An open-top box is to be constructed from a 8 in by 14 in rectangular sheet of tin by cutting out squares of equal size at each corner, then folding up the resulting flaps. let x denote the length of the side of each cut-out square. assume negligible thickness. (a) find a formula for the volume, v, of the box as a function of x. v(x) = (b) for what values of x does the formula from part (a) make sense in the context of the problem? (c) on a separate piece of paper, sketch a graph of the volume function. (d) what, approximately, is the maximum volume of the box? (include units: (units))

Just tell me how to set up the equation.

Define multiplicative inverse. give an example of a number and its multiplicative inverse.

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?