Leo determines that he needs his retirement income payments to be $2600 per month. he plans to open a payout annuity with a 30-year maturity period. the payout annuity has an annual interest rate of 4.8% compounded monthly. how much money will he need to invest initially in the account to get the payments he needs?

There is a line with slope 1/a going through the point (a, a²). find the equation of the line perpendicular to this line at this point. (don’t let this problem intimidate you! solve the problem as you would if i’d given you specific values. just use variables instead.)

Aswimming pool has an input pump for filling the pool and an output pump for emptying the pool. the input pump can fill the pool in 3 hours, and the output pump can drain the pool in 5 hours. as you go to bed, the pool is full, but a neighbor’s kid turns on the output pump. at midnight, you awake to find the pool half empty. immediately, you turn on the input pump, but you are sleepy and forget to turn off the output pump. at what time will the pool become full?

Find the maximum value of p= 4x + 5y subject to the following constraints :