In this problem you will use undetermined coefficients to solve the nonhomogeneous equation y′′+2y′+y=6te−t+3t+9 with initial values
y(0)=2 and y′(0)=1.
(a) Write the characteristic equation for the associated homogeneous equation. (Use r for your variable.)
(b) Write the fundamental solutions for the associated homogeneous equation.
(c) Write the form of the particular solution and its derivatives. (Use A, B, C, etc. for undetermined coefficients.
(d) Write the general solution.
(e) Plug in the initial values and solve for c1 and c2 to find the solution to the initial value problem.

Assume that there is a 11% rate of disk drive failure in a year. a. if all your computer data is stored on a hard disk drive with a copy stored on a second hard disk drive, what is the probability that during a year, you can avoid catastrophe with at least one working drive? b. if copies of all your computer data are stored on four independent hard disk drives, what is the probability that during a year, you can avoid catastrophe with at least one working drive?

Find the measure of angle c in the following triangle.

The probability that a u. s. resident has traveled to canada is 0.18 and to mexico is 0.09. a. if traveling to canada and traveling to mexico are independent events, what is the probability that a randomly-selected person has traveled to both? (page 109 in the book may ) b. it turns out that only 4% of u. s. residents have traveled to both countries. comparing this with your answer to part a, are the events independent? explain why or why not. (page 119 may ) c. using the %’s given, make a venn diagram to display this information. (don’t use your answer to part a.) d. using the conditional probability formula (page 114 in the book) and the %’s given, find the probability that a randomly-selected person has traveled to canada, if we know they have traveled to mexico.