# 11X1 T08 07 rates of change

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<ul><li> 1. Rates of Change e.g. A block of ice in the form of a cube has one edge 10 cm long. It ismelting 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? </li></ul>
<p> 2. Rates of Change e.g. A block of ice in the form of a cube has one edge 10 cm long. It ismelting 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 Change e.g. A block of ice in the form of a cube has one edge 10 cm long. It ismelting 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 x ?dt 4. Rates of Change e.g. A block of ice in the form of a cube has one edge 10 cm long. It ismelting 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 x ? dt dt10 5. Rates of Change e.g. A block of ice in the form of a cube has one edge 10 cm long. It ismelting 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 ? dx1 V x3 xdt dt10 6. Rates of Change e.g. A block of ice in the form of a cube has one edge 10 cm long. It ismelting 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 ? dx1 V x3 xdt dt10dV 3x 2 dx 7. Rates of Change e.g. A block of ice in the form of a cube has one edge 10 cm long. It ismelting 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 ? dx1 V x3 xdt dt10dV 3x 2 dxdV dV dx dt dx dt 8. Rates of Change e.g. A block of ice in the form of a cube has one edge 10 cm long. It ismelting 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? dx1 V x3 x dtdt10dV 3x 2 dxdV dV dx dt dx dt1 3x 210 9. Rates of Change e.g. A block of ice in the form of a cube has one edge 10 cm long. It ismelting 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? dx1 V x3 x dtdt10dV 3x 2 dxdV dV dx dt dx dt1 3x 2103x 210 10. Rates of Change e.g. A block of ice in the form of a cube has one edge 10 cm long. It ismelting 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? dx1 V x3 x dtdt10dV 3x 2 dx3 52dV dV dx dV when x 5,dt dx dt dt 101 3x 2103x 210 11. Rates of Change e.g. A block of ice in the form of a cube has one edge 10 cm long. It ismelting 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? dx1 V x3 x dtdt10dV 3x 2 dx3 52dV dV dx dV when x 5,dt dx dt dt 10 3x 21 7.5 103x 210 12. Rates of Change e.g. A block of ice in the form of a cube has one edge 10 cm long. It ismelting 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 1V x3 x dt dt10 dV 3x 2 dx3 52dV dV dx dV when x 5,dt dx dt dt 10 3x 21 7.5 103x 2 volume is decreasing at 7.5 cm3 /s10 13. (ii) A vessel is in the form of an inverted cone with a vertical angle of 90If 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 90If 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 90If 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 90If 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 90If the depth of the water in the vessel is x cm;a) find the volume of water.x 45x 18. (ii) A vessel is in the form of an inverted cone with a vertical angle of 90If the depth of the water in the vessel is x cm;a) find the volume of water. x x 45x 19. (ii) A vessel is in the form of an inverted cone with a vertical angle of 90If the depth of the water in the vessel is x cm;a) find the volume of water. x 1 2V r h x 3 45x 20. (ii) A vessel is in the form of an inverted cone with a vertical angle of 90If the depth of the water in the vessel is x cm;a) find the volume of water. x 1 2V r h x 3 451 2 x x x 3 21. (ii) A vessel is in the form of an inverted cone with a vertical angle of 90If the depth of the water in the vessel is x cm;a) find the volume of water. x 1 2V r h x 3 451 2 x x x 3 1 3 x 3 22. (ii) A vessel is in the form of an inverted cone with a vertical angle of 90If the depth of the water in the vessel is x cm;a) find the volume of water.x 1 2V r hx 3451 2 x xx 31 3 x3b) If water is poured in at a rate of 0.2 cm3 /min, find the rate the depthis 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 90If the depth of the water in the vessel is x cm;a) find the volume of water.x 1 2V r hx 3451 2 x xx 31 3 x3b) If water is poured in at a rate of 0.2 cm3 /min, find the rate the depthis 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 90If the depth of the water in the vessel is x cm;a) find the volume of water.x 1 2V r hx 3451 2 x xx 31 3 x3b) If water is poured in at a rate of 0.2 cm3 /min, find the rate the depthis increasing when the water depth is 4 cm. dx ? dtdV 1 dt 5 25. (ii) A vessel is in the form of an inverted cone with a vertical angle of 90If the depth of the water in the vessel is x cm;a) find the volume of water.x 1 2V r hx 3451 2 x xx 31 3 x3b) If water is poured in at a rate of 0.2 cm3 /min, find the rate the depthis increasing when the water depth is 4 cm. dx ? dtdV 1 dt 51V x33 26. (ii) A vessel is in the form of an inverted cone with a vertical angle of 90If the depth of the water in the vessel is x cm;a) find the volume of water.x 1 2V r hx 3451 2 x xx 31 3 x3b) If water is poured in at a rate of 0.2 cm3 /min, find the rate the depthis increasing when the water depth is 4 cm. dx ? dtdV 1 dt 51V x3dV 3 2 xdx 27. (ii) A vessel is in the form of an inverted cone with a vertical angle of 90If the depth of the water in the vessel is x cm;a) find the volume of water.x 1 2V r hx 3451 2 x xx 31 3 x3b) If water is poured in at a rate of 0.2 cm3 /min, find the rate the depthis increasing when the water depth is 4 cm. dx dx dx dV ? dtdt dV dtdV 1 dt 51V x3dV 3 2 xdx 28. (ii) A vessel is in the form of an inverted cone with a vertical angle of 90If the depth of the water in the vessel is x cm;a) find the volume of water.x 1 2V r hx 3451 2 x xx 31 3 x3b) If water is poured in at a rate of 0.2 cm3 /min, find the rate the depthis increasing when the water depth is 4 cm. dx dx dx dV ? dtdt dV dtdV 1 1 1 dt 5 21 3x 5V xdV 3 2 xdx 29. (ii) A vessel is in the form of an inverted cone with a vertical angle of 90If the depth of the water in the vessel is x cm;a) find the volume of water.x 1 2V r hx 3451 2 x xx 31 3 x3b) If water is poured in at a rate of 0.2 cm3 /min, find the rate the depthis increasing when the water depth is 4 cm. dx dx dx dV ? dtdt dV dtdV 1 1 1 dt 5 21 3x 5V x 1dV3 x2 5 x 2dx 30. (ii) A vessel is in the form of an inverted cone with a vertical angle of 90If the depth of the water in the vessel is x cm;a) find the volume of water.x 1 2V r hx 3451 2 x xx 31 3 x3b) If water is poured in at a rate of 0.2 cm3 /min, find the rate the depthis increasing when the water depth is 4 cm. dx dx dx dV dx1 ? when x 4, dtdt dV dtdt 5 4 2dV 1 1 1 dt 5 21 3x 5V x 1dV3 x2 5 x 2dx 31. (ii) A vessel is in the form of an inverted cone with a vertical angle of 90If the depth of the water in the vessel is x cm;a) find the volume of water.x 1 2 V r hx 3451 2 x xx 31 3 x3b) If water is poured in at a rate of 0.2 cm3 /min, find the rate the depthis increasing when the water depth is 4 cm. dx dx dx dV dx1 ? when x 4, dtdt dV dtdt 5 4 2dV 1 1 1 1 2 dt 5 x 5801V x3 1dV3 x2 5 x 2dx 32. (ii) A vessel is in the form of an inverted cone with a vertical angle of 90If the depth of the water in the vessel is x cm;a) find the volume of water.x 1 2V r hx 3451 2 x xx 31 3 x3b) If water is poured in at a rate of 0.2 cm3 /min, find the rate the depthis increasing when the water depth is 4 cm. dx dx dx dV dx 1 ? when x 4, dtdt dV dtdt 5 4 2dV 1 1 1 1 2 dt 5 x 5 801V x3 depth is increasing 1dV3 1 x2 5 x 2atcm/mindx80 33. (ii) A vessel is in the form of an inverted cone with a vertical angle of 90If the depth of the water in the vessel is x cm;a) find the volume of water.x 1 2V r hx 3451 2 x xx 31 3 x3b) If water is poured in at a rate of 0.2 cm3 /min, find the rate the depthis 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 1 1 2 dt 5 x 5 80 6, 7, 8, 10,1V x3 depth is increasing 12, 14 1dV 3 2 1 x 5 x 2atcm/mindx80 </p>