Linear Equations
Question:
A car wants to ascend a slope of with horizontal distance is 7 metres and height 2 metres. However, it cannot ascend a slope of more than 22.5º. Determine whether the car can ascend the slope.
Answer:
y = mx + c
2 = m x 7
m = 2 ÷ 7 = 0.29
Given that 22.5º ÷ 90º = 0.25, the car cannot ascend the slope.
Quadratic Equations
Question:
An ideal comet travels around the Earth in a parabolic motion which is given by the formula,
y = x2 - 8x + 16, where y = 0
If 0 < x < 3.5, the comet would hit the Earth. Determine if the comet would hit the Earth.
Answer:
x2 - 8x + 16 = 0
(x - 4)2 = 0
x = ±4
Given x is +4 or -4, the comet won't hit the earth.
Cubic Equations
Question:
A cart is at the top of the model roller coaster at 3 metres high. It starts to travel downwards initially, reaching ground level before ascending another slope. The initial path matches the following formula
y = -x3 + 5x2 - 7x + 3, where y = 0
Find the distance it travelled when it reaches the ground level before accending another slop.
Answer:
-x3 + 5x2 - 7x + 3 = 0
(x - 1)2(x - 3) = 0
x = ±1 or 3
Given x cannot be negative and 1 is the first distance it reaches, the distance travel when it reaches the ground level is 1 metre.