1. Rates of Changee.g. A block of ice in the form of a cube has one edge 10 cm long. It is melting so that its dimensions decrease at the rate of 1 mm/s.At what rate is the volume decreasing when the edge is 5cm long? 2. Rates of Changee.g. A block of ice in the form of a cube has one edge 10 cm long. It is melting so that its dimensions decrease at the rate of 1 mm/s.At what rate is the volume decreasing when the edge is 5cm long?x 3. Rates of Changee.g. A block of ice in the form of a cube has one edge 10 cm long. It is melting so that its dimensions decrease at the rate of 1 mm/s.At what rate is the volume decreasing when the edge is 5cm long? dVx ? dt 4. Rates of Changee.g. A block of ice in the form of a cube has one edge 10 cm long. It is melting so that its dimensions decrease at the rate of 1 mm/s.At what rate is the volume decreasing when the edge is 5cm long? dV dx 1x ? dt dt10 5. Rates of Changee.g. A block of ice in the form of a cube has one edge 10 cm long. It is melting so that its dimensions decrease at the rate of 1 mm/s.At what rate is the volume decreasing when the edge is 5cm long? dV?dx 1 V x3x dt dt10 6. Rates of Changee.g. A block of ice in the form of a cube has one edge 10 cm long. It is melting so that its dimensions decrease at the rate of 1 mm/s.At what rate is the volume decreasing when the edge is 5cm long? dV?dx 1 V x3x dt dt10dV 3x 2dx 7. Rates of Changee.g. A block of ice in the form of a cube has one edge 10 cm long. It is melting so that its dimensions decrease at the rate of 1 mm/s.At what rate is the volume decreasing when the edge is 5cm long? dV?dx 1 V x3x dt dt10dV 3x 2dx dV dV dx dt dx dt 8. Rates of Changee.g. A block of ice in the form of a cube has one edge 10 cm long. It is melting so that its dimensions decrease at the rate of 1 mm/s.At what rate is the volume decreasing when the edge is 5cm long? dV?dx 1 V x3x dt dt10dV 3x 2dx dV dV dx dt dx dt 1 3x 2 10 9. Rates of Changee.g. A block of ice in the form of a cube has one edge 10 cm long. It is melting so that its dimensions decrease at the rate of 1 mm/s.At what rate is the volume decreasing when the edge is 5cm long? dV?dx 1 V x3x dt dt10dV 3x 2dx dV dV dx dt dx dt 1 3x 2 10 3x 2 10 10. Rates of Changee.g. A block of ice in the form of a cube has one edge 10 cm long. It is melting so that its dimensions decrease at the rate of 1 mm/s.At what rate is the volume decreasing when the edge is 5cm long? dV?dx 1 V x3x dt dt10dV 3x 2dx 3 5 2 dV dV dx dV when x 5, dt dx dt dt 10 1 3x 2 10 3x 2 10 11. Rates of Changee.g. A block of ice in the form of a cube has one edge 10 cm long. It is melting so that its dimensions decrease at the rate of 1 mm/s.At what rate is the volume decreasing when the edge is 5cm long? dV?dx 1 V x3x dt dt10dV 3x 2dx 3 5 2 dV dV dx dV when x 5, dt dx dt dt 10 3x 2 1 7.510 3x 2 10 12. Rates of Changee.g. A block of ice in the form of a cube has one edge 10 cm long. It is melting so that its dimensions decrease at the rate of 1 mm/s.At what rate is the volume decreasing when the edge is 5cm long? dV? dx1V x3x dtdt10 dV 3x 2dx 3 5 2 dV dV dx dV when x 5, dt dx dt dt 10 3x 2 1 7.510 3x 2 volume is decreasing at 7.5 cm3 /s 10 13. (ii) A vessel is in the form of an inverted cone with a vertical angle of 90 If the depth of the water in the vessel is x cm; a) find the volume of water. 14. (ii) A vessel is in the form of an inverted cone with a vertical angle of 90 If the depth of the water in the vessel is x cm; a) find the volume of water. 15. (ii) A vessel is in the form of an inverted cone with a vertical angle of 90 If the depth of the water in the vessel is x cm; a) find the volume of water.x 16. (ii) A vessel is in the form of an inverted cone with a vertical angle of 90 If the depth of the water in the vessel is x cm; a) find the volume of water.x 17. (ii) A vessel is in the form of an inverted cone with a vertical angle of 90 If the depth of the water in the vessel is x cm; a) find the volume of water.x45x 18. (ii) A vessel is in the form of an inverted cone with a vertical angle of 90 If the depth of the water in the vessel is x cm; a) find the volume of water.xx45x 19. (ii) A vessel is in the form of an inverted cone with a vertical angle of 90 If the depth of the water in the vessel is x cm; a) find the volume of water.x 1 V r 2hx 345x 20. (ii) A vessel is in the form of an inverted cone with a vertical angle of 90 If the depth of the water in the vessel is x cm; a) find the volume of water.x 1 V r 2hx 3451 2 x xx 3 21. (ii) A vessel is in the form of an inverted cone with a vertical angle of 90 If the depth of the water in the vessel is x cm; a) find the volume of water.x 1 V r 2hx 3451 2 x xx 31 3 x3 22. (ii) A vessel is in the form of an inverted cone with a vertical angle of 90 If the depth of the water in the vessel is x cm; a) find the volume of water. x 1 V r 2h x 3 451 2 x x x 3 1 3 x 3 b) If water is poured in at a rate of 0.2 cm3 /min, find the rate the depth is increasing when the water depth is 4 cm. 23. (ii) A vessel is in the form of an inverted cone with a vertical angle of 90 If the depth of the water in the vessel is x cm; a) find the volume of water. x 1 V r 2h x 3 451 2 x x x 3 1 3 x 3 b) If water is poured in at a rate of 0.2 cm3 /min, find the rate the depth is increasing when the water depth is 4 cm.dx?dt 24. (ii) A vessel is in the form of an inverted cone with a vertical angle of 90 If the depth of the water in the vessel is x cm; a) find the volume of water. x 1 V r 2h x 3 451 2 x x x 3 1 3 x 3 b) If water is poured in at a rate of 0.2 cm3 /min, find the rate the depth is increasing when the water depth is 4 cm.dx?dt dV 1dt 5 25. (ii) A vessel is in the form of an inverted cone with a vertical angle of 90 If the depth of the water in the vessel is x cm; a) find the volume of water. x 1 V r 2h x 3 451 2 x x x 3 1 3 x 3 b) If water is poured in at a rate of 0.2 cm3 /min, find the rate the depth is increasing when the water depth is 4 cm.dx?dt dV 1dt 5 1 V x3 3 26. (ii) A vessel is in the form of an inverted cone with a vertical angle of 90 If the depth of the water in the vessel is x cm; a) find the volume of water. x 1 V r 2h x 3 451 2 x x x 3 1 3 x 3 b) If water is poured in at a rate of 0.2 cm3 /min, find the rate the depth is increasing when the water depth is 4 cm.dx?dt dV 1dt 5 1 V x3 dV 3 2x dx 27. (ii) A vessel is in the form of an inverted cone with a vertical angle of 90 If the depth of the water in the vessel is x cm; a) find the volume of water. x 1 V r 2h x 3 451 2 x x x 3 1 3 x 3 b) If water is poured in at a rate of 0.2 cm3 /min, find the rate the depth is increasing when the water depth is 4 cm.dx dx dx dV? dtdt dV dt dV 1dt 5 1 V x3 dV 3 2x dx 28. (ii) A vessel is in the form of an inverted cone with a vertical angle of 90 If the depth of the water in the vessel is x cm; a) find the volume of water. x 1 V r 2h x 3 451 2 x x x 3 1 3 x 3 b) If water is poured in at a rate of 0.2 cm3 /min, find the rate the depth is increasing when the water depth is 4 cm.dx dx dx dV? dtdt dV dt dV 1 1 1dt 5 2 1 3x 5 V x dV 3 2x dx 29. (ii) A vessel is in the form of an inverted cone with a vertical angle of 90 If the depth of the water in the vessel is x cm; a) find the volume of water. x 1 V r 2h x 3 451 2 x x x 3 1 3 x 3 b) If water is poured in at a rate of 0.2 cm3 /min, find the rate the depth is increasing when the water depth is 4 cm.dx dx dx dV? dtdt dV dt dV 1 1 1dt 5 2 1 3x 5 V x 1 dV3x25 x 2 dx 30. (ii) A vessel is in the form of an inverted cone with a vertical angle of 90 If the depth of the water in the vessel is x cm; a) find the volume of water. x 1 V r 2h x 3 451 2 x x x 3 1 3 x 3 b) If water is poured in at a rate of 0.2 cm3 /min, find the rate the depth is increasing when the water depth is 4 cm.dx dx dx dV dx1? when x 4, dtdt dV dtdt 5 4 2 dV 1 1 1dt 5 2 1 3x 5 V x 1 dV3x25 x 2 dx 31. (ii) A vessel is in the form of an inverted cone with a vertical angle of 90 If the depth of the water in the vessel is x cm; a) find the volume of water. x 1V r 2h x 3 451 2 x x x 3 1 3 x 3 b) If water is poured in at a rate of 0.2 cm3 /min, find the rate the depth is increasing when the water depth is 4 cm.dx dx dx dV dx1? when x 4, dtdt dV dtdt 5 4 2 dV 1 1 1 1 2dt 5x 580 1 V x3 1 dV3x25 x 2 dx 32. (ii) A vessel is in the form of an inverted cone with a vertical angle of 90 If the depth of the water in the vessel is x cm; a) find the volume of water. x 1 V r 2h x 3 451 2 x x x 3 1 3 x 3 b) If water is poured in at a rate of 0.2 cm3 /min, find the rate the depth is increasing when the water depth is 4 cm.dx dx dx dV dx 1? when x 4, dtdt dV dtdt 5 4 2 dV 1 1 11 2dt 5x 5 80 1 V x3 depth is increasing1 dV3 1x25 x 2atcm/min dx80 33. (ii) A vessel is in the form of an inverted cone with a vertical angle of 90 If the depth of the water in the vessel is x cm; a) find the volume of water. x 1 V r 2h x 3 451 2 x x x 3 1 3 x 3 b) If water is poured in at a rate of 0.2 cm3 /min, find the rate the depth is increasing when the water depth is 4 cm.dx dx dx dV dx 1? when x 4, dtdt dV dtdt 5 4 2 Exercise 7H; dV 1 1a, 2a, 4, 1 11 2dt 5x 5 80 6, 7, 8, 10, 1 V x3 depth is increasing 12, 141 dV 3 2 1x 5 x 2atcm/min dx80