Answer Happy

Question Four:- (1) When a vertical beam of light passes through a transparent substance, the rate at which its intensity I decreases is proportional to I(t), where t represents the thickness of the medium in feet. In clear sea water the intensity 3 feet below the surface is 25% of the initial intensity In of the incident beam. What is the intensity of the beam 15 feet below the surface? (2) Suppose that a cup of soup cooled from 90°C to 60°C after 10 minuter in a room whose temperature was 20°C. Use Newton's Law of Cooling to answer the following questions (i) How much longer would it take the soup to cool to 35°C? (ii) Instead of being left to stand in the room, the cup of 90°C soup is put in a freezer whose temperature is -15°. How long will it take the soup to cool from 90°C to 35°C? (3) Classify and solve the following equation. dy dx y (0) = 0. (1+x²) + 2xy = f(x), -{₁ f(x) = x, if 0 < x < 1 -x, if x ≥ 1. I