Using separation of variables solve the following wave equation problem for where and Assume that the solution has the form Calculate , , and (BE CAREFUL: and are just the functions of and . They could be something like . Any coefficient in front of them goes into . So for an answer like the goes into while the goes into . Use pi to write . If your answer includes a write it as cos(n*pi), do NOT change it to . DO change to 1 and to 0. For you can use e^x or exp(x). Keep fractions as fractions)

When a rectangle is dilated, how do the perimeter and area of the rectangle change?

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?

How can (square root of 25) ^2 be rewritten?