Question 10 Figure Q10 shows the shaded area with the equation given. Calculate: y - y? = 1 – 0.5x %3D 1 m 1 m -2 m- Figure Q10

Q: (c) dz dy dx

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Q: Find the area of the surface obtained by rotating the given curve about the x-axis. - 10 10 cos (0),…

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Q: Consider the shaded area shown in (Figure 1) Suppose that a 100 mm, b= 150 mm and r=80 mm Part A…

A: Given that a=100 mm, b=150 mm and r=80 mm. So, the moment of inertia formula is, Iy=∫aby(f(x)-g(x)dx…

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A: Consider the plane curve.

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A: To find:

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Q: d'y Find for dr? y = cot(x) dy %3D dx?

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Q: Laplace's equation reads vo = 0 %3D True False

A: The partial differential equation ∇2ϕ=0 is known as a Laplace's equation.Then ϕ is called harmonic…

Q: What Cartesian equation is equivalent to the given parametric equations? Sx (t) = 2 sint ly (t) = 4…

A: x(t)=2 sin t xt2 = sin t  square both side x24 = sin2 t ...............1   Now, y(t)= 4 cos t yt4 =…

Q: Find the moment of inertia of a solid sphere of radius a about a diameter. (Take d = 1.)

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Q: c) Use spherical coordinate to evaluate UTM TM 1²+y? Væ2 + y? + 22 dz dy dx. UTM &UTM

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Q: Figure I below shows a uniform lanmina in the form of right angled triangle OAB with right angle at…

A: 5(ii) Solution: In part (i) centroid of sector OPQ has been calculated as  Ox= 4a3π and Oy= 4a3π…

Q: Find the length of one arch of the cycloid 2(t – sin(t)), y = 2(1 – cos(t). х

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Q: Q3) find the soluation of differention equation 1) 2y' = y cot(x)

A: To find the solution of the differential equation 2y'=y cot(x) Formulae used : ∫dxx=ln |x|∫cot(x)=ln…

Q: 1/B) Find the length of the cardioid 'curve: r = 1 + cose

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Q: Find the moment of inertia, with respect to the line x=1, of the area enclosed by the loop of the…

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Q: The diagram shows an initial arm of length1 unit being rotated countercockwise about the origin to…

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Q: Evaluate y*dV, where E is the solid hemisphere x? + y? + z² 0. E (Hint: spherical coordinates)

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Q: Express the circular function cos+sin as a single cosine with a phase displacement T Rcos (+a) where…

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Q: Calculate the total charge on a plate D in the shape of an ellipse with the polar equation sin? (0)…

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Q: Determine the moment of inertia of the shaded area about the x-axis. 2" 10" y Answer: Ix Parabolic =…

A: To determine the moment of inertia about the x axis.

Q: the EXACT Salutian to the equation belaw/de not decimal apprakimatea) give %3D

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Q: Use the formula A = 27 dy 1 + dx dx to determine the surface area of the parabolic reflector…

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Q: Givea parametrie deseription fere eone with radies a and height 4, inctuding the intervats for the…

A: parametric description of cone given below;

Q: W Parkmdrc ey da klat 0KV41 Dater mine the area A the sur face 区E 242Y

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Q: What surface does the curve r(t) = -t cos(t), 121 -t sin(t), t) lie on? 121 1 x² + y? 121 Oz =…

A: First define the curve of the surface r(t) = &lt; x(t), y(t), z(t) &gt;

Q: A yo-yo which is 3 inches in diameter spins at a rate of 5000 revolutions per minute. How fast is…

A: Rounds per minute = 5000 To Find:    Speed of the edge of yo-yo spinning in miles per hour…

Q: The volume V = (4/3)πr3 of a sphericalballoon changes with the radius.At what rate (ft3/ft) does the…

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Q: Find the polar moment of inertia of the shaded area about the axis perpendicular to origin of the…

A: Answer is mentioned below

Q: Q 6/ Compute the moment of * the Inertia for the shaded area with respect to the Y- — axis? 2 ft --…

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Q: Find the motion of the mass-spring system in Fig. 72 with mass 0.125 kg, damping 0, spring constant…

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Q: The lateral surface area S of a right circularcone is related to the base radius r and height h by…

A: Since, the lateral surface area S of a right circular cone is related to the base radius 'r' and…

Q: Find the motion of the mass-spring system in Fig. 72 with mass 0.125 kg, damping 0, spring constant…

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Q: Q/B) Find the length of the cardioid curve: r 1+ cose

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Q: 1. Sketch the parametrie and arve elim inate the parameter to tind the Cartesian equation f the a.…

A: To determine the Cartesian equation of the curves.

Q: 2. Line BC tangent to circle A at B, with diameter 6 cm, BC = 4 cm, and GC I BD. D A G Find: f) mDF…

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Q: y = 2(1+cos( Ɵ)) Find the area of the surface of revolution formed by rotating the upper half of…

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Q: Eliminate the Parametor t townite the farametric sauation as a Cartosian cuetion =4 Sin Lt) 3D

A: From both equations, we find sin(t) and cos(t)

Q: Make a sketch to illustrate the bearing starting from the origin in the center. N77°E

A: Solution

Q: The value of Jacobian in cylindrical coordinate system is given by а. r b. 2 sin e с. d. r sin? 0

A: For the cylindrical co-ordinate system:                           The value of Jacobian can be…

Q: Verify the given moment(s) of inertia and find i and ỹ. Assume that each lamina has a density of p =…

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