Mathematics Question and Solution
Sir Mike Ambrose is the author of the question.
Area of the curve is;
y = -⅓(x³)+2x²
Point p coordinate is;
(⅓(32), 4)
Therefore Area Red is;
Area under the curve at the points (4, 0) and (6, 0) - Area triangle with height ⅓(32) units and base 2 units.
⅓(44) - ⅓(32)
= ⅓(12)
= 4 square units.
Area Blue is;
Area triangle with two lengths 5.69600024969 units and 10.8525470641 units, and angle (atan(3/8)+atan(3/16))°
= ½(5.69600024969)(10.8525470641)sin(atan(3/8)+atan(3/16))
= 16 square units.
It implies;
Area Red ÷ Area Blue is;
4 ÷ 16
= ¼
