4. A fireman has to reach a burning building. Determine the length of the shortest ladder that will reach over a 2 metre high fence to the burning building which is 1 metre behind the fence

5. Car A is 40 km east of Car B and begins moving west at 40 km/h. At the same moment, Car B begins to move north at 70 km/h. What is the closest distance in kilometres the cars will be from each other and at what time t, in hours, will that distance occur?

6. The radius and height of a tank cannot exceed 5 m and 12 m respectively. Is it possible to construct a tank with a volume of 900 m3? If it is possible, what are the restrictions on its radius?

7. A landlord manages 100 apartments in a complex downtown and charges his tenants monthly. When the rent is $800 a month, all of the apartments are rented. For every $15 increase in rent, one apartment becomes empty. On average, each apartment needs $60 invested in maintenance and repairs each month. The landlord wants to know how much he should charge per month in order to have the greatest profit. Could he make a greater profit without all of the apartments rented? Explain.