bored of sc
Active Member
- Joined
- Nov 10, 2007
- Messages
- 2,314
- Gender
- Male
- HSC
- 2009
Fitzpatrick Questions I simply couldn't do.
Ex 25 (a)
7) The cross section of a trough l metre long is in the shape of an isosceles triangle of base measurement 2a metre and height b metre. Water leaks from the trough at a constant rate of c metre3/min. Find the rate at which the water level is falling when the depth of the water is b/2 metre.
Answer: c/al metres/min
22) A loading chute is in the shape of a right square pyramid of base length 10m and depth 8m. Liquid is poured in the top at a rate of 4m3/min. At what rate is the level rising when the depth is 4m?
Answer: 4/25 m/min
25) A point P moves on the curve y = x3 and the co-ordinate increases at a constant rate of 5 units/second. At what rate is:
a) the y co-ordinate of P increasing when x = 1?
b) the gradient of the curve increasing when x = 1?
Answers - (a) 15 units/s
(b) 30 units/s
27) In triangle ABC, Ab = 10cm, AC = 12cm and angle A is increasing at the rate of 0.1 radian/second. At what rate is:
a) the area of triangle ABC increasing,
b) the length of BC increasing, when angle A is pi/3 radians?
Answers - (a) 3 cm2/s
(b) 3root[3/31] cm/s
Ex 25 (e)
4) Assume Newton's Law of Cooling is To = P + Ae-kt. A body, initially at room temperature 20oC, is heated so that its temperature would rise by 5oC/min if no cooling took place. Cooling does occur in accordance with Newton's Law of Cooling and the maximum temperature the body could attain is 120oC. How long would it take to reach a temperature of 100oC?
Answer: 32.2 minutes
6) A vessel is being filled at a variable rate and the volume of liquid in the vessel at any time 't' is given by V = A(1-e-kt)
(a) Show that dV/dt = k(A-V)
(b) If one quarter of the vessel is filled in 5 minutes, what fraction is filled in the next five minutes?
Answer for (b): 3/16
Thank you all in advance.
Ex 25 (a)
7) The cross section of a trough l metre long is in the shape of an isosceles triangle of base measurement 2a metre and height b metre. Water leaks from the trough at a constant rate of c metre3/min. Find the rate at which the water level is falling when the depth of the water is b/2 metre.
Answer: c/al metres/min
22) A loading chute is in the shape of a right square pyramid of base length 10m and depth 8m. Liquid is poured in the top at a rate of 4m3/min. At what rate is the level rising when the depth is 4m?
Answer: 4/25 m/min
25) A point P moves on the curve y = x3 and the co-ordinate increases at a constant rate of 5 units/second. At what rate is:
a) the y co-ordinate of P increasing when x = 1?
b) the gradient of the curve increasing when x = 1?
Answers - (a) 15 units/s
(b) 30 units/s
27) In triangle ABC, Ab = 10cm, AC = 12cm and angle A is increasing at the rate of 0.1 radian/second. At what rate is:
a) the area of triangle ABC increasing,
b) the length of BC increasing, when angle A is pi/3 radians?
Answers - (a) 3 cm2/s
(b) 3root[3/31] cm/s
Ex 25 (e)
4) Assume Newton's Law of Cooling is To = P + Ae-kt. A body, initially at room temperature 20oC, is heated so that its temperature would rise by 5oC/min if no cooling took place. Cooling does occur in accordance with Newton's Law of Cooling and the maximum temperature the body could attain is 120oC. How long would it take to reach a temperature of 100oC?
Answer: 32.2 minutes
6) A vessel is being filled at a variable rate and the volume of liquid in the vessel at any time 't' is given by V = A(1-e-kt)
(a) Show that dV/dt = k(A-V)
(b) If one quarter of the vessel is filled in 5 minutes, what fraction is filled in the next five minutes?
Answer for (b): 3/16
Thank you all in advance.
