Mathematics Question and Solution
The equation of the curve is;
0-32=-a(8-4)²
-32 = -16a
a = 2
Therefore;
y-32 = -2(x-4)²
y = -2(x²-8x+16) +32
y = -2x²+16x-32+32
y = 16x - 2x²
It implies;
(Area (2197/24)+ Area triangle with height b unit and base a unit + Area under the curve at x = 8 and x = a) = Area under the curve at x = 8 and x = 0
2197+12ab-192a²+16a³=0 ----------- (1)
Notice;
b = 16a-2a² --------- (2)
Substitute (2) in (1).
Therefore;
a = ½(13) unit
And
b = ½(39) unit
It implies;
Area shaded/Area orange in its decimal form is;
Area triangle with height 18.024982663 unit and base 6.00832755433 unit.
= ½*18.024982663*6.00832755433
= 54.1500000002 square unit.
= 5415/100
= 1083/20 square unit.
