Think About It The center of mass of a solid of constant density is shown in the figure. In Exercises 43-46, make a conjecture about how the center of mass ( x ¯ , y ¯ , z ¯ ) will change for the nonconstant density ρ ( x , y , z ) . Explain. (Make your conjecture without performing any calculations.) ρ ( x , y , z ) = k x z 2 ( y + 2 ) 2
Think About It The center of mass of a solid of constant density is shown in the figure. In Exercises 43-46, make a conjecture about how the center of mass ( x ¯ , y ¯ , z ¯ ) will change for the nonconstant density ρ ( x , y , z ) . Explain. (Make your conjecture without performing any calculations.) ρ ( x , y , z ) = k x z 2 ( y + 2 ) 2
Solution Summary: The author explains how the center of mass of a solid of constant density will change for the non-constant density.
Think About It The center of mass of a solid of constant density is shown in the figure. In Exercises 43-46, make a conjecture about how the center of mass
(
x
¯
,
y
¯
,
z
¯
)
will change for the nonconstant density
ρ
(
x
,
y
,
z
)
. Explain. (Make your conjecture without performing any calculations.)
Determine the type of points on the
X (u, v) = (u, v, u?) surface.
Differential geometry
Astronomers use a technique called stellar stereography todetermine the density of stars in a star cluster from theobserved (two-dimensional) density that can be analyzedfrom a photograph. Suppose that in a spherical cluster ofradius R the density of stars depends only on the distancefrom the center of the cluster. If the perceived star density isgiven by y(s) , where is the observed planar distance fromthe center of the cluster, and x (r ) is the actual density, it canbe shown that
y(s) = integral s to r 2 r /sqrt ( r2 - s2 ) x(r) dr
If the actual density of stars in a cluster is x (r ) = 1/2 (R-r)2 ,find the perceived density y(s)
y = ex, y = 0, x = 0, x = 3
Find the exact coordinates of the centroid.
(x, y) =
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Area Between The Curve Problem No 1 - Applications Of Definite Integration - Diploma Maths II; Author: Ekeeda;https://www.youtube.com/watch?v=q3ZU0GnGaxA;License: Standard YouTube License, CC-BY