Find the sum of each pair of vectors and match it with the magnitude of the resultant vector.
magnitude 3.5 m/s, direction angle 35
magnitude 4 m/s, direction angle 150
magnitude 4.5 m/s, direction angle 55
magnitude 3 m/s, direction angle 135
magnitude 3 m/s, direction angle 70
magnitude 5 m/s, direction angle 210°
magnitude 6 m/s, direction angle 120
magnitude 2 m/s, direction angle 240
5.83 m/s
4.05 m/s
5.29 m/s
3.32 m/s

Find the volume of the solid obtained by rotating the region enclosed by the curves y=1x and y=7^-x about the x-axis. (use symbolic notation and fractions where needed.) volume =

Statement reason 1. δabc is similar to δced. given 2. 3. definition of slope 4. slope of slope of definition of slope 5. slope of × slope of multiplying the slopes 6. slope of × slope of substitution property of equality 7. slope of × slope of simplifying the right side the table contains the proof of the relationship between the slopes of two perpendicular lines. what is the reason for statement 2? a. parallel line segments that meet a common perpendicular line are proportional in length. b. the lengths of vertical and horizontal sides in congruent triangles are in a common ratio. c. trigonometric identities determine the lengths of the legs in a right triangle. d. corresponding side lengths in similar triangles are proportional in length.

Find the measure of angle b in the following triangle