Use the method of cylindrical shells to find the volume v generated by rotating the region bounded by the given curves about the y-axis. y = 12e−x2, y = 0, x = 0, x = 1 sketch the region and a typical shell. step 1 rotating a vertical strip around the y-axis creates a cylinder with radius r = and height h = . sketch the region and a typical shell.

George is folding a piece of paper to make an origami figure. each time he folds the paper, the thickness of the paper is doubled. the paper starts out flat, with a thickness of 1 millimeter. a. write a list of six ordered pairs showing the output as the thickness of the paper when the input is the number of times it is folded. explain how you came up with your ordered pairs. b. is this relation a function? explain why or why not using the ordered pairs you came up with in part a.

David bought a poster for an art project. the poster is 2.7 feet wide and 3.9 feet tall. what is the area of the poster?

If m∠abc = 70°, what is m∠abd? justify your reasoning.  using the addition property of equality, 40 + 70 = 110, so m∠abd = 110°.  using the subtraction property of equality, 70 − 30 = 40, so m∠abd = 30°.  using the angle addition postulate, 40 + m∠abd = 70. so, m∠abd = 30° using the subtraction property of equality.  using the angle addition postulate, 40 + 70 = m∠abd. so, m∠abd = 110° using the addition property of equality.