A company that produces ribbon has found that the marginal cost of producing x yards of fancy ribbon is given by Upper C prime (x )equalsnegative 0.00001 x squared minus 0.02 x plus 58 for x less than or equals 1600, where Upper C prime (x )is in cents. Approximate the total cost of manufacturing 1600 yards of ribbon, using 5 subintervals over [0 comma 1600 ]and the left endpoint of each subinterval.

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?