29. If you unwind thread from a stationary circular spool, keeping the thread taut at all times, then the endpoint traces a curve C called the involute of the circle (Figure 9). Observe that PQ has length RO. Show that C is parametrized by c(0) = (R(cos 0+0 sin 0), R(sin 0 – 0 cos 0) Then find the length of the involute for 0 <0 < 2n. P=(x. y) FIGURE 9 Involute of a circle.

Q: 4. Use the Arc Length in Parametric Form formula to find the arc length of the curve with the given…

A: Given parametric equations, x= 3sint ,   y=3cost,     0≤t≤π3

Q: 3. What is the length of the curve r = cos3 (-) where 0 < 0 <: sos

A: See the attachment

Q: To illustrate thefact that the numbers we get for length do not depend on the waywe parametrize our…

A:

Q: Consider the following parametric curve. x = sin(8t) + cos(t), y = cos(8t) - sin(t) Find dy dx dy dx…

A:

Q: Consider the curve C parametrized by (x, y) = (3 cos (-10t), 3 sin(-10t)), for –x/2sts a/2 Then C is…

A:

Q: Identify the length of the arc having parametric equations x = t3 and y = 2t2 from t = -2 to t = 0

A:

Q: 4. Find the length of arc of the curve x3 + y3 = 1 in the first quadrant from the point where x = to…

A: If a function f(x) is defined over an interval [a,b], then the formula for arc length is: Formulae…

Q: Chapter 12, Section 12.3, Question 006 Find the arc length of the parametric curve. x = 6 cos t, y =…

A:

Q: 3. What is the length of the curve r = cos3 (-) where 0 < 0 <- 4

A:

Q: Find the arc length of the curve y = from x=2 to x=3 2x2 16

A: Use arc length formula

Q: Find the arc length of y^3 + y = x^2 + 6x on the interval [−5, −1]

A: “Since you have asked multiple questions, we will solve the first question for you(Only finding arc…

Q: 9) Find the area of the surface generated by rotating about the y-axis y = x' between (0,0) and…

A:

Q: (a) (., Consider the curve defined by ry = In(3x + sin(y)). Use implicit differenti- ation to find…

A: Consider the given equation of the curve, xy=ln3x+siny Use the implicit differentiation,…

Q: Find all of the points where the curve r = 2 cos (θ/3) intersects thecircle of radius √2 centered at…

A: For the point of intersection: We need to solve the two equations simultaneously: r = 2 cos (θ/3)…

Q: 3. Find the exact arc length of the curve I = y+}y2 from y = 1 to y = 4.

A:

Q: Find the arclength of the curve x= 4cos(6t), y= 4sin(6t) with 0 less than or equal to t less than or…

A:

Q: 2 4. Find the length of arc of the curve x3 + y3 = 1 in the first quadrant from the point where x =…

A:

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: 6- Find the avea of the Surface of revolution genetaled by revalving the x-axis the arc abaut from…

A: To find - Find the area of the surface of revolution generated by revolving about the x-axis the arc…

Q: Consider the parametric curve: x = ln (8t) y = 5t³ Which integral gives the arc length of the curve…

A:

Q: 4 Find the arc length of the curve the interval 2≤+ ≤ 5 3 given parametrically by x= 3 + ² y = + ²,²…

A: To find out the arc length of the curve.

Q: 2. What is the arc length of the polar curve r = 1- sin 0 for 0 <0< <5? 2 (a) 2(v2 – 1) 2 - V2 2/2…

A:

Q: What is the arc length of the curve x = (1/2)y2 - (1/4)ln y from y = 1 to y = e?

A: Here, we have given x is a function of y. So, we will use the following formula for finding the arc…

Q: Set up the definite integral(s) equal to the arc length of the curved defined by the parametric…

A: Use the formula of arc length in parametric form and simplify.

Q: Find the arc length of the curve x = a cos3θ, y=a sin3θ in [0,2π].

A: The arc length formula for the parametric curve on the interval [a,b] is given by: Hence compute…

Q: Find the arclength of the curve r = 5 cos(6t), y = 5 sin(6t) with 0 <t<. %3D

A:

Q: 1 Consider the curve defined by the parametric equations x = ÷ť & y=÷ť for 2<t<3 2 3 Determine the…

A: take derivative

Q: 3 The arc length of the portion of the curve y=x 2 with 0<x<4 is

A: I have append the formula used to find arc length in the solution part.

Q: 3. Find the arc length of the curve 24xy y+ 48 from y-2 to y-4 1 to from

A:

Q: 4.2. Calculate the arc length of the cardioid given by r = a(1 – cos 0) -

A: The cardioid is symmetrical in nature and ranges from θ=0 to θ=π as a half figure. We can also…

Q: The arc length of the curve r= cos 30 with 0<0 < is T V(sin 30)² + (cos 30)² do 0. o" V-9(sin 30)² +…

A: Given that: r=cos3θand  0≤θ≤π

Q: 2 4. Find the length of arc of the curve x3 + y = 1 in the first quadrant from the point where x =…

A: Let's find arc length of given curve in first quadrant.

Q: Find the arc length of the parabola y² = x from (0,0) to (1, 1). (Note that y² = x is not the same…

A: Length

Q: ..... The area of the surface generated by revolving the curve x = 1 cos (2t), y = 7+ -sin (2t) on…

A: Follow 2nd and 3rd step.

Q: A curve has parametric equations x = 2 sin t ,y = cos (2t) + 2 sin t for −π/2≤ t ≤−π/2 . Find out…

A: Given : parametric equations x = 2 sin t , y = cos (2t) + 2 sin t for −π/2 ≤ t ≤ π/2     Note :…

Q: 1-Find the exact arc length of the parametric curve without eliminating the parameter X-cos t + t…

A:

Q: Consider the curve C parametrized by(x, y) = (5 cos (−12t), 5 sin(−12t)), for −π/2 ≤ t ≤ π/2 What is…

A:

Q: Show that the arclength of the graph of y = sin x on the interval [0, 27] is equal to the circum-…

A: The length of the smooth curve ζ : [ 0 , 2π] →ℝ2  is given by I(ξ) = ∫02π ξ'(t)  dt

Q: Find the length of the following three-dimensional curve. r(t) = (6 + 3t,5 – 3t, - 1+2t), for 1sts6…

A: The length of the curve rt=ft,gt,ht in the interval a≤t≤b is given by L=∫abf't2+g't2+h't2dt. The…

Q: Show that the arc length of the graph of y = sin x on the interval [0, 2π] is equal to the…

A: Given, Equation of Ellipse is x2+2y2=2 Now divide the equation of ellipse by "2" we get,…

Q: what  is the arc length of the parametric curve x=cos2 θ y=cosθ and  θ  is bounded between 0 and π/2

A:

Q: b) y = ln (cos x) 0 <x<- 3

A: Given: y=ln(cosx) in the interval 0≤x≤π3

Q: Show that the total arc length of the ellipse x = 2 cos t, y = sin t (0 <1< 27) is given by /2 4 V1…

A: Arc length is the total distance of the boundary of any curve. If the equation of ellipse is in…

Q: Find the arc length of the graph of x = 1 8y4 + 1 4y2 over the interval [1, 2].

A:

Q: Find the arclength of the curve x 5 cos(8t), y : 5 sin(8t) with 0 <t <

A: Given: x= 5cos8t  ; y = 5sin8t     with 0≤t≤π8---------------------Aim: To find the arc lengthL of…

Q: The area of the rotational surface resulting from rotating the arc of the curve x=cos^3 t, y=sin^3 t…

A:

Q: Find the arclength of the curve æ = 5 cos(4t), y = 5 sin(4t) with 0 < t s 4

A:

Q: The arc length of the curve r= cos 30 with 0<0 ST is I V-9(sin 30)² + (cos 30)² d0 0. I V(sin 30)² +…

A: