If f is a continuous function such that the integral from 1 to 4 of f of x, dx equals 10, evaluate the integral from 2 to 8 of 2 times f of 2 times x, dx.

Express the following as a function of a single angle, cos(60) cos(-20) - sin(60) sin(-20)

Which simplifys to a+ b? a-(1-b)+1 -(1-a)-b+1 (a--1) -1)+1

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?