You are considering installing a pendulum in the amusement park visitor’s center. The time it takes a pendulum to complete a full cycle or swing depends upon the length of the pendulum. The formula is given by T = 2 π √(L/32) where T represents the time in seconds and L represents the length of the pendulum in feet. You’d like your pendulum to take 20 seconds to complete a cycle. How long will the pendulum need to be? Is this reasonable in your building, which is planned to be 20 feet high?

Use the elimination method to solve the system of equations -x+5y=-4 and 4x+3y=16

A. use the formula for continuous compounding with the original example: $1000 invested at 2% for 1 year. record the amount to 5 decimal places. use a calculator. b. compare it to the result using the original compound interest formula with n = 365 calculated to 5 decimal places. which has a larger value? explain.

Acaterer knows he will need 60, 50, 80, 40 and 50 dinner napkins on five successive evenings. he can purchase new napkins initially at 25 cents each, after which he can have dirty napkins laundered by a fast one-day laundry service (i.e., dirty napkins given at the end of the day will be ready for use the following day) at 15 cents each, or by a slow two-day service at 8 cents each or both. the caterer wants to know how many napkins he should purchase initially and how many dirty napkins should be laundered by fast and slow service on each of the days in order to minimize his total costs. formulate the caterer’s problem as a linear program as follows (you must state any assumptions you make): a. define all variables clearly. how many are there? b. write out the constraints that must be satisfied, briefly explaining each. (do not simplify.) write out the objective function to be minimized. (do not simplify.)