4. Consider the following formulas for the moments of a plane area or thin plate:
Let $g(x) \le f(x)$ be continuous functions on $x \in [a, b]$ for the area of uniform density $\rho$ bounded
by $y = f(x)$, $y = g(x)$, $x = a$, and $x = b$; the moments about the x-axis and the y-axis are
$M_y = \rho \int_a^b x(f(x) - g(x)) dx$ and $M_x = \rho \int_a^b (f(x) - g(x)) \left(\frac{f(x) + g(x)}{2}\right) dx$
For either $M_y$ or $M_x$, describe the formula heuristically (i.e. so that a third-party could understand
for themselves where the formula came from and what the pieces mean).
Section 2: Multiple Choice. Write the letter of the best choice in the space to the right of the problem.
5.
Consider the sofa pictured above (©2014 CreativeApplications.net)
and assume that it is a static system (that is, a system that does not
move) so we know the sofa is balanced. Choose the statement we
know to be true.
a. $x = \bar{x}$ is in line with the sofa leg.
b. $y = \bar{y}$ is in line with the sofa leg.
c. We cannot discern either (a) or (b).
