Mathematics Question and Solution
At t = 2, x = 3 and y = 3/4
dx/dt = 2/3
dy/dt = 13/16
Therefore;
Gradient at the tangent and of the curve at t = 2 is;
dy/dx = dy/dt÷dx/dt
= (13/16)÷(2/3)
dy/dx = 39/32
Notice;
Triangle OPQ height coordinate is (3, (3/4)).
Triangle OPQ base coordinate is (x1, 0).
Calculating x to get X1.
((3/4)-0)/(3-x) = 39/32
x = 31/13
x1 = 3-(31/13)
x1 = 18/13.
It implies;
Triangle OPQ is;
Area triangle with height ¾ unit and base (18/13) unit.
= ½*(18/13)*¾
= 27/52 square unit.
