Mathematics Question and Solution
For y = (25/16) unit.
x is;
(25/16) = (5/4)^(2x)
2x = 2
x = 1 unit.
Gradient of the curve at x equal 1 unit is;
dy/dx = (25/8)ln(5/4)
At y = 0 at the tangent, x is;
x = (50ln(5/4)-25)/50ln(5/4) units.
Therefore;
Area Yellow exactly as a single fraction is;
Area triangle with height (√(881)/16)sin(180-atan(25/16)) units and base (-(50ln(5/4)-25)/50ln(5/4)) unit.
= ½*(-(50ln(5/4)-25)/50ln(5/4))*(√(881)/16)sin(180-atan(25/16))
= (25-50ln(5/4))/(64ln(5/4)) square units.
