In the study of a nonlinear spring with periodic forcing, the equation y prime prime plus ky plus ry cubedy′′+ky+ry3equals=Upper A cosine omega tAcosωt arises. Let kequals=44, requals=33, Aequals=77, and omegaωequals=88. Find the first three nonzero terms in the Taylor polynomial approximation to the solution with initial values y(0)equals=0, y prime (0 )y′(0)equals=1.

An annual marathon covers a route that has a distance of approximately 26 miles. winning times for this marathon are all over 2 hours. the following data are the minutes over 2 hours for the winning male runners over two periods of 20 years each. earlier period 14 12 15 22 13 10 19 13 9 14 20 18 16 20 23 12 18 17 6 13 recent period 7 11 7 14 8 9 11 14 8 7 9 8 7 9 9 9 9 8 10 8 (a) make a stem-and-leaf display for the minutes over 2 hours of the winning times for the earlier period. use two lines per stem. (use the tens digit as the stem and the ones digit as the leaf. enter none in any unused answer blanks. for more details, view how to split a stem.) minutes beyond 2 hours earlier period 0 1 2 (b) make a stem-and-leaf display for the minutes over 2 hours of the winning times for the recent period. use two lines per stem. (use the tens digit as the stem and the ones digit as the leaf. enter none in any unused answer blanks.) minutes beyond 2 hours recent period (c) compare the two distributions. how many times under 15 minutes are in each distribution

Which of the following are independent events? a) knowing that it is going to rain tomorrow, and bringing an umbrella to schoolb) knowing that you have to get up early tomorrow, and going to bed before 9 p.mc) knowing that it is going to rain tomorrow, and going to bed before 9 p.md) knowing that you have a test in school tomorrow, and studying thw night before

Describe the graph of 3x+2> 2 and 3x< 6