Compute the length of the curve traced by r(t) = (4t, 7 – 4t, 5) over the interval 2 < t < 10. (Use symbolic notation and fractions where needed.)

Q: Sketch the graph of r(t) = (2t – 6, /t – 1),t>1 in the xy-plane. Show the direction of increasing t…

A: Given: The equation of curve rt=⟨2t-6,t-1⟩ where t≥1 To sketch: The graph of given curve with…

Q: 7. Determine the coefficients a, b, c and d so that the curve y = ax* + bx³ + cx² + dx + e will pass…

A: Given a function of the curve, y=ax4+bx3+cx2+dx+e To find the coefficient a,b,c, and d such that the…

Q: Find the length of the curve y = -9+4x3/2 over the interval 0 <x <1. OAZ= (1/54) 37 /37+1 CO B I =…

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Q: In  the givne equation as follows ,determine the open t-intervals on which the curve is concave…

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Q: Find the length of the curve over the given interval. r = 8, [0, π/6]

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Q: 3) Find the exact length of the curve: x = y = In(1+t); 0<t<2.

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Q: 13- Find the length of the curve a) r(t) = 4costi + 4sintj³ + 3tk³ 0< t < 3n b) r(t) = 4ti + 4tj¬ +…

A: Please refer the image,

Q: Let C be the curve y = 8/a for 2.1 < x < 3.8.

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Q: . Find the length of the curve defined by R(t) = (3t+1, 4t3/2, 4-3+2) from the point (1,0, 4) to…

A: Note : The length L of a curve r(t)→=(x(t) , y(t)  ,z(t) )  from t=a  , t=b is given by…

Q: Which of the following expressions gives the length of the curve defined by R(t) = tij +In tk…

A: We have to find arc length expression for the given vector function. Given is the curve…

Q: Find the exact length of the curve. y= In{1 – x²), o s 1. 0 sxs! 7. I Ju =

A: We will find the exact length of the curve as shown below

Q: Find the set on which the curve 7 dt t2 + 6t + 15 y = is concave downward. Answer (in interval…

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

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Q: Find the set on which the curve 8 dt t2 + 8t + 22 y = e downward. n interval notation):

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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 3ti – 6tk over the interval 8 <ts 18.

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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: compute the length of the curve over the given interval.  r(t) = (2t2 + 1, 2t2 − 1, t3), 0 ≤ t ≤ 2

A: Length of a curve is also like computing distance between two points but with the restriction that…

Q: Compute the length of the curve r(t) = (-6t,4t + 4, –5t – 3) over the interval 0 < t < 7. (Use…

A: The curve rt=-6t, 4t+4,-5t-3 over the interval 0≤t≤7

Q: compute the length of the curve over the given interval. r(t) = 2ti − 3tk, 11 ≤ t ≤ 15

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Q: 9. Find the length of the curve defined by r(t) = (t, -1sts1.

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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: Find the length of the curve defined by from = 9 to z = 10. 2 y-4lm (()²-1) =

A: find derivative

Q: 7.Find the maximum and minimum distances from (0,0) to the curve 5x2+6xy+5y2=8

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Q: Let C be the curve y = x³ – 3x2 + 4x – 1 joining the points (1, 1) and (2, 3). Find the value of…

A: We need to find value of integral.

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

A: Solve the problem using definite integral

Q: Let C be the line segment connecting 0 to ni. Then f. 1-e2z dz =

A: we have to find integration

Q: Find the length of the curve defined by the y-axis. over the interval <r< 1 about 2.r

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Q: C is the curve y = e® from (2, e²) to (0,1) and F = (x², -y), compute ſ, F-dr.

A: Given that, C is the curve y=ex from 2,e2 to 0,1 and F=x2,-y Then, F=x2,-y=x2,-ex So, F→=x2i^-exj^

Q: Find the orthogonla trajectories of the family of the curve r = csine

A: Family of curves: r = csinθ

Q: 3. Discuss how to evaluate f () dz , where C is a simple closed curve C=10 enclosing the origin.

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Q: Find the length of the curve y = a +; from a = 0 to x = 1. O None 5/2 O6/2 3 O4/2 3. 3

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Q: Compute the length of the curve r(t) = (−4t, 4t + 3, −8t + 8) over the interval 0≤t≤7 L =

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Q: 4. Prove that the following curves are intersecting with a right angle: 5y-2x+y²-x²y = 0 2y +…

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Q: Find the length of the curve defined by R(t) = (3t+1, 4t³/2, 4 - 3t²) from the point (1,0, 4) to (4,…

A: Given…

Q: Find the exact length of the curve. y = x2 - In(x), 1 < x < 4

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Q: Compute the length of the curve r(t) = (2t, In(t), t² ) over the interval1<t < 4. (Use symbolic…

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Q: The area bounded by the curve y = 6z and the lines a = 5 and z= 8 above the T aris is 234.00 square…

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Q: IFind the exact length of the curve x= 3t -t, y=3t² ,0<t<2 ||

A: We have to find the exact length of the curve. The length of the curve is given by

Q: Find the Võlumé of thé šólid generated by revolving the shaded region about the given axi About the…

A: Explanation: If we rotate the shaded region about the x-axis, we will get the cone shape. Height of…

Q: .11 Compute (1/ry, 1/(x + y)) · dr along the curve (2t, 5t), 1 < t < 4.

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Q: Use Green's theorem to find the k number that satisfies (k + 3) ∫C((k/2)*(x^k)*(y^2))dx + ((yx^(k +…

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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: Consider the path r(t) = (4t, 2t², 2 In t) defined for t > 0. Find the length of the curve between…

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Q: 3) Find the exact length of the curve y = x² – In x for 1< x < 2. 1„2

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

A: Find dy/dx, then put it in the arc length formula.

Q: Use Green's theorem to evaluate S. (5xy + x² + y²) dx + (x² – y)dy where C is a closed curve that is…

A: According to the given information, it is required to use green’s theorem to evaluate the integral.

Q: EX Find the point the curve y=x3+x²-l where the tamjent on is parallel to the X-oaxis

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Q: (a) Prove that the line 2x 3y + 26 =0 is a tangent to the curve x + y2 - 4x + 6y – 104 = 0 hence…

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