Related rates Definition and 361 Threads

Homework Statement A ladder of 25 feet long is leaning against the wall of a house. The base of the ladder is pulled away at 2 ft per second. (a) How fast is the top of the ladder moving down the wall when the base is seven feet from the wall? (b) Consider the triangle formed by the...

Homework Statement Dear All, I am having problems understanding how to deal with related rates. The problem is the following: A solid 400gm metal cube of size length 10cm expands uniformly when heated. If the length of its side expand at 0.5cm(hr), find the rate at which, after 5...

Homework Statement A 6-ft man walks away from a 15-ft lamppost at a speed of 3 ft/s. Find the rate at which his shadow is increasing in length. Homework Equations Pythagorean Theorem, Theorem of Similar Triangles (ratios of corresponding sides are equal) The Attempt at a Solution...

Homework Statement The number of yeast cells in a laboratory culture increases rapidly at first but levels off eventually. The population is modeled by the function below n=f(t)=\frac{a}{1+be^{-t}} where t is measured in hours. at time t=0 the population is 20 cells and is increasing...

Homework Statement Air is being pumped into a spherical balloon so that its volume increases at a rate of 70 cm3/s. How fast is the surface area of the balloon increasing when its radius is 5 cm3?Homework Equations A ball with radius r has the following volume (V) and surface area (S): V =...

Homework Statement If there is a container with a radius in feet given by r(z)=10/sqrt(z) and it is being filled at a constant rate of 22pi ft^3/min. find a function that gives the height of the water as a function of time.The Attempt at a Solution since the radius is a function of the...

Homework Statement A piston is seated at the top of a cylindrical chamber with radius 5 cm when it starts moving into the chamber at a constant speed of 3 cm/s. What is the rate of change of the volume of the cylinder when the piston is 2cm from the base of the chamber? Homework...

Homework Statement I am reading about related rates in my calc book but it doesn't really explain it very well. Are there any arcitcals some one can send me that goes indepth about this concept on related rates? Thank you.

Homework Statement Fluid flows out of a cone at 3 cu ft/min. If the height of the cone is three times the radius how fast is the height of the fluid decreasing when the fluid is 6 inches deep in the middle? The Attempt at a Solution 1. V= ( (pi)(r^2)(h) ) / 3 2. r = h/3 thus... V =...

Okay so I have this related rates problem for my AP Calculus Class A trough (Extruded Trapezoid) with a height of 2, Base 1 (bottom) of 2, Base 2 (top) of 6 and a extrusion of 10. (I provided a picture for better understanding) --------------------------------------… A = Area of the top...

Gravel is being dumped from a conveyor belt at a rate of 30 ft3/min and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 10 ft high? Known: dV/dt=30 ft^3/min...

Related Rates Promlem, Please Help! Homework Statement A bird of prey is perched at the top of a tree that is 40 m high. The bird watches as a delectable Kingston squirrel runs away from the base of the tree at a rate of 2 m/s. What is the rate of change of the distance between the bird...

Homework Statement At a certain moment, a plane passes directly above a radar station at an altitude of 3 miles at a speed of 300 mph. Suppose that the line through the radar station and the plane makes an angle θ with the horizontal. How fast is θ changing 50 min after the plane passes over...

Homework Statement The volume of a spherical balloon is increasing at a rate of 4m^3/min. How fast is the surface area increasing when the radius is three meters? Homework Equations V=4/3piR^3 A=4piR^2 The Attempt at a Solution V=s.a.*R/3 dv/dt=d(s.a.R/3)/dt...

Homework Statement Two sides of a triangle of fixed length measure 12m and 15m. The angle between these two sides increases at a rate of 2 degrees per minute. When the angle between these two sides is 60 degrees, at what rate is the third side increasing? Homework Equations That's the...

Homework Statement A ladder, of length 13m, is leaning against a wall. The base of the ladder begins to slide, frictionless, away from the wall; by the time the base is horizontally 12m away from the wall it is moving at a rate of 2ms-1 a)How fast is the top of the ladder sliding down the...

URGENT - related rates pool problem Homework Statement A swimming pool with a rectangular surface 18 m long and 12m wide is being filled at the rate of 0.8 cubic metres/min. At one end the pool is 1m deep and at the other end it is 2.5m deep, with a constant slope between the ends. How fast...

Homework Statement [PLAIN]http://img638.imageshack.us/img638/2218/questionscreenshot.jpg The attempt at a solution Step 1. Draw a triangle. Solve for third side (Pythagorean theorem), which I called z. z^2 = x^2 + y^2 Coordinates are given (4, 6). We know x = 4, y = 6...

Homework Statement 2 Cylindrical pools are filled simultaneously at the same rate, 1m3/min. The smaller pool has radius 5m and the water level rises at a rate of 0.5m/min. The larger pool has a radius 8m. How fast is the water level rising in the larger pool? Homework Equations V =...

When trying to solve a related rates problem, sometimes you need to relate variables. Can anyone help me with the conceptual reasoning or at least what to look for in these problems?

Homework Statement A pool is 20 ft wide, 40 ft long, 3 ft deep at the shallow end, and 9 ft deep at its deepest point. If the pool is shaped as shown (I attached a picture), and is being filled at a rate of 8 ft^3/min, how fast is the water level rising when the depth at the deepest point is...

Homework Statement "Consider the tank and water supply system as shown in the figure below. The diameter of the supply pipe, D1 = 20 mm, and the average velocity leaving the supply pipe is V1 = 0.595 m/s. A shut-off valve is located at z = 0.1 m, and the exit pipe, D2 = 10 mm. The tank...

Please answer this, it's so hard. Problem: At 12 noon, ship A travels due west at 100 knotsshiop B. After 4hours, ship B leaves the same port on the direction N30'W at 80 knots. How fast is the distance between two ships changing at 8PM in the same day? Reply please.I can't solve it...

Problem solved :)

Water is emptied from a spherical tank of radius 24 ft. The water in the tank is 8 ft deep and its level is decreasing at the rate of 2 ft/ min. At this time, what is the rate of change of the radius at the top of the water?

Homework Statement A kite 100 ft above the ground moves horizontally at a speed of 8 ft!s. At what rate is the angle between the string and the horizontal decreasing when 200 ft of string has been let out? Homework Equations tan \o = x/y The Attempt at a Solution After...

One night, a toddler is dropping eggs from a windowof a building which is 20 feet above ground. A neighbor, hearing the commotion, looks through her window which is 15 feet from the toddler's window, on the same wall of the building, and at the same height. She shines a flashlight from her...

Homework Statement A swimming pool is 20 feet wide, 40 feet long, 3 feet deep at the shallow end and 9 feet deep at its deepest point. If the pool is being filled at a rate of 0.8 feet^3/min, how fast is the water level rising when the depth at the deepest point is 5 feet? Homework Equations...

Homework Statement An inverted conical container has a diameter of 42 in and a depth of 15 in. If water is flowing out of the vertex at a rate of 35 \pi in^3 / sec, how fast is the depth of the water dropping when the height is 5 in? Homework Equations v= (1/3) \pi r^2 * h The...

Homework Statement Two boats leave a dock at the same tie. One goes south at 30 km/h and the other goes southwest at 40 km/h. What is the rate of change of the distance between the 2 boats, 30 minutes after they leave? I know how to do these questions when it's a right triangle...but since...

Homework Statement Water is leaking out an inverted conical tank at the rate of 50L/min. The tank has a diameter of 10m at the top and is 6m deep. if the water is rising at the rate of 4cm/min when the greatest depth is 3m, find the rate at which the water is being poured into the tank...

Hi, I've tried this too many ways and i can't seem to figure it out. the question is: 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 6in/min, find the rate at which the...

Hi, I've tried this too many ways and i can't seem to figure it out. the question is: 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 6in/min, find the rate at which the...

Homework Statement A spherical tank with an interior diameter of 2m is being filled with water at a rate of 10 liters per second. Determine what rate the height of the water is increasing at when the tank is half full. Homework Equations V=\frac{2\pi r^3}{3}-\pi r^2d+\frac{\pi d^3}{3}...

Homework Statement At ten am, a plane traveling east at 100km/hr is 500 km west of a jet traveling south at 200km/hr. At what rate is the distance between them changing at noon? Homework Equations The Attempt at a Solution 2aa' + 2bb' = 2cc' 2(300)(-100) + 2(400)(200) = (1000)c'...

Homework Statement A man 6m tall walks away from a light 10m above the ground. If his shadow lengthens at a rate of 2m/s, how fast is he walking? Homework Equations The Attempt at a Solution I have nothing.

Homework Statement A conical reservoir is 50m deep and 200m across the top. Water is being pumped in at a rate of 7000m^3/min, and at the same time, water is being drained out at a rate of 9000 m^3/min. What is the change in diameter when the height of the water in the reservoir is 20m...

Homework Statement A trough is 9 ft long and its ends have the shape of isosceles triangles that are 5 ft across at the top and have a height of 1 ft. If the trough is being filled with water at a rate of 14 ft3/min, how fast is the water level rising when the water is 8 inches deep...

Homework Statement A lighthouse is located off shore one mile from the nearest point P, on a straight coastline. The light makes 4 revolutions per minute. How fast is the beam of light moving along the shoreline when it is 2 miles from point P? Homework Equations The Attempt at a...

Hi I was just curious as to why calculus does not seem to work in the situation of area calculation. I came across this doing some HW and noticed that the booked worked out a seemingly similar question in two separate ways First was predicitng the chance in the length of the hypotenuse...

I have a question about a related rates, i already solved it, but i would like someone to confirm it to me . * The relation between distance s and velocity v is given by v=\frac{150s}{3+s}. Find the acceleration in terms of s. As you can see my final answer is a in terms of v and s, not s only...

Homework Statement A magic stalk starts growing at a spot 10 metres from a 4 metre lamppost. The stalk grows 1 metre per hour. Find the rate at which the length 's' of the stalk's shadow is increasing at the instant when the height h of the stalk is 3 metres. The Attempt at a Solution...

Homework Statement Water is being drained from a container which has the shape of an inverted right circular cone. The container has a radius of 5.00 inches at the top and a height of 7.00 inches. At the instant when the water in the container is 4.00 inches deep, the surface level is...

Homework Statement A swimming pool is 40 feet long, 20 feet wide, 4 feet deep at the shallow end, and 9 feet deep at the deep end. Water is being pumped into the pool at 10 cubic feet per minute. a. When the water is 3 feet deep at the shallow end, at what rate is the water level rising? b...

Homework Statement "An air traffic controller spots two planes at the same altitude converging on a point as they fly at right angles to each other. One plane is 120 miles from the point and is moving at 400 miles per hour. The other plane is 160 miles from the point and has a speed of...

1. The ladder is 24 ft long and is leaning against a house. The ladder is moving away from the house at a rate of 3 ft/s. I'm supposed to find the rate the slope of the ladder is decreasing when it is 14 ft away from the house. 3. I'm thinking its got something to do with the second...

Homework Statement A woman at point A on the shore of a circular lake with radius 2 miles wants to arrive at point C diametrically opposite A on the shore of the lake in the shortest time possible. She can walk at 4 mph and row a boat at 2 mph. To what point on the shore of the lake should...

Homework Statement The average cost per item, C, in dollars, of manufacturing a quantity q of cell phones is given by the following equation, where a and b are positive constants. C = a/q + b (a) Find the rate of change of C as q increases. Include units. I already found this, it's: -a/q^2...

Homework Statement Water is dripping into a hemispherical bowl with a radius of 8 cm at a rate of 1 cubic cm per minute. At what rate is the depth increasing when it is 4 cm. A) 1/96π B) 1/48π C) 1/24π D) 1/16π E) 1/8π Homework Equations V = (4πr3)/3 and any other relevant equations, but...

Homework Statement A 2m tall person walks toward toward a wall at 1.6 m/s. A spotlight 12 m away from the wall shines at it. How fast is the length of his shadow on the wall decreasing when he is 4m away from the wall? I tried a few different things with trig, none of which worked.