Let B (0,3) and C (4,0) . The point A is moving on the line y=2 x at the rate of 2 units/second. The area of ABC is increasing at the rate of

Step-by-step solution

aligned & Let A =( h , 2 ~h ) & OA = h ^2+4 ~h ^2 = 5 ~h & d ( OA ) dt = 5 dh dt & 2= 5 dh dt & dh dt = 2 5 aligned aligned & = A ( ABC )= 1 2 | array ccc h & 2 ~h & 1 0 & 3 & 1 4 & 0 & 1 array | & = 1 2 (3 ~h +8 ~h -12) & = 11 ~h -12 2 d dt & = 11 2 dh dt & = 11 2 2 5 & = 11 5 ( units )^2 / sec aligned