Question

Solve the following non-monic quadratic problems:

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

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

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

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

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

Answer 1