Find the determinant of the following matrix: a = [e^x cos x sin x e^x - sin x cos x e^x - cos x - sin x]. (this determinant is known as a wronskian: this will come up in chapter 4).

An empty bucket is placed under a faucet dripping at a constant rate of 4 milliliters per minute. with the given information, which of these statements is a reasonable conclusion? a there will be 24 milliliters of water in the bucket after 16 hour. b there will be 60 milliliters of water in the bucket after 14 hour. c there will be 160 milliliters of water in the bucket after 20 minutes. d there will be 100 milliliters of water in the bucket after 40 minutes.

Hiroaki wants to find 3 3/4 - 7/8 explain why he must rename 3 3/4 to do the subtraction.

Does the point (1, sqrt 7) lie on circle shown.