Calculus: Special Edition: Chapters 1-5 (w/ WebAssign)
6th Edition
ISBN: 9781524908102
Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE
Publisher: Kendall Hunt Publishing
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Chapter 13.5, Problem 54PS
To determine
To calculate: The mass of the homogeneous lamina that has the triangular surface
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3. A greenhouse has a glass dome in the shape of the paraboloid
z=8-2x²-2y2
and a flat wooden floor at z = 0. Let S be the closed surface formed by the dome and the floor,
oriented with outward unit normal.
Suppose that the temperature in the greenhouse is given by
T(x, y, z) = x²+ y²+3(z − 2)².
The temperature gives rise to a heat flux density field
F(x, y, z) -kVT
=
where k is a positive constant that depends on the insulating properties of the medium. Assume
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(a) Sketch S, clearly labelling any intercepts and the direction of the normal vector.
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F.ndS
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2. Consider two spheres of equations r² + y² + z² 2x-2y + 4z-2 and x² + y² + ² = 4x+2y+4.
(a) For which points P on the first sphere and Q on the second sphere is the distance d(P.Q)
maximum?
ent
(b) Find the volume of the solid that lies inside both of the above spheres. (Hint: First show
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V = ™h² (3R – h).)
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A. * 7(8 – 2x)² dx
B.,(2x + 8)? + f, (8 – 2x)²dx
C. (8 – y)? dy
D. (8 - y)? dy
E. (8 – y)? dy
0 8
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0 4
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Chapter 13 Solutions
Calculus: Special Edition: Chapters 1-5 (w/ WebAssign)
Ch. 13.1 - Prob. 1PSCh. 13.1 - Prob. 2PSCh. 13.1 - Prob. 3PSCh. 13.1 - Prob. 4PSCh. 13.1 - Prob. 5PSCh. 13.1 - Prob. 6PSCh. 13.1 - Prob. 7PSCh. 13.1 - Prob. 8PSCh. 13.1 - Prob. 9PSCh. 13.1 - Prob. 10PS
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