Find the mass of a thin wire shaped in the form of the curve x = 2 t , y = ln t , z = 4 t ( 1 ≤ t ≤ 4 ) if the density function is proportional to the distance above the x y -plane .
Find the mass of a thin wire shaped in the form of the curve x = 2 t , y = ln t , z = 4 t ( 1 ≤ t ≤ 4 ) if the density function is proportional to the distance above the x y -plane .
Find the mass of a thin wire shaped in the form of the curve
x
=
2
t
,
y
=
ln
t
,
z
=
4
t
(
1
≤
t
≤
4
)
if the density function is proportional to the distance above the
x
y
-plane
.
A lamina occupies the region inside the circle x2 + y2 = 10y but outside the circle x2 + y2 = 25. Find the center of mass if the density at any point is inversely proportional to its distance from the origin.
Consider the lamina on the xy-plane bounded by the circle x2 + y2 = 1 and the lines y = x and y = -x, and lies on the upper half plane, y >0. Suppose that the density of this lamina at any point is proportional to the distance of the
point from the origin.
(a) Sketch the lamina. (b) Find the mass of the lamina.
A lamina occupies the region inside the circle x² + y² = 10y but outside the circle x² + y² = 25. Find the center of mass if the density at any point is inversely proportional to its distance from the origin.
(x, y) = (0, 6.323
)
X
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