Example 28: If Hr is the rth about origin, prove moment that r-1 is the jth cumulant. -1 -j Kj, where i= 1

Q: 77. Prove, in two ways, that the arc length of a linear function f(x) = mx + c on an interval [u, b]…

A: f(x)=mx+c on an interval [a,b] Note: we prove part a) only ,in part b) theorem 6.7 not given

Q: The arc length of y=In(cos x), 0<x<• is 3 ○A In (√2-1) A. ○ B. In (1+√3) C. In (2+√√3) D. In…

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Q: 12. Evaluate 3a ds where C is the parabolic arc along y = from P(0,0) to Q(2, 2).

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Q: 1. Find the length of arc of the curve y: In r from r =3 to r = 9. 8

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Q: 2 ind the arc length for f(x) = 6-2 x² over the interval [0, 2].

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Q: Question ): The integral that represents the length of the curve y = tan(2a), where <a <, is the…

A: Given y=tan2x

Q: Which one of the following points lies on the curve r = sin 0 – 5. (5, 21) o(-s, ) o (5, 0) o(-5, n)

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Q: Q4) The standard formula for the tangent of the sum of two angles is tan x + tan y tan(x +y) 1- tan…

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Q: Q3 Point out the singularity and is ty pe of follo wing fune tions 22 () d) Sin t2 24

A: Singularity

Q: E(x?) is called the second moment about orgin

A: Given statement, EX2 is called the 2nd moment about origin.

Q: Ex: 1) Let f(x, y) = sin(xy) X to wake fa cont. function on all of R²? ,x = 0. How should you define…

A: The given function is fx,y=sinxyx, x≠0 and f(x,y) is continuous on ℝ2. To find: f(0,y).

Q: 10 eat sinh Cbt)

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Q: Keparametrize the curve rit) = with respect to its arclength measured from the point (e"20,e"2) in…

A: Given curver(t)=etsint,etcost,et Above curve is passes from the point eπ2,0,eπ2.we need to find the…

Q: 8.432 5) Setup and find the arclength of y=º from 6 15x54 using trapezoidal rule n=6. Give the final…

A: We have to find out the arc length

Q: A force of 40 pounds acts on the pipe wrench shown in the figure below. 18 in. 300 (a) Find the…

A: Consider the given figure.

Q: If an object is moving along a horizontal line, such that it's velocity, v(t) = cos(3t), what is the…

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Q: Find the point on the curve r(t) = (5 sin t)i + (5 cos t)j + 12t k at a distance 26paiunits along…

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Q: a)Find the arc length of f(x)= In(1+x³), Osx<5 Answer:

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: 35)16 pointsi se t up, but Po not , the definite integra! that computes the are enclose ol intsi Se…

A: The interval –π/4≤θ≤π/4, could be divided into  –π/4≤θ≤0 and 0≤θ≤π/4

Q: if y= Cot" (-+) y=Cot Prove that dy 1-x

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Q: Prove that the curve r(t) = (a cos t,b sin t,.csint is parameterized by length provided a=b2 +c² =…

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Q: 4. Use the arc length formula to show that the length of a linear function f(x) = mx +c on the…

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Q: Find the length of one turn of the helix given by r(t) == cos(t)i + sin(t)j + 1 1 99 25 -tk.

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Q: a: A foree given by ř =gî+2-42 is applied at he pont (l,-t,2). Find 1he moment of Ē about The pont…

A: Concept Used: The Moment (or torque) of the force F⇀ about a point O is calculated by  MO=r×F where…

Q: Q3 Pomt out -lhe singularity and i's ty pe off follo wing fune trons a) I 2*(I+2) Sinh2 29

A: We will find types of singularity to the problems. Singularity have two type ...       1&gt;.…

Q: Consider a curve given by Ř(t) = (2 cos t, 12t + 3, -2 sin t). Let f(t) be a function such that f(1)…

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Q: Q: Prove the transfurm; formula's by definition of Laplace

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Q: The cable AB carries a tension of 400 N. Determine the moment about O (positive if counterclockwise,…

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Q: Find the length of the arc of x2 +y2 = 64 from x=-1 to x=-3, in the %3D second quadrant. 2.61 units…

A: The curve in the second quadrant can be represented as, x2+y2=64 y=64−x2 The derivative of the…

Q: Please solve

A: Parametrization of tangent lines is given by

Q: Suppose a particle begins to move from the origin(t = 0) following the curve in space. r(t) =…

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Q: (a) If f(x,y) = e" siny – e" sinx then verify that fry = fyz-

A: This question is related to partial derivatives.

Q: Find the length of one arch of the cycloid x= 5(t-sin(t)), y= 5(1-cos(t)).

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Q: 7.38. Calculate the second moment of area for a 2 × 6 piece of lumber about the x-x and y-y axes, as…

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Q: 10) Set up, but do not evaluate, an integral tor the Length the curve of dx

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Q: lo) Use a tangent plane to approx. the value of the following tunction. at the point (2.1L- 14.D)…

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Q: Find the length of the curve. r(t) = cos(3t) i + sin(3t)j + 3 In(cos(t)) k, 0 <t< n/4 %3D

A: Find the length of the curve:…

Q: Find the length of the catenary y = a cosh from x = 0 and x = a X1.

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Q: Possible units of the moment M, are

A: Moment= Force ×  perpendicular distance

Q: The graph of y = 2x (x+ 1) and y = 1 (x>0) intersect at one point, x=r, as shown to the right. Use…

A: Let the given functions be, hx=2x2x+1gx=1x Equate both the functions,…

Q: •T/4 Evaluate 4 sec(0) tan(0)de using the Fundamental Theorem of Calculus, Part 2. TT/4 4 sec(0)…

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Q: dt | 65. Use the substitution u = tanh t to evaluate cosh? 1+ sinh?t"

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Q: A particle travels along the helix C given by 7 (t) = cos ti + sin tj + 2tk and is subject to a…

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Q: Find the length of one arch of the cycloid x= 6(t-sin(t)) y= 6(1-cos(t))

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Q: E(X is called the second moment about orgin ylgn İhi

A: In this question we have to verify about the second moment about origin in the concept of mean and…

Q: 74. A particle moves in the xy-plane along the elliptical path x = 2 cos t, y = sin t, where x and y…

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