use Eq. (3) to find the length of the path over the given interval.  (1 + 2t, 2 + 4t), 1 ≤ t ≤ 4

Q: Calculate the length of the path over the given interval. c(t) = (3t2, 4t*), 1<t< 4

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Q: Evaluate the line integral 6ydx + 4xdy where C is the straight line path from (2, 3) to (5, 5). Jc…

A:

Q: In the accompanying diagram, trans- versal RS intersects parallel lines +> XY and WZ at E and H,…

A: Given: RS is transversal line that means it intersects two parallel lines (XY and WZ). Therefore…

Q: use Eq. (3) to find the length of the path over the given interval. (3t + 1, 9 − 4t), 0 ≤ t ≤ 2

A: We have to find the length of the curve 3t+1,9-4t ,0≤t≤2

Q: Find the length of the path over the given interval.(1 + 2t, 2 + 4t), 1 ≤ t ≤ 4

A: The given curve is rt=1+2t, 2+4t,   1≤t≤4. It derivative is r't=2, 4. It is known that the length of…

Q: Consider the path r(t) = (4t,2t 2 ,2lnt) defined for t > 0. Find the length of the curve between the…

A: Given the path r(t) = (4t, 2t2, 2ln t), t&gt;0. Find the length of the curve (4, 2, 0) and (20, 50,…

Q: Evaluate the line integral 4ydx + 2xdy where C is the straight line path from (4, 2) to (8, 4).…

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Q: Find the length of the path over the given interval. (3 + 2t, 8 + 8t), 1st< 10

A: Given data: Let,

Q: Calculate the length of the path over the given interval. c(t) = (9t + 1,9 – 9t), 0 <t < 2

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Q: Sketch and identify the path traced by the point P(x, y) if x = 1+. y =1- t> 0.

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Q: Q4) Compute f z'dz, where C is the path formed by the line segment from -3 to 3 and the semicircle…

A: There is no such introduction for the solution.I have explained it within the solution.Please go…

Q: Determine the value(s) of k such that the lines 2y= -kx +6 and 3y-x= 2kx+3 are parrallel.

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Q: Evaluate ∫C x ds, where C is the straight-line segment x = t, y = t/2, from (0, 0) to (4, 2).

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Q: Find the length of the curve x = 5-t, for 1 < t < 2. length = y = 3-t, z = 3t 5,

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Q: Calculate the length of the path over the given interval. (4t2, 8t² – 1), 0 <t<4

A:

Q: Use the side-splitter theorem to solve for x in the triangle below.

A: Given,

Q: Find the exact length af te of the curve, 2. x-

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Q: 6a. Find . F dr, where F(x, y) = , and C consists of the circle x' + y = 4 from (2,0) to (v2, v2)…

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Q: Find the total length of the loop of the curve 6y² = x(x – 2)² between x = 0 and x = 2. %3D

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Q: Ć be the Shortest Path that connects t to TTL and I - Je Casah z 4) dZz. Fhen I-o?

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Q: What is the length of the graph of y = In(x<+1) - x from x = 0 to x = 3?

A: Given  The graph equation is y=lnx2+1-x  from  x=0 to x= 3 .   Formula :- Arc length of curve…

Q: Evaluate 100e dz, where C is the polygonal path consisting of the line segments from z = Oto z =…

A: For the solution follow the next step.

Q: Suppose that P is twice as far from (0, 0) as P is from (6, 0 Find such a point on the x-axis.

A: Let A0,0 and B6,0. It is given that P is twice as far from A0,0 as from B6,0. We know that if point…

Q: 3. Scye¬*² ds; C is the path r(t) = (t, 3t, –6t), for 0 <t < In 8. %3D

A: Given rt=t,3t,-6t Let Fx,y,z=ye-xz The formula for the line integral is given by:…

Q: Evaluate the line integral 2ydx + 5xdy where C is the straight line path from (1, 2) to (6, 5). Г…

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Q: Compute the length of the curve over the given interval. r(t) =〈3t, 4t − 3, 6t + 1〉, 0 ≤ t ≤ 3

A: Given rt=3t,4t−3,6t+1,  0≤t≤3Formula→Arc length=∫abr't dtr't=f't2+g't2+h't2    rt=xt,yt,zt

Q: Compute the length of the curve r(t)= (-3t, 3t + 7,–7t + 1) over the interval 0 <t <7

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Q: use Eq. (3) to find the length of the path over the given interval. (2t2, 3t2 − 1), 0≤ t ≤ 4

A:

Q: Determine whether the work done along the path C is positive, negative, or zero. y O positive…

A: Consider that the sign of the work depend on the orientation of the path C. here the circulation can…

Q: Family OF lines parring through (0, -4)

A: Given that family of lines passing through (0,-4). To find differential equation based on above…

Q: Evaluate 36e dz, where C'is the polygonal path Oto consisting of the line segments from z = 0to z =…

A: The given integral is                                       ∫C36ezdz,  where C is the polynomial…

Q: Compute the length of the curve r(t)= (-5t, 4t – 3, – 5t + 5) over the interval 0 <t< 7

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

Q: Evaluate (0₂2). [(x² + y² ]ds along the path C, defined as counterclockwise along the circle x² + y²…

A:

Q: The distance between the two lines x = 1+ t,y = -2+ 3t, z = 4 – tand x = 2s, y = s, z = s is

A: Please see the explanation below

Q: Sketch the following path and compute its length (i+t(-1-i), -1- i(t - 1), -1+eit-2)-1, te (2,3], te…

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Q: Determine whether the work done along the path C is positive, negative, or zero. y

A: The work done along the path C is

Q: Calculate the length of the path over the given interval. (4t², 8t² – 1), 0 <t< 4 |

A:

Q: Find the exact length of the curve. y = In(1 - x²), o s x s

A: Solve the problem using definite integral

Q: [a] Find the shortest distance from the point (2, -1, 4) to the straight line x = 2, y = 3+tand z =…

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Q: How is the line y = 1 converted by mapping w = e? ?

A: In this question, we convert the line y=1 by mapping w=e^z.

Q: Compute the length of the curve r(t) = (-4t, 5t — 3, -2t + 3) over the interval 0 ≤ t ≤9 L =

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Q: use Eq. (3) to find the length of the path over the given interval. (3t2, 4t3), 1≤ t ≤ 4

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Q: Evaluate ds, where C is the path defined by c(t) = (t², 9t, 4t³3/2) where 0 <t < 2.

A: Given integral c z^2/x ds, C(t) =(t^2, 9t, 4t^3/2)  where 0&lt;= t&lt;=2

Q: Compute fs(-y + ye®Y)dx + (x + xe®Y)dy, where S is the path: start at (0,0) and then go right 5…

A: Consider the provided question, According the given statement the path S is shown in the figure…

Q: Find the length of the curve defined by y = 3 In 3 from x = 8 to x = 9.

A: Use derivative of function and length of curve formula .

Q: By using the calculus of variations, prove that the shortest distance between two points in the y z…

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Q: Find the exact length of the curve. y = 4 글2-글 In(x), 1 < x < 4

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Q: y = In(1 – a²) ; 0 < æs

A: Solution:-