The wheel of a car has a radius of 0.400 m. The engine of the car applies a torque of 415 N·m to this wheel, which does not slip against the road surface. Since the wheel does not slip, the road must be applying a force of static friction to the wheel that produces a countertorque. Moreover, the car has a constant velocity, so this countertorque balances the applied torque. What is the magnitude of the static frictional force?

(30 total points) suppose a firm’s production function is given by q = l1/2*k1/2. the marginal product of labor and the marginal product of capital are given by: mpl = 1/ 2 1/ 2 2l k , and mpk = 1/ 2 1/ 2 2k l . a) (12 points) if the price of labor is w = 48, and the price of capital is r = 12, how much labor and capital should the firm hire in order to minimize the cost of production if the firm wants to produce output q = 18?

In a fixed-term, level-payment reverse mortgage, sometimes called a reverse annuity mortgage, or ram, a lender agrees to pay the homeowner a monthly payment, or annuity, and expects to be repaid from the homeowner’s equity when he or she sells the home or obtains other financing to pay off the ram. consider a household that owns a $150,000 home free and clear of mortgage debt. the ram lender agrees to a $100,000 ram for 10 years at 6 percent. assume payments are made annually, at the beginning of each year to the homeowner. calculate the annual payment on the ram.

Sally has a high-paying management position with a fortune 500 company, but she is tired of working for corporate america. so sally has decided to start a business, and she knows she will be successful as an entrepreneur because entrepreneurs typically