3.44 each rear tire on an experimental airplane issupposed to be filled with a pressure of 40 pound per squareinch(psi).let x denote the actual air pressure for the right tireand y denote the actual air pressure for the left tire. suppose that xand y are random varibles with the jointdensity
f(x, y)= k(x^2+y^2, 30< -x< 50;
30< -y< 50
0, elsewhere
a.) find k
b.) find p(30< -x< -40 and 40< -y< 50)
c.) find the probability that both tires areunderfilled.

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?