3. (8 points) Rose is making a postcard decorated with ecks of gold dust! The part of the postcard that Rose is decorating with ecks of gold dust this year is in a shape of isosceles trapezoid with top width equal to 4cm, the bottom width equal to 10 em. and both legs equal to 5 cm1 shown as below. 4cm 10cm Suppose that the density of gold dust on the postcard is given by {)(y) mg/cm2, where 3; represents distance to the base of length 10 cm. (a) (5 points) Write a general Riemann sum that approximates the amount of gold dust on the postcard. Start by slicing into in slices; your nal approximation should be in terms of 7:. Be sure to explain clearly how you are slicing and all the details of your work, including what your notation means. (b) (2 points) Write a denite integral giving the exact amount of gold dust in the postcard. (c) (1 point) This year, Rose would like to save money by using less gold dust. W'hich of the following density functions Rose should use? Briey explain your reasoning. You do not need to evaluate any of the integrals. 1. Rose should use py) = 4 i y in order to save money. ii. Rose should use Ml?!) = y in order to save money