If ar2 + br + c = 0 has equal roots r1, show that L[ert] = a(ert)" + b(crt)' + cert = a(r - r1 )2er1. Since the right side of is zero when r = r1, it follows that exp(r1,t) is a solution of L[y] = ay" + by' + cy = 0. Differentiate with respect to r and interchange differentiation with respect to r and with respect to t, thus showing that Since the right side of is zero when r = r1 conclude that t exp(r1 t) is also a solution of L[V] =0. Determine a suitable form of Y(t) if the method of undetermined coefficients is to be used. y" + 2y' + 5y = 3et-t cos2t - 2te-2t cost

What is the number 321,000,000 in scientific notation? also what is the number? ?

Segment ab is shown on the graph. which shows how to find the x-coordinate of the point that will divide ab into a 2: 3 ratio using the formula

Apoll is being conducted at a mall nothingto obtain a sample of the population of an entire country. what is the frame for this type of​ sampling? who would be excluded from the survey and how might this affect the results of the​ survey? what is the frame for this type of​ sampling? a. the frame is people who need new clothes. b. the frame is people who shop at the mall. c. the frame is people who like to shop. d. the frame is the entire population of the country. who would be excluded from the survey and how might this affect the results of the​ survey? a. any person that does not need new clothes is excluded. this could result in sampling bias due to undercoverage. b. any person who does not shop at the mall is excluded. this could result in sampling bias due to undercoverage. c. any person who does not shop at the mall is excluded. this could result in nonresponse bias due to people not participating in the poll. d. there is nobody that is being excluded from the survey.