Find the length of the curve 7 (t) = (3 cos(4t), 3 sin(4t), 4t) for –5

Q: 5. Determine the equation of the tangent line to (a) r= 2 sin e at = (b) r =1+ cos 0 at 8 =

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Q: 1. Find the length of the curve given by e' (sin t+cos t) , yY = e'(cos t – sin t), x = 1<t< 4 .

A: The length of a parametric curve is given by L=∫abx't2+y't2dt Now, we have…

Q: Find the exact slope of the tangent line to the 4 cos(t) parametric curve at the point ly = 7 sin(t)…

A: To Determine: Exact slope of the tangent line to the parametric curve :

Q: Find an equation of the tangent line at the given point on the curve. (a) x = 2 – 3 cos 0, y = 3+ 2…

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Q: Find the length of the curve 7 (t) = (3 cos(t), 3 sin(t), 5t) for – 4 <t <1 Give your answer to two…

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

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Q: 2. Find the point on the curve r(t) = (12 sin t, -12 cos t, 5t) at a distance 137 units along the…

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Q: What is the point of intersection of the tangent lines to the curve r(t) = sin(πt)i + 8sin(πt)j +…

A: Let us consider the given curve r(t) the tangent line is obtained as Find the derivative of the…

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

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Q: Find the length of the curve. r(t) = cos(2t) i + sin(2t) j + 2 ln cos t k,     0 ≤ t ≤ π/4

A: Consider the length of the curve is, r(t)=costi+sintj+(lncost)k Then,…

Q: Calculate the arc length of the curve f(x)=(2/3)(x²+1)ª2) in the interval [–1,1]

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Q: 15. Suppose you start at the point (0, 0, 3) and move 5 units along the curve x = 3 sin t, y = 4t, z…

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Q: Find the point on the ellipse x = 2 cos t, y = sin t, 0 … t … 2pi closest to the point (3/4, 0).…

A: To Find: Point on the ellipse x=2cost, y=sint, 0≤t≤2π, closet to the point 34,0. Concept: Distance…

Q: 3. Find the length of the curve y = In (cos x), 0 <x <

A: we have to find length of the curve

Q: Find T', N and B for the curve r(t) = (2 cos(5t), 2 sin(5t), 4t) at the point t = 0

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Q: find y'' for the curve cosx-siny=4

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Q: Find the derivative 4cos4t sin4t 2cot4t -1/2 cot4t Other: of the parametrically defined curve : x(t)…

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Q: Find the length of the curve y = ln(sec x ), x is an element of [0, pi/4]

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Q: Find the arclength of the curve x = 3 cos(5t), y = 3 sin(5t) with 0 <t< 20 %3D

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Q: Find Sc F · dr for F = 3yi – (sin y)j on the curve counterclockwise around the unit circle C…

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Q: A particle moves in the xy-plane in such a way that its path is defined by x = e^t cos t and y = e^t…

A: Given that, x = e^t cos t y = e^t sin 2t Differentiating x with respect to t we get, dx/dt = e^t cos…

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

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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: Find the lengths of the curves x = 8 cos t + 8t sin t, y = 8 sin t - 8t cos t, 0 … t … pi/2

A: The length of the curve of any given function by the formula L=∫t1t2dxdt2+dxdt2dt. Here t1 and t2…

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 exact length of the curve. y = ln(cos x),   0≤ x ≤ π/3

A: Formula used: L=∫ab1+dydx2dx

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

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

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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: (11) Find the tangent line(s) to the parametric curve given by * = t5 - 4t3 y = t2 at (0, 4)

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Q: Calculate the length of the curve r=a*sin(^3)(x/3) for (x(1)=0, x(2)=3pi)

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

A: Since you have posted multiple question in this question which are not interlinked so i have solved…

Q: 13. Find the point on the curve 7(t) = (2 sin t, 2 cos t, t), 0<ts 7, where the tangent line is…

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Q: Find the exact length of the curve. y = In(cos(x)), TC 0 < x<.

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Q: Find the length of the curve 7 (t) = (4 cos(5t), 4 sin(5t), 5t) for – 3 < t < 9 Give your answer to…

A: Given: r→t =4cos(5t), 4sin(5t), 5t  for -3≤t≤9

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: Find the maximum, minimum and inflection points of the fur y= 3 sin 2x at [0, T].

A: Solution:-

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

A: Given y=x416+12x2, x=2 to x=3

Q: Find T, N and B for the curve F(t) = (2 cos(5t), 2 sin(5t), 3t) at the point t -0 Give your answers…

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Q: Find the exact length of the curve. x = 9 cos(t) − cos(9t), y = 9 sin(t) − sin(9t), 0 ≤ t ≤ pi

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Q: Find the length of the curve x = 8 cos t + 8t sint,y= 8 sin t – 8t cos t ; 0 < t %3D -

A: The length of the parametric curve is given by  L=∫abx't2+y't2dt.

Q: Find the length of the curve 7 (t) = (4 cos(t), 4 sin(t), 3t) for – 1 <t< 4

A: Here we have to calculate arc length in given interval.

Q: Calculate the length of the curve γ (t) = (cos(2t), sin(2t)) t ∈ [0, π].

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Q: Find the distance traveled by a particle with position (x, y) as tvaries in the given time interval.…

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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 an equation of the tangent to the curve at the point corresponding to the given value of the…

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Q: Find the lengthof the curve r= a sin (0/2), 0s 0S T, a>0

A: The formula for finding arc length is L = ∫0πr2+ drdθ2dθ, where r = a sin2(θ2)

Q: 3) Find the exact length of the curve. y = In(cos r), 0 < x<

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

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Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.