53 - 5,3ху - у + 4,8ху - 6у = 53 - (5,3ху - 4,8ху) - (6у + у) = 53 - 0,5ху - 7у
при х = 4/13; у = 13/7
53 - 0,5 · (4/13 · 13/7) - 7 · 13/7 = 53 - 1/2 · 4/7 - 13 = (53 - 13) - 2/7 = 40 - 2/7 = 39 целых 5/7.
Ответ: 39 целых 5/7.
Sin(x-π/8)>1/2
π/6+2πn<x-π/8<5π/6+2πn
π/8+π/6+2πn<x<π/8+5π/6+2πn
7π/24+2πn<x<19π/24+2πn
x∈(7π/24+2πn;19π/24+2πn)
Производная y'=-8x(7-x^2)^3
(16807(117649)^7)7,2574552 × 1049=3,9917904 × 10^43