Suppose there is an integer k such that every man on a desert island is willing to marry exactly k of the women on the island and every woman on the island is willing to marry exactly k of the men. also, suppose that a man is willing to marry a woman if and only if she is willing to marry him. show that it is possible to match the men and women on the island so that everyone is matched with someone that they are willing to marry.

Ahigh-altitude spherical weather balloon expands as it rises, due to the drop in atmospheric pressure. suppose that the radius r increases at the rate of 0.02 inches per second, and that r = 36 inches at time t = 0. determine the equation that models the volume v of the balloon at time t, and find the volume when t = 360 seconds. v(t) = 4π(0.02t)2; 651.44 in3 v(t) = 4π(36 + 0.02t)2; 1,694,397.14 in3 v(t) = four pi times the product of zero point zero two and t to the third power divided by three.; 4,690.37 in3 v(t) = four pi times the quantity of thirty six plus zero point zero two t to the third power divided by three.; 337,706.83 in3