11X1 T08 07 rates of change
-
Upload
nigel-simmons -
Category
Education
-
view
259 -
download
0
Transcript of 11X1 T08 07 rates of change
![Page 1: 11X1 T08 07 rates of change](https://reader033.fdocuments.us/reader033/viewer/2022060118/558c2f55d8b42a353e8b45f1/html5/thumbnails/1.jpg)
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?
![Page 2: 11X1 T08 07 rates of change](https://reader033.fdocuments.us/reader033/viewer/2022060118/558c2f55d8b42a353e8b45f1/html5/thumbnails/2.jpg)
Rates of Change
x
e.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?
![Page 3: 11X1 T08 07 rates of change](https://reader033.fdocuments.us/reader033/viewer/2022060118/558c2f55d8b42a353e8b45f1/html5/thumbnails/3.jpg)
Rates of Change
x ?dVdt
e.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?
![Page 4: 11X1 T08 07 rates of change](https://reader033.fdocuments.us/reader033/viewer/2022060118/558c2f55d8b42a353e8b45f1/html5/thumbnails/4.jpg)
Rates of Change
x ?dVdt
110
dxdt
e.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?
![Page 5: 11X1 T08 07 rates of change](https://reader033.fdocuments.us/reader033/viewer/2022060118/558c2f55d8b42a353e8b45f1/html5/thumbnails/5.jpg)
Rates of Change
x ?dVdt
110
dxdt
3V x
e.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?
![Page 6: 11X1 T08 07 rates of change](https://reader033.fdocuments.us/reader033/viewer/2022060118/558c2f55d8b42a353e8b45f1/html5/thumbnails/6.jpg)
Rates of Change
x ?dVdt
110
dxdt
3V x
23dV xdx
e.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?
![Page 7: 11X1 T08 07 rates of change](https://reader033.fdocuments.us/reader033/viewer/2022060118/558c2f55d8b42a353e8b45f1/html5/thumbnails/7.jpg)
Rates of Change
x ?dVdt
110
dxdt
3V x
23dV xdx
dV dV dxdt dx dt
e.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?
![Page 8: 11X1 T08 07 rates of change](https://reader033.fdocuments.us/reader033/viewer/2022060118/558c2f55d8b42a353e8b45f1/html5/thumbnails/8.jpg)
Rates of Change
x ?dVdt
110
dxdt
3V x
23dV xdx
dV dV dxdt dx dt
e.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 1310
x
![Page 9: 11X1 T08 07 rates of change](https://reader033.fdocuments.us/reader033/viewer/2022060118/558c2f55d8b42a353e8b45f1/html5/thumbnails/9.jpg)
Rates of Change
x ?dVdt
110
dxdt
3V x
23dV xdx
dV dV dxdt dx dt
e.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 1310
x 23
10x
![Page 10: 11X1 T08 07 rates of change](https://reader033.fdocuments.us/reader033/viewer/2022060118/558c2f55d8b42a353e8b45f1/html5/thumbnails/10.jpg)
Rates of Change
x ?dVdt
110
dxdt
3V x
23dV xdx
dV dV dxdt dx dt
e.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 1310
x 23
10x
23 5when 5,
10dVxdt
![Page 11: 11X1 T08 07 rates of change](https://reader033.fdocuments.us/reader033/viewer/2022060118/558c2f55d8b42a353e8b45f1/html5/thumbnails/11.jpg)
Rates of Change
x ?dVdt
110
dxdt
3V x
23dV xdx
dV dV dxdt dx dt
e.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 1310
x 23
10x
23 5when 5,
10dVxdt
7.5
![Page 12: 11X1 T08 07 rates of change](https://reader033.fdocuments.us/reader033/viewer/2022060118/558c2f55d8b42a353e8b45f1/html5/thumbnails/12.jpg)
Rates of Change
x ?dVdt
110
dxdt
3V x
23dV xdx
dV dV dxdt dx dt
e.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 1310
x 23
10x
23 5when 5,
10dVxdt
7.5
3volume is decreasing at 7.5 cm /s
![Page 13: 11X1 T08 07 rates of change](https://reader033.fdocuments.us/reader033/viewer/2022060118/558c2f55d8b42a353e8b45f1/html5/thumbnails/13.jpg)
(ii) A vessel is in the form of an inverted cone with a vertical angle of If the depth of the water in the vessel is x cm;a) find the volume of water.
90
![Page 14: 11X1 T08 07 rates of change](https://reader033.fdocuments.us/reader033/viewer/2022060118/558c2f55d8b42a353e8b45f1/html5/thumbnails/14.jpg)
(ii) A vessel is in the form of an inverted cone with a vertical angle of If the depth of the water in the vessel is x cm;a) find the volume of water.
90
![Page 15: 11X1 T08 07 rates of change](https://reader033.fdocuments.us/reader033/viewer/2022060118/558c2f55d8b42a353e8b45f1/html5/thumbnails/15.jpg)
(ii) A vessel is in the form of an inverted cone with a vertical angle of If the depth of the water in the vessel is x cm;a) find the volume of water.
90
x
![Page 16: 11X1 T08 07 rates of change](https://reader033.fdocuments.us/reader033/viewer/2022060118/558c2f55d8b42a353e8b45f1/html5/thumbnails/16.jpg)
(ii) A vessel is in the form of an inverted cone with a vertical angle of If the depth of the water in the vessel is x cm;a) find the volume of water.
90
x
![Page 17: 11X1 T08 07 rates of change](https://reader033.fdocuments.us/reader033/viewer/2022060118/558c2f55d8b42a353e8b45f1/html5/thumbnails/17.jpg)
(ii) A vessel is in the form of an inverted cone with a vertical angle of If the depth of the water in the vessel is x cm;a) find the volume of water.
90
x
x45
![Page 18: 11X1 T08 07 rates of change](https://reader033.fdocuments.us/reader033/viewer/2022060118/558c2f55d8b42a353e8b45f1/html5/thumbnails/18.jpg)
(ii) A vessel is in the form of an inverted cone with a vertical angle of If the depth of the water in the vessel is x cm;a) find the volume of water.
90
x
x45
x
![Page 19: 11X1 T08 07 rates of change](https://reader033.fdocuments.us/reader033/viewer/2022060118/558c2f55d8b42a353e8b45f1/html5/thumbnails/19.jpg)
(ii) A vessel is in the form of an inverted cone with a vertical angle of If the depth of the water in the vessel is x cm;a) find the volume of water.
90
x
x45
x 213
V r h
![Page 20: 11X1 T08 07 rates of change](https://reader033.fdocuments.us/reader033/viewer/2022060118/558c2f55d8b42a353e8b45f1/html5/thumbnails/20.jpg)
(ii) A vessel is in the form of an inverted cone with a vertical angle of If the depth of the water in the vessel is x cm;a) find the volume of water.
90
x
x45
x 213
V r h
213
x x
![Page 21: 11X1 T08 07 rates of change](https://reader033.fdocuments.us/reader033/viewer/2022060118/558c2f55d8b42a353e8b45f1/html5/thumbnails/21.jpg)
(ii) A vessel is in the form of an inverted cone with a vertical angle of If the depth of the water in the vessel is x cm;a) find the volume of water.
90
x
x45
x 213
V r h
213
x x
313
x
![Page 22: 11X1 T08 07 rates of change](https://reader033.fdocuments.us/reader033/viewer/2022060118/558c2f55d8b42a353e8b45f1/html5/thumbnails/22.jpg)
(ii) A vessel is in the form of an inverted cone with a vertical angle of If the depth of the water in the vessel is x cm;a) find the volume of water.
90
x
x45
x 213
V r h
213
x x
313
x3b) If water is poured in at a rate of 0.2 cm /min, find the rate the depth
is increasing when the water depth is 4 cm.
![Page 23: 11X1 T08 07 rates of change](https://reader033.fdocuments.us/reader033/viewer/2022060118/558c2f55d8b42a353e8b45f1/html5/thumbnails/23.jpg)
(ii) A vessel is in the form of an inverted cone with a vertical angle of If the depth of the water in the vessel is x cm;a) find the volume of water.
90
x
x45
x 213
V r h
213
x x
313
x3b) If water is poured in at a rate of 0.2 cm /min, find the rate the depth
is increasing when the water depth is 4 cm.
?dxdt
![Page 24: 11X1 T08 07 rates of change](https://reader033.fdocuments.us/reader033/viewer/2022060118/558c2f55d8b42a353e8b45f1/html5/thumbnails/24.jpg)
(ii) A vessel is in the form of an inverted cone with a vertical angle of If the depth of the water in the vessel is x cm;a) find the volume of water.
90
x
x45
x 213
V r h
213
x x
313
x3b) If water is poured in at a rate of 0.2 cm /min, find the rate the depth
is increasing when the water depth is 4 cm.
?dxdt
15
dVdt
![Page 25: 11X1 T08 07 rates of change](https://reader033.fdocuments.us/reader033/viewer/2022060118/558c2f55d8b42a353e8b45f1/html5/thumbnails/25.jpg)
(ii) A vessel is in the form of an inverted cone with a vertical angle of If the depth of the water in the vessel is x cm;a) find the volume of water.
90
x
x45
x 213
V r h
213
x x
313
x3b) If water is poured in at a rate of 0.2 cm /min, find the rate the depth
is increasing when the water depth is 4 cm.
?dxdt
15
dVdt
313
V x
![Page 26: 11X1 T08 07 rates of change](https://reader033.fdocuments.us/reader033/viewer/2022060118/558c2f55d8b42a353e8b45f1/html5/thumbnails/26.jpg)
(ii) A vessel is in the form of an inverted cone with a vertical angle of If the depth of the water in the vessel is x cm;a) find the volume of water.
90
x
x45
x 213
V r h
213
x x
313
x3b) If water is poured in at a rate of 0.2 cm /min, find the rate the depth
is increasing when the water depth is 4 cm.
?dxdt
15
dVdt
313
V x2dV x
dx
![Page 27: 11X1 T08 07 rates of change](https://reader033.fdocuments.us/reader033/viewer/2022060118/558c2f55d8b42a353e8b45f1/html5/thumbnails/27.jpg)
(ii) A vessel is in the form of an inverted cone with a vertical angle of If the depth of the water in the vessel is x cm;a) find the volume of water.
90
x
x45
x 213
V r h
213
x x
313
x3b) If water is poured in at a rate of 0.2 cm /min, find the rate the depth
is increasing when the water depth is 4 cm.
?dxdt
15
dVdt
313
V x2dV x
dx
dx dx dVdt dV dt
![Page 28: 11X1 T08 07 rates of change](https://reader033.fdocuments.us/reader033/viewer/2022060118/558c2f55d8b42a353e8b45f1/html5/thumbnails/28.jpg)
(ii) A vessel is in the form of an inverted cone with a vertical angle of If the depth of the water in the vessel is x cm;a) find the volume of water.
90
x
x45
x 213
V r h
213
x x
313
x3b) If water is poured in at a rate of 0.2 cm /min, find the rate the depth
is increasing when the water depth is 4 cm.
?dxdt
15
dVdt
313
V x2dV x
dx
dx dx dVdt dV dt
21 1
5x
![Page 29: 11X1 T08 07 rates of change](https://reader033.fdocuments.us/reader033/viewer/2022060118/558c2f55d8b42a353e8b45f1/html5/thumbnails/29.jpg)
(ii) A vessel is in the form of an inverted cone with a vertical angle of If the depth of the water in the vessel is x cm;a) find the volume of water.
90
x
x45
x 213
V r h
213
x x
313
x3b) If water is poured in at a rate of 0.2 cm /min, find the rate the depth
is increasing when the water depth is 4 cm.
?dxdt
15
dVdt
313
V x2dV x
dx
dx dx dVdt dV dt
21 1
5x
21
5 x
![Page 30: 11X1 T08 07 rates of change](https://reader033.fdocuments.us/reader033/viewer/2022060118/558c2f55d8b42a353e8b45f1/html5/thumbnails/30.jpg)
(ii) A vessel is in the form of an inverted cone with a vertical angle of If the depth of the water in the vessel is x cm;a) find the volume of water.
90
x
x45
x 213
V r h
213
x x
313
x3b) If water is poured in at a rate of 0.2 cm /min, find the rate the depth
is increasing when the water depth is 4 cm.
?dxdt
15
dVdt
313
V x2dV x
dx
dx dx dVdt dV dt
21 1
5x
21
5 x
21when 4,
5 4dxxdt
![Page 31: 11X1 T08 07 rates of change](https://reader033.fdocuments.us/reader033/viewer/2022060118/558c2f55d8b42a353e8b45f1/html5/thumbnails/31.jpg)
(ii) A vessel is in the form of an inverted cone with a vertical angle of If the depth of the water in the vessel is x cm;a) find the volume of water.
90
x
x45
x 213
V r h
213
x x
313
x3b) If water is poured in at a rate of 0.2 cm /min, find the rate the depth
is increasing when the water depth is 4 cm.
?dxdt
15
dVdt
313
V x2dV x
dx
dx dx dVdt dV dt
21 1
5x
21
5 x
21when 4,
5 4dxxdt
180
![Page 32: 11X1 T08 07 rates of change](https://reader033.fdocuments.us/reader033/viewer/2022060118/558c2f55d8b42a353e8b45f1/html5/thumbnails/32.jpg)
(ii) A vessel is in the form of an inverted cone with a vertical angle of If the depth of the water in the vessel is x cm;a) find the volume of water.
90
x
x45
x 213
V r h
213
x x
313
x3b) If water is poured in at a rate of 0.2 cm /min, find the rate the depth
is increasing when the water depth is 4 cm.
?dxdt
15
dVdt
313
V x2dV x
dx
dx dx dVdt dV dt
21 1
5x
21
5 x
21when 4,
5 4dxxdt
180
depth is increasing 1at cm/min
80
![Page 33: 11X1 T08 07 rates of change](https://reader033.fdocuments.us/reader033/viewer/2022060118/558c2f55d8b42a353e8b45f1/html5/thumbnails/33.jpg)
(ii) A vessel is in the form of an inverted cone with a vertical angle of If the depth of the water in the vessel is x cm;a) find the volume of water.
90
x
x45
x 213
V r h
213
x x
313
x3b) If water is poured in at a rate of 0.2 cm /min, find the rate the depth
is increasing when the water depth is 4 cm.
?dxdt
15
dVdt
313
V x2dV x
dx
dx dx dVdt dV dt
21 1
5x
21
5 x
21when 4,
5 4dxxdt
180
depth is increasing 1at cm/min
80
Exercise 7H; 1a, 2a, 4,6, 7, 8, 10,
12, 14