Show that y = x is a solution of x^2y ′′ − x(2 + x cot x)y′ + Use the method of variation of parameters to find the general solution of the nonhomogeneous equation x^2y ′′ − x(2 + x cot x)y′ + (2 + x cot x)y = x^3 sin x.

Areal estate agent earns $32,000 a year plus $1,000 for each apartment he sells. write an equation that shows the relationship between the number of apartments abe sells,n, and the total amount he earns in a year,e. what is the total amount abe would earn from selling 10 apartments in one year

Aretha wanted to gather data about the cost of local bowling leagues in her area. she plotted the data and determined that the average bowling league costs consist of a one-time registration fee and a monthly fee modeled by the equation y = 15x + 20. identify and interpret the y-intercept in this model. the y-intercept is 20. this is the cost per month. the y-intercept is 20. this is the cost of registration. the y-intercept is 15. this is the cost of registration. the y-intercept is 15. this is the cost per month.

Iam at home. /: i am playing video games. translate the following statement into symbolic form.