Mathematics Question and Solution
Shaded area is;
Area under the curve at points (-1, 0) and (7, 0) - Area triangle with height 4 unit and base 8 unit.
= ⅓(208) - ½(4*8)
= ⅓(160) space unit.
Area S is;
Area under the curve at points (-2, 0) and (7, 0) - Area triangle with height 4 unit and base 8 unit - Area triangle with height 1 unit and base (7/4) unit - Shaded area.
= 72 - ½(4*8) - ½(1(7/4)) - ⅓(160)
= (43/24) space unit.
Area R is;
Area triangle with height 4 unit and base 2 unit - Area triangle with height 1 unit and base (7/4) unit - Area S.
= ½(4*2) - ½(1(7/4)) - (43/24)
= (4/3) space unit.
Therefore;
Area R : Area S : Area Shaded Exactly is;
(4/3) : (43/24) : ⅓(160)
= 24(4/3) : 24(43/24) : 24(⅓(160)
= 32 : 43 : 1280
