Question 1 (a) Find the first moment of area, Qx and Qy for the rectangle with axes origin as shown in Fig. 1. (b) Find the second moment of area, Ix and I, for the same rectangle and origin. y B/2 Figure 1

Q: Question 5 a. A company that manufactures dog food wishes to pack the food in closed cylindrical…

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Q: Evaluate || ldAwhere R is the region in the first quadrant that is outside the circle r=1 and R…

A: Put x = r cos(theta)        y = r sin(theta).

Q: Question 5 Which of the following represents the area inside r = 2, and between the lines 0 = and r…

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Q: Question 11 Find the radius of curvature at the given point, y = sinx at (pi/2, 1). The radius is…

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Q: 10. Identify the surface that is given by: p (sin? (6) cos (0) + cos ()) = 4

A: (10) Consider the given expression as shown below:

Q: 3- The equations X= a -a sind, Y=a- a cosd,(0<0<2n Represent one arch of a cycloid .show that the…

A: To calculate the surface area of revolution about the x-axis, use the following formula:…

Q: QUESTION 17 How fast is the surface area of a sphere changing when the radius is 25 cm if the radius…

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Q: 11. In the figure, TA is produced to touch the circle at P; TB is produced to touch the circle at Q.…

A: topic - circle and tangents

Q: Question (1): The arc of the parabola y = x2 from (1,1) to (2,4) is rotated about y-axis. Find the…

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Q: QUESTION 1 Calculate F.dr if F=(sinx, x'y) and C is the triangle oriented counterclockwise with…

A: Line integral

Q: QUESTION 7 Find the area of the region that lies inside both curves. = 8 + 2 sin , r = 7

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Q: QUESTION 2 The surface area of a sphere is given by S=4tr?. The rate of change of the surface area…

A: The surface area of the sphere is, S=4πr2 Then, the rate of change of the surface area as the radius…

Q: Question: Discuss the Singulortdier and Poles of Zěsinz fr2)=

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Q: Question #2) Find the absolute extrema when f(x,y) = xe – x² – e :R is the rectangular regioi with…

A: Both questions are independent to each other so according to the guidelines , I am solving first…

Q: Question 18 Find the center of 2 circles tangent to x2 + v? = 100 at (6,-8) having a radius of 15…

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Q: 3- The equations X= að -a sinð, Y= a- a cosº,(0<< 2n Represent one arch of a cycloid .show that the…

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Q: B Fig 1 1 y = (3x)3 A I. Find the co-ordinates of A and B X II. Find the area enclosed by the curves…

A: Please see the below picture for detailed solution.

Q: Question 9. A circular helix in xyz-space has the following parametric equations, where θ ∈ R. x(θ)…

A: 9. The given parametric equations are,x(θ)=4cosθy(θ)=4sinθz(θ)=3θ

Q: Question#4: Use Green's theorem, evaluate | F.dr for the following function: а : F = grad sin x cos…

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Q: Question 3. The parametrized curve x = cos(t) – 5sin(t), %3D 101 y = -10cos(t)+ sin(t) is an…

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Q: Sketch the curve. r = 6 + 2 cos(?)   Find the area it encloses.

A: We first draw this and then calculate it

Q: The graph of the equation x2/3 + y2/3 = 1 is an astroid. Find the area of the surface generated by…

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Q: Question 1 The area of the surface generated by revolving the line x =y from x=0 to x=2 about the…

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Q: A.Sketch the two curves: B. 1. r1 = 3 cos 0. 2. r2 = 1+ cos e Find the area of the region that lies…

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Q: Question 7 Determine the area of the triangle bounded by the coordinate axes and the tangent to x² -…

A: This is a problem related to area calculation by integration. Based on the general formula and…

Q: Question 1 Let D be the region of the plane bounded by the curve C parameterized by 7(t) = [3 cos(t)…

A: It is given that, r→(t)=[3cos(t)-cos(3t)]i^+[sin(3t)-3sin(t)]j^, 0≤t≤2π   It can be written as,…

Q: QUESTION 17 How fast is the surface area of a sphere changing when the radius is 25 cm if the radius…

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Q: Question 3. (2,) are the coordinates of the Centre of Mass for the lamina with mass per unit area 2…

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Q: Question Seven: A ball with a radius of 13 cm has cut the ball at a level 5 cm off its center. Find…

A: As per our guidelines I am solving only first question please resubmit other question.

Q: -7. х 3D sin?t, у— cos t yA

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Q: 10. A vase is designed by rotating the section of the curve x(x – 1)² + 0.5 between x = 0 and r =…

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Q: QUESTION 14 The equation of the tangent plane to z=f(xy) =x² siny at the point (1,0,0) is given by…

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Q: Question 006: Complete the following question involving the Rotational Surface Area Use the Surface…

A: we have to find the area of the surface

Q: Question 18 Find the area bounded by the curve y 8 square units 4 square units 16 square units 10…

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Q: QUESTION 13 Calculate the area of the smaller region (to the left of the parabola) bounded by (x+…

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Q: Question 1 of 8 - /5 View Policies Current Attempt in Progress Find the arc length of the parametric…

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Q: QUESTION 5 Calculate F.dr if F=(sinx,x²y³) and C is the triangle oriented counterclockwise with…

A: Solution is given below

Q: QUESTION 14 Which one of the following points lies on the curve r= sin 0-5. (5, 0) o (5, 2n) o (-5,…

A: In this we find that point which lies on the given curve.

Q: Question 10. Find the angle between the curve r(t) = (t, sint, cos t), and the curve y + z2 = 1, x =…

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Q: Question Seven a) Show that: dx = sin" +c b) If x-a cost+ In an), y=a sint , show that = tan x. dx…

A: radius o curvature  is given by  R=y'2+132y''

Q: Question 1 The region D is enclosed by + y = 2, ya, and y-axis. Give D as a type I region, and a…

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Q: Question 5 (Total Area). | Caleulate the total area between the curve y = -2r and the curve y = 2r -…

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Q: QUESTION 7 The tangent plane to the graph of the surface z=In(x2+y2) at the point (1,0,0) contains…

A: To find the value of t

Q: Question 3, Let o(0, 6) = (cos e sin o, sin 0 sin ø, cos o) be a parametrization of the unit sphere.…

A: let σθ,ϕ=cosθ sinϕ, sinθ sinϕ , cosϕ be a parametrization of the unit sphere. claim- to show that…

Q: Question 7 of 10 What is the surface area of the cube below? C C A. 320 units² B. 512 units2 C. 384…

A: I am attaching image so that you understand each and every step.

Q: (a) Circle: x = h +r cos 0, y = k + r sin 0 (b) Ellipise: x = h + a cos 0, y = k + b sin 0 (c)…

A: We have to find out in rectangular form

Q: Question 2 Find the length of the curve r(t) = (3 cos t)i + (3 sin t)j + 2ek, Osts3.

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Q: Find the area that lies inside both curve: r = 1 – cos(θ) and r = 1 + cos(θ). Draw.

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Q: Question (5): Find the volume of the largest right circular cone that can be inscribed in a sphere…

A: In the above figure let DC=r be the radius of the circle and AD=h be the height of the cone , OD=x ,…

Q: CHAPTER 1. CURVES 22 Exercise 1.3.1 Find the length of the arc in one period of the cycloid x = t –…

A: To find- Find the length of the arc in one period of the cycloid x = t - sint, y = 1 - cost. The…