Find an arc-length parametrization of the line passing through (1, 0, 1) and (1, 2, 3). Upload an image of your beautiful, neat, good-handwriting work.

Q: Calculate the arc length of y = ((72x)/2 – (72x)2) over the interval [2,8].

A: For Y=F(x) , a≤x≤blength of the curve = ∫ab1+dydx2 , dx                        or                arc…

Q: Find an arc length parametrization of the line y = 2x – 6 %3D |

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Q: Find an arc-length parameterization of the line passing through (1, 0, 1) and (1, 2, 3).

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Q: Find the ordinate of the center of curvature of the curve y² = 4x at point (2, 4) from the x-axis.

A: Given option are wrong, option c should be '-16'.

Q: State the theorem of Arc Length.

A: State the theorem of Arc Length.   The arc length is x360°2πR. here R is the radius of the arc and x…

Q: Find an arc length parameterization of the given two-dimensional curve and give the corresponding…

A: Given problem:- Find an arc length parameterization of the given two-dimensional curve and give the…

Q: The VVF Ct)= describes a helix. Find the tangent line to the helix at the point (0, 1, "/2).

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Q: Find the arc-length of the segment of the curve parametric

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Q: calculate the arc length over the given interval. y = 4x − 2, [−2, 2]

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Q: Find the arc length of y3 + y = x2 + 6x on the interval [ -5, -1 ]. Also, determine the surface of…

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Q: Find the length of the curve y = 4x, 0<y< 2. Arc length =

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Q: For a point moving with uniform circular motion, the distance traveled per unit timeby the point is…

A: "For a point moving with uniform circular motion, the distance traveled per unit timeby the point is…

Q: Find the arc length from (0, 3) clockwise to (2, √5) along the circle x2 + y2 = 9.

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Q: The arc length function of the curve y = 2 In x taking the point Po(1, –) 4 as a starting point is

A: see 2nd step

Q: The cables of a horizontal suspension bridge are supported from two towers 40 ft high and 150 ft…

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Q: find the length of the latus rectum of the curve rsin^2x=cosx

A: rsin2x=cosxLet us change into cartesian coordinates uvPut u=rcosx and v=rsinxr×v2r2=urv2=uThis is…

Q: Find the arc length of the graph of y^2=4x^3, between points (0, 0) and (2, 4sqrt(2)).

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Q: Find an arc length parametrization of a helix of height 20 cm that makes four full rotations over a…

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Q: Exercise 7. Show that the curvature of a circle of radius r is , and the curvature of the line is…

A: Show that the curvature of a circle of radius r is 1r and the curvature of the line is zero.

Q: Find the Parametrization of the line.

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Q: Find the arc length (8) of the curve 7 (t) = ( – 2e*, – 4e*, – 2e*) fo %3D c - - -

A: Explanation and solutions is given below....

Q: A DVD has a diameter of 4.75 in. and rotates at 360.r/min. What is the linear velocity of a point on…

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Q: What is a parametrized curve? Give an example?

A: A curve or a vector in three dimensional or in two dimensional space is such that it basically…

Q: Use either a computer algebra system or a table ofintegrals to find the exact length of the arc of…

A: Given curve is x=ln1-y2

Q: Represent as a parametric curve the rotation of a rod of length 2 that makes 1 full turn every 3…

A: Rotation in a plane, let it be xy- plane. There are two possibilities, center of rotation is the one…

Q: Find the arc length of y³+y=x²+6x on the interval [-5,-1].

A: Solution:   Given that,      y3+y=x2+6x,  interval -5, -1         Then, differentiating with…

Q: Suppose that a projectile is fired into a headwind that pushes  it back so as to reduce its…

A: Given a projectile is fired into a headwind that pushes  it back so as to reduce its horizontal…

Q: Assume that the Earth revolves around the sun in a circular orbit of radius of 149,600,000 km (which…

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Q: A flashlight shaped like a parabloid has its light source at the focus located 1.5 cm from he base…

A: First let's see what this paraboloid looks like in 2 dimensions. Light source at the focus located…

Q: Find the arc length of the curve y = 2/3x 3/2 from (1, 2/3) to (2, 4/ 3).

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

Q: Find the arc length of y = ²√x(3-x) for 0 ≤ x ≤ 3. - Express your answer in decimal form rounded…

A: Given problem:- Find the arc length of y = (1/3)√x(3-x) for 0 ≤ x ≤ 3.

Q: Calculate the angular velocity of a point moving with uniform circularmotion.

A: When an object moves along a circle at constant speed, v, its angular velocity about the circle's…

Q: On a bicycle you have two pulleys. Even though they have proper names let's call them the pedal gear…

A: A)The circumference of the pedal gear is given by:So for every revolution the gear chain moves 4π…

Q: 2. Reparametrize R using the arc length as parameter from the point P(-1, √37,5).

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Q: Find the length of arc from (2,1) to (4,4) of the curve x = 2√y

A: Let us consider curve x=g(y). The arc length of graph of g(y) from point (a, f(a)) and b,f(b) Arc…

Q: Find the linear speed v for a point on the edge of a flywheel of radius 2 m, rotating 42 times per…

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Q: Explain what it means for a curve to be parameterized by its arc length.

A: Explain what it means for a curve to be parameterized by its arc length.

Q: Compute for the tangential velocity of a wheel rotating at a speed of 2000 rpm such that the radius…

A: Formula for tangential velocity Vt is: Vt=2πrt  here r is the radius of the wheel and t is the time…

Q: Find the arclength of the curve: y = 5(x + 2)3/2,2 <x<7

A: The arc length is given by, S=∫ab1+f'x2dx   Find the derivative of the function y=5x+23/2.…

Q: Find a parameterization for a circle of radius 4 with center (-4,4,-6) in a plane parallel to the yz…

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Q: Find a parametrization for the curve described below. the line segment with endpoints (4,1) and…

A: The line segments between  (xo , yo)  and  ( x1, y1)  can be expressed as:x(t) = (1 − t)xo + tx1…

Q: Use either a computer algebra system or a table ofintegrals to find the exact length of the arc of…

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Q: Calculate Sc 2xyds, where C is the arc of x²+²=4 from the point (2,0) to the point (1,√3)

A: We know that ∫C f(x,y) ds=∫ab f( x(t), y(t) ) dxdt2+dydt2 dt

Q: Compute the arc length exactly. Please round your final answer to three decimal places. 1 y = -x -In…

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Q: 3. Parametrize the circle of radius 5 having centre (8, –3) and hence find a tangent vector and the…

A: We have to find parametric equation, tangent vector and tangent line for the given circle.

Q: Find the arc length (in parametric form) over the interval: 0stsi

A: The arclength can be obtained by using the expression L=∫t1t2dxdt2+dydt2dt. Here, dxdt is the…

Q: Find the arc length of the curve 3y=4x from (3,4) to (9,12).

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Q: Find the arc length of y^3+y=x^2+6x on the interval [-5,-1]. Using the same arc, determine the…

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