Suppose b is any integer.
a) if b mod 12 = 5, what is 6b mod 12? in other words, if the division of b by 12 gives a remainder of 5, what is the remainder when 6b is divided by 12?
your solution should show that you obtain the same answer no matter what integer you start with.
b) using the definition by mod find an expression for b in terms of 12, 5, and an integer m.

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