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Moments of InertiaIn Exercises 53- 56, find
(a)
(b)
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Chapter 14 Solutions
Bundle: Calculus: Early Transcendental Functions, Loose-leaf Version, 6th + WebAssign Printed Access Card for Larson/Edwards' Calculus: Early Transcendental Functions, 6th Edition, Multi-Term
- Multivariable calculus. Let F vector = <x,y,z> and use the Divergence Theorem to calculate the (nonzero) volume of some solid in IR3 by calculating a surface integral. (You can pick the solid).arrow_forward4 Find the centroid of the next plate area You y A₁ -x C₁ xa -x C₂ A₂ Xarrow_forwardCalculate the fluid force on one side of the plate The fluid force on one side of the plate is using the coordinate system shown below. Assume Ib. the density is 62.4 lb/ ft3. ... у (f) Surface of pool x (ft) -у3 — 2 Depth \y| (x,y) 7arrow_forward
- Determine the x- and y-coordinates of the centroid of the shaded area. 7" y -8" Answers: (X,Y)= (i 3" 13" 8" " x ) in.arrow_forwardUseDivergence theor em to find the ouward flux of F = 2xz i - 3xy j - zk across the boundary of theregion cut from the first octant by the planey +z = 4 and the elliptical cy linder 4x +y = 16. %3Darrow_forwardConsider the lamina in the shape of the triangle whose vertices are (0, 0), (L, 0), and (0,L) for some L ∈ R+. Calculate the moments of inertia, Ix and Iy, for this lamina whose density is proportional to the square of the distance from the vertex opposite the hypotenuse.arrow_forward
- Use spherical coordinates. (a) Find the volume of the solid that lies above the cone ? = pi/3 and below the sphere ? = 8 cos(?) (b) Find the centroid of the solid in part (a). (x, y, z) =arrow_forwardEvaluate the circulation of G = xyi + zj + 4yk around a square of side 4, centered at the origin, lying in the yz-plane, and oriented counterclockwise when viewed from the positive x-axis. Circulation = Jo F. dr =arrow_forwardry dA where D is the triangular region with vertices (0,0), (1,0), (0,3) Evaluate the double integral I = Darrow_forward
- Locate the centroid x of the solidarrow_forwardFind the surface area of the "Coolio McSchoolio" surface shown below using the formula: SA = integral, integral D, ||ru * rv||dA %3D The parameterization of the surface is: r(u,v) = vector brackets (uv, u + v, u - v) where u^2 + v^2 <= 1 A.) (pi/3)(6squareroot(6) - 8) B.) (pi/3)(6squareroot(6) - 2squareroot(2)) C.) (pi/6)(2squareroot(3) - squareroot(2)) D.) (pi/6)(squareroot(6) - squareroot(2)) E.) (5pi/6)(6 - squareroot(2))arrow_forwardwww Use the surface integral in Stokes' Theorem to calculate the flux of the curl of the field F = zi + 5xj+yk across the surface S. r(r,0) =r cos 0i +r sin 0j+ (4-r) k, 0srs2,0 s0s 2x in the direction away from the origin.arrow_forward
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,
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