Let $f(x) = \lfloor x \lfloor x \rfloor \rfloor$ for $x \ge 0.$ (a) Find all $x \ge 0$ such that $f(x) = 1.$
(b) Find all $x \ge 0$ such that $f(x) = 3.$
(c) Find all $x \ge 0$ such that $f(x) = 5.$
(d) Find the number of possible values of $f(x)$ for

Nthe opening scene of the movie raiders of the lost ark, indiana jones replaces a golden statue with a bag of sand. the platform on which the statue is placed is designed to detect the mass of the statue. if the bag of sand has a different mass than the statue, then a mechanism triggers and destruction ensues. the density of gold is about 20\text{ g/cm}^320 g/cm 3 20, space, g, slash, c, m, start superscript, 3, end superscript. the density of sand can be estimated at 2.5\text{ g/cm}^32.5 g/cm 3 2, point, 5, space, g, slash, c, m, start superscript, 3, end superscript. the gold statue can be modeled as a cylinder with height 25\text{ cm}25 cm25, space, c, m and radius 8\text{ cm}8 cm8, space, c, m. in terms of \piπpi, what is the mass of sand indiana jones needs to avoid triggering the mechanism?