A student wrote a proof about the product of two rational numbers: 1. Let 3 = and let y = à, where a and c are defined to be integers, and b and d are nonzero
integers.
2. By substitution, ry =
3. By applying the closure property of integers and nonzero integers on multiplication, ac is an
integer and bd is a nonzero integer.
What conclusion can the student now make about the product ty?

Determine whether the following statements are true and give an explanation or counterexample. bold a. when using the shell method, the axis of the cylindrical shells is parallel to the axis of revolution. bold b. if a region is revolved about the y-axis, then the shell method must be used. bold c. if a region is revolved about the x-axis, then in principle it is possible to use the disk/washer method and integrate with respect to x or the shell method and integrate with respect to y.

A, b, c, and d have the coordinates (-8, 1), (-2, 4), (-3, -1), and (-6, 5), respectively. which sentence about the points is true? a. a, b, c, and d lie on the same line. b. and are perpendicular lines. c. and are parallel lines. d. and are intersecting lines but are not perpendicular. e. and are parallel lines.

Is it greater than or less than7*3_9*2