Solve the following non-monic quadratic problems:

a) Rick's driving speed was measured over a 10.minute period andthe following relationship was found to exist: s = -4t² + 31t, whats is the speed in kilometres per hour after t minutes. When wasRick travelling at 60 km/h?

b) The temperature inside a tent was measured over a period oftime and the following quadratic relationship was found to exist: T= -2h² + 11h + 21, where T is the temperature in degrees Celsiusafter h hours. When was the temperature 0 degrees and when was thetemperature 26 degrees?

c) A tourist, high above the ground enjoying the sights from ahot-air balloon, unfortunately drops a camera and watches it fallto the ground. The height of the camera above the ground , h (inmetres) t seconds after it has been dropped can be represented bythe relationship: h = -5t² + 192. At what height above the groundwas the camera dropped and how long does it take for the camera tofall to the ground?

d) A policeman on a motorbike is following a car along ahighway. After a short time, the driver of the car notices thepoliceman and starts to slow down, finally stopping on the side ofthe road. The speed of the car during this time can be representedby the quadratic function S = -3t² + 17t + 70, where S is the speedof the car in kilometres per hour, t minutes after the policemanstarted following. Calculate how long the car was undersurveillance for until it stopped and figure out if during thistime, did the driver break the speed limit of 100km/h?

e) Hayden's owners are going to build a dog kennel for him. Itwill be 1m high and twice as long as it is wide, and it will havean opening at one end. The opening has an area of 0.5m². When theyare finished, they are going to paint the outside of it, includingthe base of the kennel, to keep it waterproof. Write an algebraicexpression for the area of the kennel that is to be painted.