. 2 L = S°. dr r2 + de de.

A: Use the formula given to find length of curve.

Q: Find the length of the curve 7(t) = (cos(4t), sin(4t), 5t) for – 8 <t< 1 Give your answer to two…

A: use the arc length formula for finding length.

Q: A) Find the distance traveled by a particle with position (x, y) as t varies in the given time…

A:

Q: Find the lengths of the following curves: e. x = 8cost + 8t sint and y = 8 sin t – 8t cos t, 0stsn/2

A:

Q: Find the length of the curve x=1+2sin at, y=3–2 cos at, 0<t<l

A:

Q: 2. Find the length of the curve r(t) = e'i + e' sin 2tj + e' cos 2tk, 0st< 2n.

A:

Q: Let C be the curve parameterized by Y: [0, b] R³, y(s) = (12 cos(s²), 12 sin(s), 9 s²). Find b>0…

A: The given problem is to find the value of b for which the given length of curve of the given…

Q: Find the length of the curve y = ln (cos x), 0&lt;= x&lt;= pai/3

A:

Q: Find the length of the curve. x = cos t y = sint 0 <t< 2n

A:

Q: Consider the curve where a =0 (a) Compute(t) at t = [0, +∞). (b) Find the tangent line at the point…

A:

Q: 1. Find the length of the curve r(t) = (sin 2t, cos! cos 2t) from t =0 to t 2n. %3D II

A: 1)- Given: r→t=sin 2t, cos 2t from t=0 to t=2π. The objective is to determine the length of the…

Q: A glider is soaring upward along the helix r(t) = (cos t)i + (sin t)j + tk. How long is the glider’s…

A: Given: The path of glider as r→t=cost i^+sint j^+t k^, To find: The length of the glider's path from…

Q: Q4: Find the length of the curve r = 4 sin 0

A:

Q: A curve is written parametrically with x and y defined as functions of t: x=t2 +1, y = 4r° +3. Find…

A: Take the derivative of x and y with respect to t then use the formula for the arc length.

Q: from x-2 to x-3 2. Find the arc length of the curve y = 16

A:

Q: Find dy/dx and d2y/dx2. x = cos(2t),    y = cos(t),    0 &lt; t &lt; π   For which values of t is…

A:

Q: Given the parametric equation x=(4/5)t5/2 and y= (1/4)t4-t find the arc length of the curve on the…

A:

Q: Find T, Ñ and B for the curve 7(t) = (2 cos(4t), 2 sin(4t), 5t) at the point t = 0 Give your answers…

A:

Q: Find T, Ñ and B for the curve 7 (t) = (3 cos(3t), 3 sin(3t), 5t) at the point t = 0 Give your…

A: Space Curves and T, N, B vectors The unit tangent vector T, the unit normal vector N and the unit…

Q: Find the length of the curve. r(t) = cos(3t) i + sin(3t)j + 3 In(cos(t)) k, 0 <t< n/4 %3D

A: Find the length of the curve:…

Q: Determines the length of the curve in the indicated interval x = 3 sin t+ 3t, y = 3cos t, 0stsm O 12…

A: Given curve is x=3sint+3t and y=3cost, 0≤t≤π. We have to determine the length of the curve on the…

Q: Use the formula below to find the length of the curve defined by the equation x= cos^2 t , y = sin^2…

A:

Q: Find the exact length of the curve. y = (x-x2)1/2 + sin-1((x1/2))

A: The arc length formula is given as

Q: Find the length of the curve r(t) = (e* cos t, et sin t , et), – In 4 <t<0.

A:

Q: Find the length of the curve. x- 5 sin t+ 5t, y= 5 cos t, 0 st< O A. 5T O B. 20 O C. 10 O D. 30

A:

Q: Find the arc length of the curve 7(t) = (2t/2, cos 2t , sin 2t) for 0<t <1

A: Differentiate f(t), g(t) and h(t) with respect to t, to obtain the tangent vector r→'t. rt=2t32,…

Q: Q2: Find the slope of the curve r = -1 + cos 0 0-T/2

A:

Q: Find the length L of the curve R(t) = 4 cos(5t) i – 4sin(5t) j + tk over the interval [3, 6]. L =…

A: Given:

Q: Find the length of the curve defined by the following function for 0 <t < 2n. 7(t) = (– cos 2t)i +…

A:

Q: 9. Find the length of the curve: r = 1+ cos(28),0 < 0 < 2m

A:

Q: Q1. Find the length of the of the curve y = In(cos x) from x = 0 to x = . %3D

A: Explanation of the solution is given below...