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	Related rates		2007-10-26
		From David: A trough is 12 feet long and 3 feet across the top.(look like an upsidedown triangle square). Its ends are isosceles triangles with altitudes of 3 feet. a) If water is being pumped into the trough at 2 cubic feet per minute, how fast is the water level rising when h is 1 foot deep? b) If the water is rising at a rate of 3/8 inch per minute when h=2, determine the rate at which water is being pumped into the trough. thank you so much for helping me out Answered by Stephen La Rocque.
	The rate of change of the area of a triangle		2007-10-22
		From Ahlee: So my question is: The included angle of the two sides of a constant equal length s of an isosceles triangle is ϑ. (a) Show that the area of the triangle is given by A=1/2s^2 sinϑ (b) If ϑ is increasing at the rate of 1/2 radian per minute, find the rate of change of the area when ϑ=pi/6 and ϑ=pi/3. (c) Explain why the rate of change of the area of a triangle is not constant even though dϑ/dt is constant Answered by Penny Nom.
	A rectangular trough		2007-10-18
		From David: A rectangular trough is 2 meter long, 0.5 meter across the top and 1 meter deep. At what rate must water be poured into the trough such that the depth of the water is increasing at 1m/min. when the depth of the water is 0.7m. I know this involves implicit differentiation somehow, but the 3 variables, since V=l*w*h for a rectangle is confusing me. I'm not sure whether one of the variables should be fixed or not, since I'm not getting anywhere with this right now. Any help would be great. Answered by Stephen La Rocque and Penny Nom.
	A conical cup		2007-10-18
		From Nicholas: Water is leaking out of a small hole at the tip of a conical paper cup at the rate of 1cm^3/min. The cup has height 8cm and radius 6cm, and is initially full up to the top. Find the rate of change of the height of water in the cup when the cup just begins to leak. Since V= (pi/3)r^2h, how do I eliminate a variable or change the equation so I that I can answer the question? Thanks. Answered by Penny Nom.
	Related rates		2007-10-15
		From Alexis: Example 1. An observer is tracking a small plane flying at an altitude of 5000 ft. The plane flies directly over the observer on a horizontal path at the fixed rate of 1000 ft/min. Find the rate of change of the distance from the plane to the observer when the plane has flown 12,000 feet after passing directly over the observer. Answered by Stephen La Rocque.
	Water flowing into a tank		2007-09-21
		From andrew: Hi, I've been having real trouble visualizing this problem as apposed to a conical tank. It says the base of a pyramid-shaped tank is a square with sides of length 12 feet. The vertex of the pyramid is 10 feet above the base. The tank is filled to a depth of 4 feet, water is flowing into the tank at the rate of 2 cubic feet per minute. Find the rate of change of the depth of water in the tank. Answered by Harley Weston.
	Water in a conical tank		2007-09-10
		From Greg: Joe is conducting an experiment to study the rate of flow of water from a conical tank. The dimensions of the conical tank are: Radius at the initial water level = 13.7 cm Radius at the reference point = 12.8 cm Initially the tank is full of water. There is a circular orifice at the bottom of the conical tank with a diameter of 0.635 cm. The water drains from the conical tank into an empty cylindrical tank lying on its side with a radius of 0.500 ft and a length L (ft). Joe observed the water discharged with an average velocity of 1.50 m/s as the water level lowered from the initial height of 14.0 cm to 5.00 cm in the conical tank. Answer the following: 1. If the initial height of water in the conical tank is 14.0 cm (measured from the reference point, see Fig. 1), how long in seconds will it take for the water level to drain to a height of 5.00 cm?? NOTE: Height refers to the vertical height. What formula would I use to find out how long in seconds it takes for the water level to drop? Answered by Harley Weston.
	A circular blob of molasses		2007-05-28
		From Julie: A circular blob of molasses of uniform thickness has a volume of 1 m^3. The thickness of the molasses is decreasing at a rate of 0.1 cm/hour. At what rate is the radius of the molasses increasing when the radius is 8 m? Thanks, Julia Answered by Penny Nom.
	A growing heap of sand: related rates		2007-04-23
		From Charles: Sand falls on to a horizontal ground at the rate of 9m ^ 3 per second and forms a heap in the shape of a right circular cone with vertical angle 60. Show that 10 seconds after the sand begins to fall, the rate at which the radius of the pile is increasing is 3 ^ (1/3) * (4/pi) ^ (1/3) m per minute. Answered by Stephen La Rocque and Penny Nom.
	Liquid is being poured into the top of a funnel		2007-04-19
		From neroshan: Liquid is being poured into the top of a funnel at a steady rate of 200cm^3/s. The funnel is in the shape of an inverted right circular cone with a radius equal to its height. It has a small hole at the bottom where the liquid is flowing out at a rate of 20 cm^3/s. How fast is the height of the liquid changing when the liquid in the funnel is 15 cm deep? At the instant when the height of the liquid is 25cm, the funnel becomes clogged at the bottom and no more liquid flows out. How fast does the height of the liquid change just after this occurs? Answered by Penny Nom.
	Water is being pumped into a trough		2007-04-09
		From Michael: Water is being pumped into a trough that is 4.5m long and has a cross section in the shape of an equilateral triangle 1.5m on a side. If the rate of inflow is 2 cubic meters per minute how fast is the water level rising when the water is 0.5m deep? Answered by Stephen La Rocque.
	At what rate is the area of the triangle changing?		2007-02-24
		From mac: two sticks 3.5 feet long are hinged together and are stood up to form an isosceles triangle with the floor. The sticks slide apart, and at the moment when the triangle is equilateral, the angle is increasing at the rate of 1/3 radian/sec. At what rate is the area of the triangle increasing or decreasing at that moment? Mac Answered by Penny Nom.
	Water in a triangular trough		2007-01-30
		From Trina: the trough is 5 feet long and its vertical cross sections are inverted isosceles triangles with base 2 feet and height 3 feet. water is draining out of the trough at a rate of 2 cubic feet per minute. at any time t, let h be the depth and v be the volume of water in the trough. a. find the volume of water in the trough when it is full b. what is the rate of change in h at the instant when the trough is .25 full by volume? c. what is the rate of change in the area of the surface of the water at the instant when the trough is .25 full by volume? Answered by Penny Nom.
	Wheat is poured on a conical pile		2006-11-17
		From Rachel: wheat is poured through a chute at the rate of 10 cubic feet per minute and falls in a conical pile whose bottom radius is always half the altitude. how fast will the circumference of the base be increasing when the pile is 8 feet high? Answered by Penny Nom.
	A melting snowball		2006-11-06
		From Jay: A snowball melts at a rate proportional to its surface area. Show that its radius shrinks at a constant rate. If it melts to 8/27 of its original volume in 20 minutes, how long will it take to melt completely? Please I need your help. Answered by Stephen La Rocque.

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