Evaluate (x2 + y2) dv e where e lies between the spheres x2 + y2 + z2 9 and x2 + y2 + z2 16.

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6.9 Hyperbolic Functions and Hanging Cables. 477. represent a portion of the curve x 2 − y 2 = 1, as may be seen by writing x 2 − y 2 = cosh2 t − sinh2 t = 1

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Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. 8, x2 + y2 + z2 − 2x − 4y = 0 and touch the plane 4x + 3y = 25. 14. Find the center and radius of the circle x2+y2+z2−8x+4y+8z−45 = 0 and x − 2y + z − 3 = 0. 15. Show that the spheres x2 + y2 + z2 + 6y + 2z + 8 = 0 and x2 + y2 + z2 + 6x + 8y + 4z + 20 = 0 cut orthogonally. Find their plane of intersection.

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The volume of the solid that lies between the paraboloid z=2x2+2y2 and the plane z=8. The volume of the solid bounded by the cylinder x2+y2=16 ... and below z2+x2+y2=z. Get the detailed answer: Use spherical coordinates. Evaluate // Vx2 + y2 2 dV, where E lies above the cone z-Vx2.+y 2 and between the spheres x2 + y2 +z2 =

E xyzdV = Z 10 0 Z z 0 Z y 0 xyzdxdydz= Z 10 0 Z z 0 1 2 y3zdydz = 1 8 Z 1 0 0z5dz= 1 48 106 6. Use spherical coordinates to evaluate the triple integral RRR E exp(p 2(x +y2+z2)) x 2+y +z dV, where Eis the region bounded by the two spheres x2 +y2 +z2 = 1 and x 2+ y + z2 = 36. Solution: In spherical coordinates, we have that x = rcos sin˚, y ... Problem 23 Easy Difficulty. Use spherical coordinates. Evaluate $ \iiint_E (x^2 + y^2)\ dV $, where $ E $ lies between the spheres $ x^2 + y^2 + z^2 = 4 $ and $ x^2 + y^2 + z^2 = 9 $. Identify the graph of the equation 9x2 + 16y2 = 144. The given equation is equivalent to x2/16 + y2/9 = 1. Hence, the graph is an ellipse with semimajor axis of length a = 4 and semiminor axis of length b = 3. (See Fig. 5-12.) The vertices are (−4, 0) and (4, 0). Since c = a 2 − b 2 = 16 − 9 = 7, the eccentricity e is c /a = 7 / 4 ≈ 0 ...