Amass weighing 6 pounds stretches a spring 2 feet. the mass is attached to a dashpot device that offers a damping force numerically equal to β (β > 0) times the instantaneous velocity. determine the values of the damping constant β so that the subsequent motion is overdamped, critically damped, and underdamped. (if an answer is an interval, use interval notation. use g = 32 ft/s2 for the acceleration due to gravity.) (a) overdamped

If a is a nonzero real number then the reciprocal of a is

2x minus y equals 6, x plus y equals negative 3

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.