A 1-kilogram mass is attached to a spring whose constant is 24 N/m, and the entire system is then submerged in a liquid that imparts a damping force numerically equal to 11 times the instantaneous velocity. Determine the equations of motion if the following is true.

(a) the mass is initially released from rest from a point 1 meter below the equilibrium position x(t) = -3/5 e^-8t + 8/5 e^-3t m (b) the mass is initially released from a point 1 meter below the equilibrium position with an upward velocity of 11 m/s x(t) 2e^-8t -e^-3t m

Martha has a deck of cards. she has lost some of the cards, and now the deck only contains nine spades, eleven diamonds, eight clubs, and twelve hearts. martha predicts that whenever she draws a card from the deck without looking, she will draw a club one-fifth of the time. which activity would best allow martha to test her prediction? a. randomly draw a card from the box and see if it is a club. b. randomly draw a card. then, continue to draw another card until all eight clubs are drawn. c. randomly draw and replace a card 120 times. then, observe how close to 30 times a club is drawn. d. randomly draw and replace a card 100 times. then, observe how close to 20 times a club is drawn.

What is the similarity ratio of a cube with volume 729m^3 to a cube with volume 3375 m^3

Determine domain and range, largest open interval, and intervals which function is continuous.