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	Rates & Ratios		2021-04-11
		Kenneth pose la question : Is it correct to think that a rate can have units that are the same? Usually rates have units that are different to each other. Penny Nom lui répond.
	Related rates		2018-02-11
		angelo pose la question : hi admin please help me answer this question. thank you! At a certain instant of time, the angle A of a triangle ABC is 60 degrees and increasing at the rate of 5degrees per second, the side AB is 10cm and increasing at the rate of 1cm per second, and side AC is 16cm and decreasing at the rate of 1/2 cm per second. Find the rate of change of side AB? Penny Nom lui répond.
	Walking up and down a hill		2017-09-19
		Justina pose la question : At 2:20 p.m. Jack is at the top of the hill and starts walking down at the exact same time that Jill, who is at the bottom of the hill, starts walking up. If they maintain the uphill speed of 2mph and downhill speed of 4mph and the distance from the bottom to the top of the hill is 1.5 mi, at what time will Jack and Jill meet? Penny Nom lui répond.
	Up a hill and down again		2017-09-17
		justina pose la question : Jack and Jill travel up a hill at a speed of 2mi/h.they travel back down the hill at a speed of 4mi/h.what is their average speed for the entire trip? express your answer as a mixed number Penny Nom lui répond.
	Filling a pool with two hoses		2017-02-20
		Charlene pose la question : A large hose will fill a pool in 40 minutes while it takes a smaller hose 60 minutes to fill the same pool. The same pool takes 80 minutes to drain if the drain is open. Suppose one day both the hoses are turned on, but by accident the drain was left open. How long would it take to fill the pool that day? Penny Nom lui répond.
	Water leaking from a trough		2016-12-28
		Kathryn pose la question : A trough is 6 m long, and has uniform cross-section of an equilateral triangle with sides 1 m. Water leaks from the bottom of the trough, at a constant rate of 0.1 m3/min. Find the rate at which the water level is falling when the water is 0.2m deep. Penny Nom lui répond.
	Two tax rates		2016-04-21
		Vishal pose la question : Total amount paid annually $444 for 2014 which is inclusive for tax. tax rate for first six month is 7% then it is changed to 15% for second six months. calculate the total basic amount paid before tax. the basic amount on which tax paid in first and second six month is same. Penny Nom lui répond.
	Filling a tub		2015-01-02
		Mr pose la question : The cold tap can fill a bath in 5minutes,the hot tap in 15,and the waste pipe empty the full bath in 10 minutes. All three are fully open for 2 minutes,after which the waste-pipe is closed. How much longer will it take to fill the bath? Penny Nom lui répond.
	Rates, percentages and units		2014-12-30
		Kenneth pose la question : Hello: If percentages have no units, why are some percentages called rates, as in interest rate, or perhaps a tax rate of 7% as an example? A rate has units of different quantities. I thank you for your reply. Robert Dawson lui répond.
	Water in a conical funnel		2014-02-11
		Marcus pose la question : Water is running out of a conical funnel at the rate of 1 inch^3/sec. If the radius of the base of the funnel is 4 in. and the altitude is 8 in., find the rate at which the water level is dropping when it is 2 in. from the top. Penny Nom lui répond.
	Related rates		2014-01-30
		Veronica pose la question : A container is the shape of an inverted right circular cone has a radius of 1.00 inches at the top and a height of 5.00 inches. At the instant when the water in the container is 1.00 inches deep, the surface level is falling at the rate of -2.00 inches/second. Find the rate at which the water is being drained. Penny Nom lui répond.
	A man and a kite		2014-01-29
		Veronica pose la question : A man flies a kite at a height of 120 meters. The wind carries the kite horizontally away from him at a rate of 8 meters/second. How fast is the distance between the man and the kite changing when the kite is 130 meters away from him? Penny Nom lui répond.
	Water flowing out of a tank		2013-11-03
		Carolyn pose la question : The flow of water out of a hole in a tank is known to be proportional to the square root of the height of water above the hole. That is, dV/dt (proportional to) sq root (h) The tank has a constant cross-sectional area A, show that the height of water in the tank is given by h = ((-kt+C)/2)^2 If the tank is 9 metres high, and it takes 5 hours for it to drain from full to half full, how much longer will we have to wait until it is completely empty? Penny Nom lui répond.
	Related rates		2013-02-17
		Ishaak pose la question : A hemispherical bowl is filled with water at a uniform rate. When the height of water is h cm the volume is π(rh^2-1/3 h^3 )cm^3, where r s the radius. Find the rate at which the water level is rising when it is half way to the top, given that r = 6 and the bowl fills in 1 minute. Penny Nom lui répond.
	Two cars approach a right-angled intersection		2012-04-10
		Michael pose la question : Two cars approach a right-angled intersection, one traveling south a 40km/h and the other west at 70km/h. When the faster car is 4km from the intersection and the other case if 3km from the intersection, how fast is the distance between the car cars changing? Penny Nom lui répond.
	Water is flowing into a cup		2011-12-19
		Tim pose la question : A cup has a radius of 2" at the bottom and 6" on the top. It is 10" high. 4 Minutes ago, water started pouring at 10 cubic " per minute. How fast was the water level rising 4 minutes ago? How fast is the water level rising now? What will the rate be when the glass is full? Penny Nom lui répond.
	Two trains passing each other		2011-12-07
		Tamkeen pose la question : two trains 245m and 315m long are travelling toward each other at 90km/h and 54km/h respectively on parallel lines . how long do the train take to pass one another train the time they meet each other? Penny Nom lui répond.
	Four carpenters can build eight houses in 10 days.		2011-11-23
		Kenneth pose la question : Four carpenters can build eight houses in 10 days. Two carpenters can build how many houses in 15 days? Penny Nom lui répond.
	Water pouring into a conical tank		2011-11-21
		Patience pose la question : Hi my name is patience and I'm having a problem with this question. Water pours into a conical tank of semi vertical angle 30 degrees at the rate of 4 cm^3/s, where h is the depth of the water at time t. At what rate is the water rising in the tank when h = 10 cm? Thank you Penny Nom lui répond.
	A reservoir has the shape of an inverted cone		2011-10-03
		Roger pose la question : a reservoir has the shape of an inverted cone whose cross section is an equilateral triangle. if water is being pumped out of the reservoir at a rate of 2m^3/sec, at what rate is the depth of the water changing when the depth is 40 meters? Penny Nom lui répond.
	A hemispherical bowl with a lead ball inside		2011-09-27
		Jean pose la question : "(a) Water is being poured into a hemispherical bowl of radius 3 inch at the rate of 1 inch^3/s. How fast is the water level rising when the water is 1 inch deep ? (b) In (a), suppose that the bowl contains a lead ball 2 inch in diameter, and find how fast the water level is rising when the ball is half submerged." Penny Nom lui répond.
	How many meters long should the race be?		2011-05-26
		Lee pose la question : Nathan can walk at a rate of two meters per second while David can easily go three-and-a-half meters per second. David offers Nathan a 45 meter head start. How many meters long should the race be in order for Nathan to win by a nose Penny Nom lui répond.
	Find the rate at which the searchlight rotates		2011-04-17
		Meredith pose la question : A searchlight is position 10 meters from a sidewalk. A person is walking along the sidewalk at a constant speed of 2 meters per second. The searchlight rotates so that it shines on the person. Find the rate at which the searchlight rotates when the person is 25 meters from the searchlight. Penny Nom lui répond.
	A conical container and a spherical balloon		2011-04-06
		Steven pose la question : Water is running out of a conical container 12 feet in diameter and 8 feet deep (vertex down) and filling a spherical balloon. At the instant the depth of the water in the cone is 4 feet, the radius of the sphere is approximately 4 feet. The rate of change of the depth of the water in the cone at the instant is approximately ______________ times the rate of change of the radius of the balloon. Penny Nom lui répond.
	A camera's line of sight		2011-02-26
		MJ pose la question : A rocket that is rising vertically is being tracked by a ground level camera located 3 mi from the point of blast off when the rocket is 2 mi high its speed is 400mph At what rate is the (acute) angle between the horizontal and the camera's line of sight changing Penny Nom lui répond.
	At what rate is the grain pouring from the chute?		2011-02-26
		MJ pose la question : Suppose that grain pouring from a chute forms a conical heap in such a way that the height is always 2/3 the radius of the base. At the moment when the conical heap is 3 m high, its height is rising at the rate of 1/2 m/min. At what rate (in m^3/min) is the grain pouring from the chute? Penny Nom lui répond.
	A player runs from second base to third base		2011-01-30
		Marie pose la question : A baseball diamond is a square with side 90 feet in length. A player runs from second base to third base at a rate of 18 ft/sec. At what rate is the area of the trapezoidal region, formed by line segments A, B, C, and D changing when D is 22.5 Distance A is the players distance from first base when running from 2nd to third. Distance D is his distance from 3rd base. Distance C is the distance from 3rd to 3rd to Home. Distance B is the distance from Home to First. I have found dA/dt in a previous problem. Penny Nom lui répond.
	A circular oil slick of uniform thickness		2010-05-22
		Susan pose la question : Hi, I have this problem on a homework assignment and just can't seem to figure it out: A circular oil slick of uniform thickness is caused by a spill of 1 m^3 of oil. The thickness of the oil is decreasing at the rate of .001m/h. At what rate is the radius of the slick increasing when the radius is 8. Penny Nom lui répond.
	Working together		2010-05-04
		Felicia pose la question : Sarah takes 3 hours longer to paint a floor than it takes Kate. when they work together it takes 2 hours. How long would each take to do the job alone? Penny Nom lui répond.
	Related rates and a rectangular sponge		2010-04-06
		Heather pose la question : A rectangular sponge is increasing its length at 4cm/min, decreasing its width at 2cm/min, and increasing its height at 3cm/min. When its length, width and height are 40, 30, and 20 respectively, find the rate of change of volume and surface area. Penny Nom lui répond.
	Sand falling off a conveyer		2010-04-02
		Katherine pose la question : sand is falling off a conveyer onto a pile at the rate of 1.5 cubic feet per minute. The diameter of the base is approximately twice the altitude. At what rate is the height of the pile changing when it is 10 feet high? Penny Nom lui répond.
	Sand in an hourglass		2010-03-20
		Luke pose la question : Harley Weston lui répond.
	A related rates problem		2010-03-03
		Amanda pose la question : A circle is inscribed in a square. The circumference of the circle is increasing at a rate of 6 inches per second. As the circle expands, the square expands to maintain the tangency. Determine the rate at which the area of the region between the circle and square is changing at the moment when the cricle has an area of 25(pi) square inches. Penny Nom lui répond.
	15 men can do a piece of work in 7 days		2010-02-20
		Kenneth pose la question : If 63 books cost $126, what will 125 books cost? If 15 men can do a piece of work in 7 days, in how many days can 21 men do the same work? Penny Nom lui répond.
	Related Rates Problem		2010-01-12
		Neven pose la question : A woman raises a bucket of cement to a platform 40 ft above her head by means of a rope 80 ft long that passes over a pulley on the platform. If she holds her end of the rope firmly at head level and walks away at 5ft/s, how fast is the bucket rising when she is 30 ft away from the spot directly below the pulley? (G. F. Simmons, Calculus with Analytic Geometry, pg.142) Penny Nom lui répond.
	Related Rates of a Cylinderical Trough with a Horizontal Axis		2009-12-26
		Emily pose la question : A cylinder is lying on it's side and being filled with water at a constant rate. Let the current height of water be t=0. When t=4, the cylinder is half full. When t=12, the cylinder is completely full. When is the rate of the height change increasing? Janice Cotcher lui répond.
	A pile of sand		2009-12-16
		Malik pose la question : Sand is leaking out of a hole at the bottom of a container at a rate of 90cm3/min. As it leaks out, it forms a pile in the shape of a right circular cone whose base is 30cm below the bottom of the container. The base radius is increasing at a rate of 6mm/min. If, at the instant that 600cm3 have leaked out, the radius is 12cm, find the amount of leakage when the pile touches the bottom of the container. Harley Weston lui répond.
	How fast is the distance between the two cars decreasing?		2009-12-08
		Jenny pose la question : Two cares are on a collision course toward point P. The paths of the two cars make a 30 degree angle with each other. The first car is 40 km from P, and traveling toward P at 16 km/hour. The second car is 50 km from P, traveling at 20 km/hour. How fast is the (straight line) distance between the two cars decreasing. (Hint: Law of Cosines) Harley Weston lui répond.
	Mowing 17 lawns		2009-06-18
		kevin pose la question : I need help setting up a equation to solve the following question: If a gardener can mow 3 lawns in 7 hours, how long should it take him to mow 17 lawns. I can solve the problem, but I don't know how to set up the equation. Penny Nom lui répond.
	Mixing drinks		2009-05-02
		samantha pose la question : If Steven can mix 20 drinks in 5 minutes, Sue can mix 20 drinks in 10 minutes and Jack can mix 20 drinks in 15 minutes. How much time will it take all 3of them working together to mix the 20 drinks? Stephen La Rocque and Claude Tardif lui répond.
	Filling a container with water		2009-04-22
		frank pose la question : With one house pipe it takes 8 hours to fill a container with water. How long will it take with 4 house pipes of the same size and the same water pressure and same container? Robert Dawson lui répond.
	Sand falls from a conveyor belt		2009-04-01
		Tracy pose la question : Sand falls from a conveyor belt at the rate of 10 cubic feet per minute onto a conical pile. The radius of the base is always equal to half the pile's height. How fast is the height growing when the pile is 5ft high? Stephen La Rocque lui répond.
	A spherical Tootsie Roll Pop		2009-04-01
		Tracy pose la question : A spherical Tootsie Roll Pop you are sucking on is giving up volume at a steady rate of .8 ml/min. How fast will the radius be decreasing when the Tootsie Roll Pop is 20 mm across? Harley Weston lui répond.
	Related rates		2009-03-14
		Jeevitha pose la question : The side of an equilateral triangle decreases at the rate of 2 cm/s. At what rate is the area decreasing when the area is 100cm^2? Stephen La Rocque lui répond.
	Water drains from a conical tank		2009-03-11
		Tyler pose la question : Water drains from a conical tank at the rate of 5ft/min^3. If the initial radius of the tank is 4' and the initial height is 10'. a) What is the relation between the variables h and r? (height and radius) b) How fast is the water level dropping when h=6'? Thanks for the help, i'm stumped. Penny Nom lui répond.
	Related rates		2009-03-09
		Megan pose la question : A plane flying with a constant speed of 330 km/h passes over a ground radar station at an altitude of 3 km and climbs at an angle of 30°. At what rate is the distance from the plane to the radar station increasing a minute later? Harley Weston lui répond.
	Three people working in pairs		2009-02-21
		bevaz pose la question : A and B can together do a piece of work in 6 days, B and C together in 20 days and C and A in 7.5 days. how long will they require separately for the work? Penny Nom lui répond.
	Rates		2009-02-10
		Jennifer pose la question : write each phrase in simplest form 30oz in 24 gl 48leaves on 9 plants Harley Weston lui répond.
	Water flowing from a cone to a cylinder		2009-01-23
		Ray pose la question : Water is passing through a conical filter 24 cm deep and 16 cm across the top into a cylindrical container of radius 6 cm. At what rate is the level of water in the cylinder rising when the depth of the water in the filter is 12 cm its level and is falling at the rate of 1 cm/min? Harley Weston lui répond.
	Related rates		2008-11-26
		Lyudmyla pose la question : How fast is the volume of a cone increasing when the radius of its base is 2 cm and growing at a rate of 0.4 cm/s, and its height is 5 cm and growing at a rate of 0.1 cm/s? Harley Weston lui répond.
	How fast is the length of his shadow changing?		2008-11-22
		Desiree pose la question : A spotlight on the ground shines on a wall 12 m away. If a man 2 m tall walks from the spotlight toward the building at a speed of 2.3 m/s, how fast is the length of his shadow on the building decreasing when he is 4 m from the building? Harley Weston lui répond.
	A conical funnel		2008-11-12
		Rachael pose la question : Hello, I am a 10th grader in AP Calc, and can not figure out this question: Water is running out of a conical funnel at the rate of 1 inch^3/sec. If the radius of the base of the funnel is 4 in. and the altitude is 8 in., find the rate at which the water level is dropping when it is 2 in. from the top. Harley Weston lui répond.
	Filling a tank with 2 taps		2008-11-10
		Murray pose la question : 2 taps turned on together can fill a tank in 15 minutes. By themselves, one takes 16 minutes longer than the other to fill the tank.Find the time taken to fill the tank by each tap on it's own. Penny Nom and Victoria West lui répond.
	Water is leaking from a conical tank		2008-10-24
		Kimberly pose la question : Water is leaking out of an inverted conical tank at a rate of 12000 cm3/min at the same time that water is being pumped into the tank at a constant rate. The tank has height 6 m and the diameter at the top is 4 m. If the water level is rising at a rate of 20 cm/min when the height of the water is 2 m, find the rate at which water is being pumped into the tank. Stephen La Rocque lui répond.
	Melting ice on a hemisphere		2008-10-20
		heather pose la question : The top of a silo is the shape of a hemishere of diameter 20 ft. if it is coated uniformly with a layer of ice, and if the thickness is decreasing at a rate of 1/4 in/hr, how fast is the volume of ice changing when the ice is 2 inches thick? Penny Nom lui répond.
	Related rates		2008-10-16
		Gisela pose la question : As sand leaks out of a hole in a container, it forms a conical pile whose altitude is always the same as its radius. If the height of the pile is increasing at a rate of 6 in/min, find the rate at which the sand is leaking out when the altitude is 10in. Penny Nom lui répond.
	The rate of change of the volume of a cone		2008-10-15
		Barbara pose la question : Suppose that both the radius r and height h of a circular cone change at a rate of 2 cm/s. How fast is the volume of the cone increasing when r = 10 and h = 20? Harley Weston lui répond.
	Liquid is being pored into the top of a funnel		2008-05-25
		Stella pose la question : Liquid is being pored 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 in the bottom where the liquid is flowing out at a rate of 20cm^3/s. How fast is the height of the liquid changing when the liquid in the funnel is 15cm deep? At the instance when the height of the liquid is 25cm, the funnel becomes clogged at the bottom and no mo re liquid flows out. How fast does the height of the liquid change just after this occurs? Stephen La Rocque lui répond.
	Working together		2008-04-26
		Joanna pose la question : If 8 men took 15 days to paint a building . How many more men are needed to paint the building in 6 days ? Stephen La Rocque lui répond.
	Related rates		2008-04-25
		Mary pose la question : A rectangular box is 10 inches high. It's length increases at a rate of 2 inches per second and it's width decreases at the rate of 4 inches per second. When the length is 8 inches and the width is 6 inches, what is the rate of change of the volume? Stephen La Rocque lui répond.
	A train and a boat		2008-03-15
		Sabrina pose la question : A railroad bridge is 20m above, and at right angles to, a river. A person in a train travelling at 60 km/h passes over the centre of the bridge at the same instant that a person in a motorboat travelling at 20km/h passes under the centre of the bridge. How fast are the two people separating 10s later? Harley Weston lui répond.
	It takes Mark 3 hours to paint a picture		2008-02-27
		Suzanne pose la question : If Mark takes 3 hours to paint a picture and it takes Henry three times as long to paint the same picture, then: How many pictures can each paint in 10 hours? How many pictures can they paint together in 10hours? Penny Nom lui répond.
	Two job offers		2008-02-10
		Kelly pose la question : Raja has been offered two jobs. Each of these jobs takes 24 weeks to complete. One job pays $3440 every 8 weeks. The other job pays $2700 every 6 weeks. Raja wants to accept the job that pays more per week. Show how to use equations to help Raja make her choice. Penny Nom lui répond.
	A spherical bubble gum bubble		2007-12-31
		Houston pose la question : Bazooka Joe is blowing a spherical bubble gum bubble. Let V be the volume in the bubble, R the inside of the bubble, and T the thickness of the bubble. V, T, and R are functions of time t. (a) Write a formula for V in terms of T and R. Hint: Draw a picture (b) Assume that the amount of bubble gum in the bubble is not changing. What is V'(t)? (c) After 5 minutes of blowing a bubble gum bubble, the bubble is 3ft in diameter and .01 feet thick. If the inside radius of the bubble is expanding at a rate of .5 feet per minute, how fast is the thickness changing? Hint: Remember that the volume of gum in the bubble does not change over time. Harley Weston lui répond.
	Related rates - tree growth		2007-12-09
		Christy pose la question : How do I go about answering this question, I know I have to find dv/dt, but I'm not sure how to start. The volume of a certain tree is given by V= 1/12pie C^2h where C is the circumference of the tree at the ground level and h is the height of the tree. If C=5feet and growing at the rate of 0.2feet per yer, and if h=22feet and is growing at 4 feet per year, find the rate of growth of the volume, V. Stephen La Rocque and Harley Weston lui répond.
	Related Rates (streetlamp and shadow)		2007-11-09
		Casey pose la question : A street light is mounted at the top of a 15ft pole. A man 6ft tall walks away from the pole at a rate of 5ft per second. How fast is the tip of his shadow moving when he is 40ft from the pole? Stephen La Rocque and Penny Nom lui répond.
	Related Rates (a water trough)		2007-11-07
		Christina pose la question : A rectangular trough is 3ft long , 2ft across the top and 4 ft deep. If water flows in at the rate of 2ft^3/min, how fast is the surface rising when the water is 1 ft deep ? Stephen La Rocque lui répond.
	How to solve related rates problems		2007-10-27
		David pose la question : Can you plz explain how and where you come up with an equation to solve this? Find the rate of change of the distance between the origin and a moving point on the graph of y = sin x if dx/dt = 2 centimeters per second. Stephen La Rocque lui répond.
	Related rates		2007-10-26
		David pose la question : 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 Stephen La Rocque lui répond.
	The rate of change of the area of a triangle		2007-10-22
		Ahlee pose la question : 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 Penny Nom lui répond.
	A rectangular trough		2007-10-18
		David pose la question : 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. Stephen La Rocque and Penny Nom lui répond.
	A conical cup		2007-10-18
		Nicholas pose la question : 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. Penny Nom lui répond.
	Related rates		2007-10-15
		Alexis pose la question : 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. Stephen La Rocque lui répond.
	Water flowing into a tank		2007-09-21
		andrew pose la question : 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. Harley Weston lui répond.
	Water in a conical tank		2007-09-10
		Greg pose la question : 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? Harley Weston lui répond.
	A circular blob of molasses		2007-05-28
		Julie pose la question : 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 Penny Nom lui répond.
	A growing heap of sand: related rates		2007-04-23
		Charles pose la question : 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. Stephen La Rocque and Penny Nom lui répond.
	Liquid is being poured into the top of a funnel		2007-04-19
		neroshan pose la question : 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? Penny Nom lui répond.
	Water is being pumped into a trough		2007-04-09
		Michael pose la question : 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? Stephen La Rocque lui répond.
	At what rate is the area of the triangle changing?		2007-02-24
		mac pose la question : 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 Penny Nom lui répond.
	Water in a triangular trough		2007-01-30
		Trina pose la question : 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? Penny Nom lui répond.
	Wheat is poured on a conical pile		2006-11-17
		Rachel pose la question : 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? Penny Nom lui répond.
	A melting snowball		2006-11-06
		Jay pose la question : 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. Stephen La Rocque lui répond.
	Water is being pumped into the pool		2006-10-24
		Jon pose la question : A swimming pool is 12 meters long, 6 meters wide, 1 meter deep at the shallow end, and 3 meters deeps at the deep end. Water is being pumped into the pool at 1/4 cubic meters per minute, an there is 1 meter of water at the deep end. a) what percent of the pool is filled? b) at what rate is the water level rising? Stephen La Rocque lui répond.
	How fast is the water level rising		2006-08-12
		Erin pose la question : Water runs into a conical tank at the rate of 9ft3/min. The tank stands point down and has a height of 10 ft. and a base radius of 5 ft. How fast is the water level rising when the water is 6 ft. deep? (V=1/3 pi r2 h). Penny Nom lui répond.
	If all of them work together, ...		2006-07-27
		Kakron pose la question : Pipe A can fill in 20 mins and pipe B can fill in 30 mins and pipe C can empty the same in 40 mins. If all of them work together, find the time taken to fill the tank? Stephen La Rocque lui répond.
	Rates and percentages		2006-06-20
		Todd pose la question : If rates are about to rise 1.84%, from the current 5.30% that they are currently at. What amount are they going to increase to? I ask because many publications print an answer that is 7.14% but I don't see that as correct because the first line would have to say an increase of 184 basis points for that to be correct. My answer to this is about 5.4%. Am I thinking correctly? secondly, if rates are about to move to 7.14% from 5.3% what percentage move is this? I get an answer of about 35%. am I off on this or is everyone else that I ask not calculating correctly? Claude Tardif lui répond.
	Wes and Tony live 360 km apart.		2006-04-01
		Thiru pose la question : Wes and Tony live 360 km apart. If Wes travels at 80 km/h towards Tony. And Tony travels at 100 km/h towards Wes, how long will it take before they meet. Penny Nom lui répond.
	Worker A can do a piece of work in 15 days,...		2006-03-23
		Kenneth pose la question : Worker A can do a piece of work in 15 days, worker B in 12 days, and worker C in 10 days. Worker A works 2 days, worker B 3 days, and worker C 3 days. In what time can worker A and worker B finish the job by working together? Penny Nom lui répond.
	One worker can perform a certain job in 8 days		2006-02-28
		Kenneth pose la question : One worker can perform a certain job in 8 days, another worker in 10 days and a third worker in 12 days. In what time can all three perform it working together? Stephen La Rocque lui répond.
	Related rates and an oil spill		2006-02-12
		Brandon pose la question : An Oil Tanker Spills 100,000 cubic meters of oil, which forms a slick that spreads on the water surface in a shape best modeled by a circular disc is increasing at a rate of 3m/min (it doesn't state what is increasing at 3m/min, so I'm assuming Radius until I can ask my teacher.) At t=T, the area of the "circular" slick reaches 100pi Sq. meters. A) how fast is the area of the slick increasing at t=T B)How fast is the thickness of the slick decreasing at t=T C)Find the rate of change of the area of the slick with respect to the thickness at t=T. Penny Nom lui répond.
	Two related rates problems		2005-12-29
		Shimaera pose la question : #1. A manufacturer determines that the cost of producing x of an item is C(x)=0.015x2+12x+1000 and the price function is p(x)=250+2x/10. Find the actual and marginal profits when 500 items are produced. #2. At 9 a.m a car is 10km directly east of Marytown and is traveling north at 100 km/h. At the same time, a truck leaves Marytown traveling east at 70 km/h. At 10 a.m, how is the distance between the car and the truck changing? Penny Nom lui répond.
	One car leaves a spot traveling at 100 km per hour		2005-12-28
		Jason pose la question : One car leaves a spot traveling at 100 km per hour. The second car leaves the same spot 15 minutes later and traveling at 120 km per hour. How long does it take for the second car to catch up to the first car? Penny Nom lui répond.
	The bathtub curve		2005-10-13
		David pose la question : My father asked me to submit a question about the so-called 'bathtub curve'. If you cut a bathtub in half lengthwise down it's middle, the edge of the tub would describe the 'bathtub curve' which can be used to demonstrate typical failure rates of products. This curve is characterised by high initial (infant mortality) failure rates at it's beginning, which drop quickly to a very low level. Failures then increase gradually to the "end of life" stage where the failure rate takes off dramatically again. If anyone in the math department knows about the so-called 'bathtub curve' my father would really appreciate the equation. Chris Fisher and Edward Doolittle lui répond.
	A point is moving on the graph of x^3 + y^2 = 1 in such a way that		2005-09-17
		Gina pose la question : A point is moving on the graph of x3 + y2 = 1 in such a way that its y coordinate is always increasing at a rate of 2 units per second. At which point(s) is the x coordinate increasing at a rate of 1 unit per second. Penny Nom lui répond.
	At what rate is the circumference of the circle increasing?		2005-08-08
		John pose la question : A mathematics professor is knitting a sweater. The main part of the sweater is knit in a large spiral, ending up with a diameter of 30 inches. She knits at a constant rate of 6/7 square inches per minute. 1. At what rate is the circumference of the circle increasing when the diameter is 2 inches? 2. How long will it take her to finish this piece of the sweater? Penny Nom lui répond.
	A lighthouse is located on a small island,...		2005-07-14
		Brittnee pose la question : A lighthouse is located on a small island, 3 km away from the nearest point P on a straight shoreline, and its light makes four revolutions per minute. How fast is the beam of light moving along the shoreline when it is 1 km from P? Penny Nom lui répond.
	Three debts		2005-02-03
		Kat pose la question : If I have three debts and 49% percent of total debt is loaned at 9% intrest, 34% of the debt is at 21% intrest and 17% of the total debt is at 14% intrest, how do I calculate the average rate of intrest on total debt? Penny Nom lui répond.
	Ratios and rates		2004-10-27
		Kenneth pose la question : What is the difference between a ratio and a rate? Penny Nom lui répond.
	Related rates and baseball		2004-04-26
		Bethany pose la question : A baseball diamond is the shape of a square with sides 90 feet long. A player running from second to third base at a speed of 28 feet/ second is 30 feet from second base. At what rate is the player's distance from home plate changing? Penny Nom lui répond.
	Snow in the driveway		2004-04-09
		Patricia pose la question : Following a severe snowstorm, Ken and Bettina Reeves must clear their driveway and sidewalk. Ken can clear the snow by himself in 4 hours, and Bettina can clear the snow by herself in 6 hours. After Bettina has been working for 3 hours, Ken is able to join her. How much longer will it take them working together to remove the rest of the snow? Penny Nom lui répond.
	A changing rectangle		2004-04-03
		A student pose la question : The width x of a rectangle is decreasing at 3 cm/s, and its length y is increasing at 5 cm/s. At what rate is its area A changing when x=10 and y=15? Penny Nom lui répond.
	Some calculus problems		2004-04-01
		Weisu pose la question : I have questions about three word problems and one regular problem, all dealing with derivatives. Find all points on xy=exy where the tangent line is horizontal. The width x of a rectangle is decreasing at 3 cm/s, and its length y is increasing at 5 cm/s. At what rate is its area A changing when x=10 and y=15? A car and a truck leave the same intersection, the truck heading north at 60 mph and the car heading west at 55 mph. At what rate is the distance between the car and the truck changing when the car and the truck are 30 miles and 40 miles from the intersection, respectively? The production P of a company satisfies the equation P=x2 + 0.1xy + y2, where x and y are the inputs. At a certain period x=10 units and y=8 units. Estimate the change in y that should be made to set up a decrease of 0.5 in the input x so that the production remains the same. If you could just give me some hints on these questions, I'd really appreciate it. Thanks! Penny Nom lui répond.
	A pyramid-shaped tank		2004-02-13
		Annette pose la question : The base of a pyramid-shaped tank is a square with sides of length 9 feet, and the vertex of the pyramid is 12 feet above the base. The tank is filled to a depth of 4 feet, and water is flowing into the tank at a rate of 3 cubic feet per second. Find the rate of change of the depth of water in the tank. (Hint: the volume of a pyramid is V = 1/3 B h , where B is the base area and h is the height of the pyramid.) Harley Weston lui répond.
	Storyteller figurines		2003-02-10
		A student pose la question : It takes 3/4 of an hour to bake a storyteller figurine. If only one figurine can be baked at a time, how many can be baked in 6 hours? Penny Nom lui répond.
	Two airplanes leave Dallas		2003-02-06
		A student pose la question : TWO AIRPLANES LEAVE DALLAS AT THE SAME TIME AND FLY IN OPPOSITE DIRECTIONS. ONE AIRPLANE TRAVELS 80 MILES PER HOUR FASTER THAN THE OTHER. AFTER THREE HOURS, THEY ARE 2940 MILES APART. WHAT IS THE RATE OF EACH AIRPLANE? Penny Nom lui répond.
	Filling A swimming pool		2002-11-21
		Sarah pose la question : A swimming pool is being filled by three pumps. Alone pump A would take 6 hours, pump B would take 3 hours, and pump C would take 3 hours. If all three pumps are used to fill the pool, what fraction of the process is pump A. Penny Nom lui répond.
	Two tanks of water		2002-11-08
		A student pose la question : A 2000 L tank containing 550 L of water is being filled with water at the rate of 75 L per minute from a full 1600 L tank. How long will it be before the two tanks have the same amount of water? Penny Nom lui répond.
	Two rate problems		2002-09-30
		Rebecca pose la question : There are two small holes in the bottom of a tub filled with water. If opened, one hole will empty the tub in three hours; the other will empty it in six hours. If both holes are opened at the same time, how long will it take to empty the tub? An airplane flies 400 miles per hour in calm air. It can cover 900 miles flying with the wind in the same time that it can cover 700 miles against the wind. What is the speed of the wind? Penny Nom lui répond.
	Painting a car		2002-09-24
		A student pose la question : Dan can paint a car in 4 hours. Luke can pain the same car in 6 hours. Working together, how long would it take them to pain the same car? Penny Nom lui répond.
	A good rule of thumb when driving		2002-06-13
		Lisa pose la question : A good rule of thumb when driving is that you should be about one car length away from the car in front of you for every 10 miles per hour that you are travelling. Suppose you follow this rule perfectly (so you are exactly the correct distance away). You are waiting at a stop light with your front bumper just touching the car in front of you. The light turns green and the car in front accelerates at a constant rate "r". Calculate how you should accelerate in order to follow the rule. Penny Nom lui répond.
	Related rates		2002-04-17
		Molly pose la question : A tanker spilled 30 ft cubed of chemicals into a river, causing a circular slick whose area is expanding while its thickness is decreasing. If the radius of the slick expands at the rate of 1 foot per hour, how fast is them thickness of the slick decreasing when the area is 100 feet squared? Penny Nom lui répond.
	A lighthouse and related rates		2001-11-29
		Melissa pose la question : A lighthouse is located on a small island 3 km away from the nearest point P on a straight shoreline, and its light makes 4 revolutions per minute. How fast is the beam of light moving along the shoreline when it is 1 km from P? Penny Nom lui répond.
	Working together		2001-04-26
		Stephanie pose la question : Tom takes 10 hours to piant a mural on the wall of Evergreen School. Carol takes 6 hours to do the same job. If they work together, how long will it take them to paint the mural? Claude Tardif and Penny Nom lui répond.
	Two boats		2001-04-19
		Pat pose la question : Two boats head directly toward each other, one of them traveling 12 miles per hour and the other traveling 17 miles per hour. They begin at a distance of 20 miles from each other. How far apart are they one minute before they collide? Penny Nom lui répond.
	Two ferry boats		2001-03-25
		Gil pose la question : Two ferry boats leave from opposite shores. One is faster than the other. They meet 720 yards from the nearest shore. They proceed to destination and upon returning they meet 400 yards from the other shore. What is the exact width of the river. Penny Nom lui répond.
	Processing speed		2001-01-26
		Zac pose la question : A COMPUTOR IS ADVERTISED AS HAVING A PROCESSING SPEED OF 11 MILLION INSTRUCTIONS PER SECOND. ON THE AVERAGE, HOW LONG DOSE IT TAKE TO PROCESS ONE INSTRUCTION AT SUCH A SPEED? Leeanne Boehm lui répond.
	Working together on a job		2000-10-23
		Nicole pose la question : WORKING TOGETHER ON A JOB: Patrice, by himself can paint 4 rooms in 10 hours. If he hires April to help they can do the same job together in 6 hours. If he lets April work alone , how long will it take her to paint 4 rooms? Claude Tardif lui répond.
	Related Rates		2000-05-07
		Derek pose la question : How can you show that if the volume of a balloon is decreasing at a rate proportional to its surface area, the radius of the balloon is shrinking at a constant rate. Harley Weston lui répond.
	Two calculus problems		2000-03-03
		Tara Doucet pose la question : The height of a cylinder with a radius of 4 cm is increasing at rate of 2 cm per minute. Find the rate of change of the volume of the cylinder with respect to time when the height is 10 cm. A 24 cm piece of string is cut in two pieces. One piece is used to form a circle and the other to form a square. How should the string be cut so the sum of the areas is a maximum? Harley Weston lui répond.
	A moving point on the graph of y=sinx		2000-02-22
		Veronica Patterson pose la question : Find the rate of change of the distance between the origin and a moving point on the graph of y=sinx if dx/dt=2 centimeters per second. Harley Weston lui répond.
	Play ball		2000-02-03
		Jessie pose la question : Here's a calc question that is probably a lot easier than I am making it. If you have a legendary "baseball problem" for the related rates section of Calc I, and you are given that the runner is running from 2nd to 3rd base at a given rate, and the umpire is standing at home plate, and you are given the distance between the bases on the field, how do you find the rate of change of the angle between the third base line (from the point of the umpire) and the runner? Here is a sample prob: Runner is moving from 2nd to 3rd base at a rate of 24 feet per second. Distance between the bases is 90 feet. What is the rate of change for the angle (theta, as described previously) when the runner is 30 feet from 3rd base? Harley Weston lui répond.
	A decreasing ellipsoid		1999-12-15
		A student instructor pose la question : The volume of an ellipsoid whose semiaxes are of the lengths a,b,and c is 4/3 *pi*abc. Suppose semiaxes a is changing at a rate of A cm/s , the semiaxes b is changing at B cm/s and the semiaxes c is changing at C cm/s . If the volume of the ellipsoid is decreasing when a=b=c what can you say about A,B,C? Justify. Harley Weston lui répond.
	Two calculus problems		1999-12-13
		Alan pose la question : I have 2 questions that are very new to me, they were included on a quiz and the material was never covered. Our teacher never explained the purpose and detailed explanation of how to solve the problem. Could you help? Thanks. Question 1: A ball is falling 30 feet from a light that is 50 feet high. After 1 sec. How fast is the shadow of the ball moving towards the light post. Note that a ball moves according to the formula S=16t^2 Question 2: How many trapezoids must one use in order for the error to be less than 10^-8 if we want to find the area under the curve Y=1/X from 1 to 2. Find the exact area, Graph the function and use the trap rule for the "N" that you found. Harley Weston lui répond.
	Two calculus problems		1999-12-01
		O'Sullivan pose la question : Question #1 Assume that a snowball melts so that its volume decreases at a rate proportional to its surface area. If it takes three hours for the snowball to decrease to half its original volume, how much longer will it take for the snowball to melt completely? It's under the chain rule section of differentiation if that any help. I've set up a ratio and tried to find the constant but am stuck. Question #2 The figure shows a lamp located three units to the right of the y-axis and a shadow created by the elliptical region x^2 + 4y^2 < or= 5. If the point (-5,0) is on the edge of the shadow, how far above the x axis is the lamp located? The picture shows an x and y axis with only the points -5 and 3 written on the x axis. the lamp is on the upper right quadrant shining down diagonally to the left. There's an ellipse around the origin creating the shadow. It's formula is given as x^2 + 4y^2=5. Harley Weston lui répond.
	Clockwise or Counterclockwise?		1999-10-27
		Tim pose la question : A particle moves around the circle x2 + y2 = 1 with an x-velocity component dx/dt = y Find dy/dt Does the particle travel clockwise or counterclockwise around the circle? Why? Harley Weston lui répond.
	A circle in a square		1999-05-26
		Jose V Peris pose la question : A circle is inscribed in a square. The circumference of the circle is increasing at a constant rate of 6 inches per second. As the circle expands, the square expands to maintain the condition of tangency. find the rate at which the perimeter of the square is increasing. find the rate of increase in the area enclosed between the circle and the square at the instant when the area of the circle is 25(pi) square inches. Harley Weston lui répond.
	Related rates		1999-05-13
		Tammy pose la question : The sides of a rectangle increase in such a way that dz/dt=1 and dx/dt=3*dy/dt. At the instant when x=4 and y=3, what is the value of dx/dt? (there is a picture of a rectangle with sides x and y, and they are connected by z, which cuts the rectangle in half) Harley Weston lui répond.
	Lunes		1999-02-04
		Kai G. Gauer pose la question : A prof once told me that a certain type of lune is quadrable given that the diameter is an integer. She used the construction of a right isosceles triangle within a semicircle and later constructed another semicircle on the base of the first semicircle and used area subtraction to show equality to a smaller triangle with quadrable area. What happens when the original inscribed triangle is no longer isosceles? She mentioned something about other lunes also being quadrable; but not all. What are the dimensions of other such lunes? Note: I'm not certain if I still have my hercules account; please simply post on Q&Q. Thanks! Chris Fisher lui répond.
	A Car Wash		1998-04-04
		Lisa Gotimer-Strolla pose la question : Al washes a car in six hours. Fred washes a car in eight hours. How long will it take them to wash a car together? Harley Weston lui répond.
	A Tightrope Walker.		1998-02-19
		Amy Zitron pose la question : A tightrope is stretched 30 feet above the ground between the Jay and the Tee buildings, which are 50 feet apart. A tightrope walker, walking at a constant rate of 2 feet per second from point A to point B, is illuminated by a spotlight 70 feet above point A.... Harley Weston lui répond.
	Bathtub		1998-01-04
		Jeffrey Yau pose la question : A bathtub, with two taps, can be filled in 20 minutes using only the cold water tap. It can be filled in 30 minutes using only the hot water tap. The flow of each tap is not changed when both taps are turned on. It takes 24 minutes to drain the full tub. Starting with an empty tub and the drain plug in place, the cold water turned on. Five minutes later the hot water is also turned on, and five minutes after that the drain plug is removed. How many additional minutes, after the plug is removed, would it take to fill the tub? Harley Weston lui répond.
	Ajax, Beverley, Canton and Dilltown		1997-03-14
		S. Johnson pose la question : The following towns are placed on a coordinate system. Ajax at (-x,z), Dilltown at (-10,0), Canton at (0,0) and Beverly at (0,10). The roads from Beverly to Canton and from Canton to Dilltown are perpendiculat to each other and are each 10 miles in length. A car traveling at all times at a constant rate, would take 30 minutes to travel straight from Ajax to Canton, 35 minutes to travel from Ajax to Canton via Beverly, and 40 minutes to travel from Ajax to Canton via Dilltown. What is the constant rate of the car, to the nearest tenth of a mile per hour. Chris Fisher and Harley Weston lui répond.

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