Consider the differential equation y '' − 2y ' + 10y = 0; ex cos(3x), ex sin(3x), (−[infinity], [infinity]). Verify that the given functions form a fundamental set of solutions of the differential equation on the indicated interval. The functions satisfy the differential equation and are linearly independent since W(ex cos(3x), ex sin(3x)) = ≠ 0 for −[infinity] < x < [infinity]. Form the general solution. y =

Each equation given below describes a parabola. which statement best compares their graphs? x = 2y^2 x = 8y^2

The pyramid shown has a square base that is 24 centimeters on each side. the slant height is 16 centimeters. what is the lateral surface area?

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?