Each base in this prism like figure is a semicircle with a radius of 7cm what is the volume of the shape?

Show algebraically that f and g are inverse functions f(x)=x^2/-6; g(x)=square root of 2x+12

Which is the graph of the function y=2(4)^x

1- is the product of two rational numbers irrational or rational? first, make a hypothesis by multiplying two rational numbers. then, use variables such as x=a/b and y=c/d and the closure property of integers to prove your hypothesis. 2- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis. 3- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in part b?