Perform the following tasks for the equations below: (1) Find a general solution of the associated homogeneous equation. (2) Use the method of undetermined coefficients to find a particular solution of the given equation. (3) Write down the general solution of the given equation. (4) Find the solution satisfying the given initial conditions. y''-6y'-7y=-9e^{-2t}, \quad y(0)=6, \quad y'(0)=3y ′′ −6y ′ −7y=−9e −2t ,y(0)=6,y ′ (0)=3

The length of each stair is 11 inches. what is the rise, r, for each stair? round to the nearest inch. 2 inches 7 inches 17 inches 24 inches

Igor stravinsky tires sells approximately 3,760,000 car tires and 1,200,000 truck tires each year. about 47,000,000 care tires and 26,000,00 truck tires are sold each year in the united states. what is stravinsky's market share in each of these two markets (cars and trucks)?

The number of chocolate chips in an 18-ounce bag of chocolate chip cookies is approximately normally distributed with a mean of 1252 chips and standard deviation 129 chips. (a) what is the probability that a randomly selected bag contains between 1100 and 1500 chocolate chips, inclusive? (b) what is the probability that a randomly selected bag contains fewer than 1125 chocolate chips? (c) what proportion of bags contains more than 1225 chocolate chips? (d) what is the percentile rank of a bag that contains 1425 chocolate chips?