HOW DO YOU SEE IT The center of mass of the lamina of constant density shown in the

Chapter 14, Problem 48

(choose chapter or problem)

HOW DO YOU SEE IT? The center of mass of the lamina of constant density shown in the figure is \(\left(2, \frac{8}{5}\right)\). Make a conjecture about how the center of mass \((\bar{x}, \bar{y})\) changes for each given nonconstant density \(\rho(x, y)\). Explain. (Make your conjecture without performing any calculations.)

(a) \(\rho(x, y)=k y\)

(b) \(\rho(x, y)=k|2-x|\)

(c) \(\rho(x, y)=k x y\)\

(d) \(\rho(x, y)=k(4-x)(4-y)\)

Text Transcription:

(2,8/5)

(bar x,bar y)

rho(x,y)

rho(x, y)=ky

rho(x, y)=k|2-x|

rho(x, y)=kxy

rho(x, y)=k(4-x)(4-y)