An engineer wishes to design a roller coaster so that the cars will not fall when they are at the top of their
circular path.
A 500 kg roller coaster car is designed to travel at 20
m/s at the top of the circle. The engineer wants to
make the circle as large as possible while still being
at least one quarter the maximum radius for safety
reasons. How large can the radius of the circle be?

Sasha has just gotten a new job in a nearby city. after comparison shopping, she found that renting a nice two-bedroom apartment would cost around $800 per month. her utilities would cost about $150 per month. sasha has enough money saved for a down payment, and she found that she can buy a three-bedroom house or condo with a mortgage payment of $1,000 per month, including taxes and homeowner's insurance. her utilities would cost about $200 per month. what is the advantage of buying the house over renting the apartment?