6. Do the following tasks using Mathematica. y²dA, where R is the region bounded by the curves xy = 1 , xy = 2 , R x * y ^ 2 = 1 and x * y ^ 2 = 2 Transform R into uv plane by making an appropriate change of variables in order to find the integral. (a) Plot R in both ry and uv planes. (b) Find the Jacobian of the transformation (c) Evaluate the integral using the transformation

For the following sequence determine the common difference (if it is an arithmetic sequence) or the common ratio (if it is a geometric sequence).

Which expression is equivalent to sq-80

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?