Given the parametric equation x=(4/5)t5/2 and y= (1/4)t4-t find the arc length of the curve on the interval 0 less than or equal to t less than or equal to 1

Q: Find the point on the curver(t) = (12 sin t)i - (12 cos t)j + 5t k at a distance 13p units along the…

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Q: Find the arc length (s) of the curve r(t) = (cos(3t), 5t, sin(3t)) for 1 <t < 5

A: r(t)⇀={cos(3t),5t,sin(3t)}Now we can evaluate that x(t)=cos(3t)y(t)=5tz(t)=sin(3t) We know that the…

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

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Q: Find the arc length (s) of the curve r(t) = (- e*, 2e, – 4e*) for 0 <t < In(3) S =

A: To find the arc length of the curve

Q: Find the arc length (s) of the curve 7(t) = (4 cos( – 4t), 2/5 cos( – 4t), 6 sin( – 4t)) for 0 <t <…

A: Given that  The curve is  To find the arc length of the curve

Q: 1. Find the arc length of the curve y = 4xi + 3 from x = 1 to x 2. Leave your answer as a radical.

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Q: If the arc length s of the curve C:r (t) = cos(t)i + sin(t)j+2tk from t = 0 to t = b is 20 units,…

A: The arc length of a parametric curve defined by the vector r→=f(t), g(t), h(t) defined over the…

Q: Find the arclength of the curve in the given interval. x = 3 cos? t , y= 3 cost sin t , 0 s<t <t

A: solution is written in below steps.

Q: Find the arc length (s) of the curve r(t) = (2t, 4 cos(3t), 4 sin(3t)) for 1 <t < 4 S =

A: Application of integration and partial derivatives use to solve this problem.

Q: Find the arc length of the curve r(t) = (2t3/2, cos 2t, sin 2t) from t = 0 to t = 1. %3D

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Q: Q1:(i) Find the arc length of the curve a(t) = t sin t, t cos t, 3 betweent=0 and t= 1.

A: As  per our  guideline, I can solve  onle one question  at once,further can be reposted. Thanks for…

Q: Find the arc length of the curve given in parametric form by c(t) = (t^3, t^2) for 0 ≤ t ≤ 1.

A: Let f(t)=x(t), y(t) be a curve expressed in the parametric form on [a,b]. The  length of the curve…

Q: Find arc-length of the following curve 0 <t < 2 x = sin (t) Y = cos'(t)

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Q: Consider the parametric curve: x = sin² (t) y = -9t Which integral gives the arc length of the curve…

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Q: Find the arc length of the curve y = e" from x-0 to x-1.

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Q: Find the arc length of the curve below on the given interval. とマ 1 X=- , for 2sys4 8y 4 The length…

A: We know that length of curve x=f(y) from y=a to y=b is L=∫ab1+dxdy2dy

Q: What is the arc length of the given parametric curve x = cos3t; y = sin3t;0 <t< 2n. O 37 None of…

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Q: Use the arc length formula 2 dx dy L + dt dt dt to find the arc length of the curve. x = cos 12t, y…

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Q: Consider the parametric equation  x = t2 - 1 and y = t2 + 2t. (a) find (dy)/(dx) and (d2y)/(dx2).…

A: Given parametric equations - x = t2-1t2 = x+1t = x+1         .................(1)y =…

Q: Consider the parametric curve: x = ln(t + 5) y = −6t5 Which integral gives the arc length of the…

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Q: Given R(t) = (1 – 4 cos t)î + 3 cosĵ + 5 sin tk, find the a. arc length of the portion of R(t) from…

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

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Q: Find the arc length of the curve on the given interval. Parametric Equations     x = √t, y = 3t − 1…

A: Given: Parametric Equations x = √t, y = 3t − 1 Interval 0 ≤ t ≤ 1

Q: Use the arc-length formula of the parametric equation and evaluate the arc-length of the curve while…

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Q: 1. Find the equation of the tangent line to the curve: x = Vt, y = e² at t=1. d?y at t=1 for the…

A: Solve by using differentiation.

Q: 2 cos(t) T at the point 4 Find the slope of the tangent line to the parametric curve ly = 1 sin(t)

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: Find the point on the curve r(t) = (12 sin t)i - (12 cos t)j + 5t k at a distance 13pai units along…

A: Given,

Q: Given: parametric curve H defined by x(t) = tan¯¹t and y(t) = e¹t, where t € R (a) Find the slope of…

A: Given that parametric curve H defined by x(t) = tan-1t       and    y(t) = e4t , t ∈R           we…

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: If the arc length s of the curve C:r (t) = cos(t)i + sin(t)j+ 3tk from t 0 to t = bis 20 units, then…

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Q: Find the arc length of the following curve on the given interval. y = 1/2(e^x+e^-x) [ln2,…

A: Find  the  arc  length  of  the following  curve  on  the given interval. y = 1/2(e^x+e^-x) [ln2,…

Q: Consider the following. x = sinh(t), y = cosh(t) (a) Eliminate the parameter to find a Cartesian…

A: Solution: The objective is to eliminate the parameter to find a Cartesian equation of the curve

Q: Given the parametric curve x = t – sin(t),y = 1 - cos (t), find an equation for the line tangent to…

A: Given: x=t-sint y=1-cost at t=pi/3

Q: Find the length of the arc of the curve having the parametric equations x = t³3 and y = from t = 0…

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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

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Q: 9) Find the exact (arc) length of the curve. x = 2t – sin(2t), y = 1 – cos(2t), 0<t<r. -

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Q: The arc length of the curve defined by the equations x(t) 10 cos(11t) and y(t) = 3t for 1 <t< 5 is…

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Q: Consider the curve r=[(e^(t))*cos(3t), (e^(t))*sin(3t), e^(t)] Compute the arclength function s(t):…

A: The arc length function is given as: st=∫atr'tdtrt=etcos3t,etsin3t,et  with initial point 0

Q: dx L% = 1+ dy dy

A: Given equation of curve; y  = (x/2)3/2 , x = 0 to x = 2

Q: Consider the parametric curve: X = sin² (t) y = -9t Which integral gives the arc length of the curve…

A: Topic = Integration

Q: 1 cos(t) ly = 3 sin(t) Find the slope of the tangent line to the parametric curve at the point

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Q: Find an equation of the tangent(s) to the curve with parametric equations E = t cos t, y =t sin t nt…

A: follow next step

Q: Find the exact arc length of the curve x = e2" (sin t – cos t),y= e2t(sin t + cos t) (-1<t< 1).

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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: Find the arc length (s) of the curve r(t) = (5e“, – 2e“, – 3e“) for 0 <t < In(2) S =

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Q: Find the arc length of the curve x = cos 2t, y = sin 2t, 0 < t < 5 27 -2T

A: The arc length of the curve x=cos2t, y=sin2t, 0≤t≤π2

Q: 1.) Use the arc length formula to find the length of the curve y = 3x + 2 on the interval 0 ≤ x ≤ 3.

A: Given data  y=3x+2 Interval ÷ 0≤x≤3 Formula for arc length is given by  L=∫ab1+dydx2dx

Q: Consider the parametric curve: X = = 7et y = 3t5 Which integral gives the arc length of the curve…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Find (2x + xy)ds, where C is the arc of the curve y = sin (x) for 0 ≤ x ≤ π

A: The given problem is to evaluate the given line integral of the given function over the given curves…

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.