12. prove that sin x and cos x are orthogonal functions in the vector space co, of exercise 10, with the inner product defined there
10. let cab be the vector space of all continuous real-valued functions with domain a s xs b prove that defined in cj by (f, g) xg(x) dx, is an inner product in c

Match the following terms with their definitions. 1. bisector of a segment ray ba and ray bc are opposite rays if a, b, and c are collinear and b (the endpoint of both rays) is between a and c. 2. opposite rays a ray, , is the set of points beginning at point a and going infinitely in the direction of point b. 3. collinear points a line or segment that intersects the segment at its midpoint. 4. betweenness of points a set of two or more points all on the same line. 5. ray the distance between the endpoints of a segment. 6. space point b is between a and c if a, b, and c are collinear and the equation ab + bc = ac is true, where ab, bc, and ac are the distances between points a and b, b and c, and a and c, respectively. 7. midpoint of a segment a set of two or more points all on the same plane. 8. coplanar points the point on a segment that divides the segment into two equal segments. 9. length of a segment the set of all possible points. 10. line segment the set of two different endpoints and all points between them.

Identify the graph of y = ln x + 1.

Find the number of liters in 12.8 gal of gasoline. round to the nearest hundredths