please show work on doc i really need solutions. thanks! :-)

MCR3U - Assignment #5 /33

Please provide full solutions to the following problems.

1. Solve each equation using the indicated method. Express the answer exactly and where appropriate, as an approximate root rounded to the nearest hundredth. [12]

   1. (by factoring)

   2. (quadratic formula)

   3. (any method)

1. A car traveling at v kilometers per hour will need a stopping distance, d, in meters without skidding that can be modeled by the function . Determine the speed at which a car can be traveling to be able to stop within 37m. [3]

1. A diver followed a path defined by: in her dive, where t is the time, in seconds, and h, is her height above the water in meters.

   1. At what height did the diver start her dive? [1]

   2. For how long was she in the air before hitting the water? [4]

1. A right-angled triangle has a hypotenuse with a length of 13 units. The triangles second longest side is 7 units longer tahn the shortest side. Determine the length of the shortest side. Recall: . [4]

1. A rectangle’s length is two metres longer than twice its width. If both length and width are increased by 3 metres, the original area is doubled. Determine the area of the original rectangle. [4]

1. In the diagram, the square has side lengths of 6m. The square is divided into three right triangles and one isosceles triangle. The areas of the three right triangles are equal.

   1. Find the value of x. [4]

   2. Find the area of the acute isosceles triangle. [2]