Bumblebee Problem: A bumblebee flies past a flower. It decides to go back for another look. Just before it reaches the flower, it turns and flies off. Its displacement from the flower, d(t), in feet, is given by d(t) = 0.2t 3 1.8t 2 + 3t + 5.6 where t is time, in seconds. Figure 15-5h shows the graph of this function. Figure 15-5h a. What is the bees average velocity from t = 6 to t = 6.01 seconds? (Average velocity is the average rate for the timedisplacement function.) b. Write an expression for the bees average velocity from 6 seconds to t seconds. By simplifying the resulting fraction, calculate algebraically its instantaneous velocity at t = 6 seconds. c. On a copy of Figure 15-5h, plot a line through the point at t = 6 with slope equal to the instantaneous velocity at time t = 6. How does the line relate to the graph? d. Figure 15-5h indicates graphically that there are no positive values of t for which the bee is at the flower. Show algebraically that this is true. e. At what negative value of t was the bee at the flower? At what positive time was it closest to the flower? How close?
CLA 322 Monsters 4/12/2016 Western Phoenix continued: “Now the Phoenix's bright eye grows dim and the pupil becomes palsied by the frost of years, like the moon when she is shrouded in clouds and her horn beings to vanish in the mist. Now his wings, wont to cleave the clouds of heaven, can scarce raise them from the earth. Then, realizing that his span of life is at an end and in preparation for a renewal of his splendour, he gathers dry herbs from the sun-warmed hills, and making an interwoven heap of the branches of the precious tree of Saba he builds that pyre which shall be at once his tomb and his cradle. On this he takes his seat and as he grows weaker greets the Sun with his sweet voice; offering up prayers and supplications he begs that those fires will give him renewal of st