Related rates Definition and 361 Threads

A ruptured oil tanker causes a circular oil slick on the surface of the ocean. When its radius is 150 meters, the radius of the slick is expanding by 0.1 meter/minute and its thickness is 0.02 meter. At that moment: (a) How fast is the area of the slick expanding? (b) The circular slick...

Coffee drains from a conical filter, with diameter of 15cm and a height of 15 cm into a cylindrical coffee pot, with a diameter of 15 cm at 2 cm^2/ sec. At a certain time, the coffee in the filter is 13 cm deep. a) How fast is the depth of coffee in the filter changing at that time? b) How...

A square is inscribed in a circle. As the square expands, the circle expands to maintain the four points of intersection. The perimeter of the square is expanding at the rate of 8 inches per second. Find the rate at which the circumference of the circle is increasing. Perimeter = p...

I am trying to do the problem below but I don't understand how to do it. Can you please show me how to do it? DON'T give me the answer, explain to me how to get the answer. http://img134.imageshack.us/img134/9168/untitled1au7.jpg Point C moves at a constant rate along semicircle centered...

I'm stuck on this question: "A man is sipping soda through a straw from a conical cup, 15 cm deep and 8 cm in diameter at the top. When the soda is 10 cm deep, he is drinking at the rate of 20 cm^3/s. How fast is the level of the soda dropping at that time?" So you are given height = 15...

Hey, I have this one practise calculus question that I just can't seem to get. Any help would be greatly appreciated: A light is on the ground 40ft from a building. A man 6ft tall walks from the light towards the building at 6ft/s. How rapidly is his shadow on the building becoming shorter...

Hey, I have this one practise calculus question that I just can't seem to get. Any help would be greatly appreciated: A light is on the ground 40ft from a building. A man 6ft tall walks from the light towards the building at 6ft/s. How rapidly is his shadow on the building becoming shorter...

Eh, this is sort of a simple question. Milt Famey hits a line drive to center field. As he rounds second base, he heads directly for third base, running at 20 ft per second. Write an equation expressing.. blah blah blah. I'm not asking to do the mathematical part. I just don't know...

This is a related rate problem. A man starts walking north at 4 ft/s from a point P. Five minutes later a woman starts walking south at 5 ft/s from a point 500 ft due east of P. At what rate are the people moving apart 15 min after the woman starts walking? I'm just trying to interpret...

At a rate of 8ft^3/min, water is pouring into a conical cistern, if the height of a cistern is 12ft and the radius of it's circular opening is 6ft, how fast is the water level rising when the water is 4ft deep?

So i have receive a problem in my calculas class that i have been working on for about 2 weeks and have come up empty handed in my attempt to find the answer, the question is quite lengthly, but is as follows: a cruiser is steaming on a straight course at 20 knots. An airplane, flying so low...

Related Rates.. again...? A swimming pool is 50 feet long and 20 feet wide. Its depth varies uniformly from 2 feet at the shallow end to 12 feet at the deep end. (The figure shows a cross-section of the pool.) Suppose that the pool is being filled at the rate of 1000 gal/min. At what rate is...

1. A ship with a long anchor chain is anchored in 11 fathoms of water. The anchor chain is being wound in at a rate of 10 fathoms/minute, causing the ship to move toward the spot directly above the anchor resting on the seabed. The hawsehole ( the point of contact between ship and chain) is...

I've been practicing related rates problems, and I want to confirm a few things. - When a pebble is dropped in water producing a circular wave, the rate that it travels outward is the rate of the changing radius, correct? In other words, dr/dt? Also, I have two questions I can't really...

Can someone check if i did these two questions right please? The questions are: 1. A baseball diamond is a perfect square with each side measuring 90 feet in length. A player runs from the first base to second base at a speed of 25 ft/s. How fast is she moving from home plate when she is...

A particle is moving along the graph of y=x^1/3. Suppose x is increasing at the rate of 3 cm/s. At what rate is the angle of inclination, theta, changing when x=8? [Hint: when x=8, theta approx. 0.24 rad] I'm stuck on problem. I know x=8, y=2 and the hyp=2.87. They want the...

Hey guys, I'm having some trouble figuring out this problem and was wondering if someone would be kind enough to look over my work so I know that I am doing it correctly =). ------------------------------------------------------------------------- There is an open right cylinder cone that...

Here is the question: Two people start from the same point. One walks east at 3 mi/h and the other walks northeast at 2 mi/h. How fast is the distance between the people changing after 15 minutes? I have: dx/dt= 3 mi/h, dy/dt= 2 mi/h, dz/dt= ? x= 3*.25= .75, y= 2*.25= .50 The instructor...

The problem given in my book is: I set up and solved the problem this way: dx/dt = 500 mi/h x = 2mi y = 1mi (constant) Distance: s2 = y2 + x2 s2 = 1 + x2 s = (1 + x2)1/2 d/dt[s] = d/dt[sqrt(1 + x2)1/2] ds/dt = (1/2)(1 + x2)-1/2 * (2x(dx/dt)) ds/dt = (1 + x2)-1/2 *...

"A street light is mounted at the top of a 15-ft-tall pole. A man 6ft tall walks away from the pole with a speed of 5ft/s along a straight path. How fast is the tip of his shadow moving when he is 40 ft from the pole?" This is how I did it: \frac{15}{6} = \frac{x+y}{y} 0 = \frac{y(\frac{dy}{dx}...

Hi. I am getting absolutely embarassed by these related rates problems. Here is one that I simply keep getting wrong: The volume of an expanding sphere is increasing at a rate of 12 cubed cm per second. When the volume is 36\pi, how fast is the surface area increasing? V=\frac...

hey guys, just wondering if i did this correctly a spherical balloon is to be filled with water so that there is a constant increase in the rate of its surface area of 3cm2/sec . a) Find the rate of increase in the radius when the radius is 3cm. b) Find the volume when the volume is...

Water is leaking out of an inverted conical tank at a rate of 10000cm^3/min at the same time that water is being pumped into the tank at a constant rate. The tank is 6m high and the diameter at the top is 4m. If the water level is rising at a rate of 20cm/min when the height of the water is...

I've been working on this problem for a while now and I can't seem to make it work. Maybe I could get a hint? I understand I'm given dv/dt = 180 as well as r = 6 and h = 2r/5 = 36/5 The equation I'm using is v = Bh/3 or v = (pi)(r^2)(h)/3 I go on to take the derivative and input my...

Hey Guys, I learning about Related rates and although I understand the basic concepts, I'm stuggling with this problem - When two resistors r1 and R2 are connected in parallel, the total resistance R is given by the equation 1/R=1/R1+1/R2. If R1 and R2 are increasing at rates of .01 ohm/sec...

Hi everyone, Well its that great time of year...the time of feverishly studying for finals and I have been doing some practice questions and there are a few that I'm stuck on. My first question I am embarassed to ask, it should be so simple, yet I cannot get the right answer. 1) A highway...

Sand falls from a conveyor belt at the rate of 10 \frac{ft^{3}}{min} onto a conical pile. The radius of the base of the pile is always equal to half the pile's height. How fast is the height growing when the pile is 5 ft high? So r = \frac{1}{2} h . That means when h = 5 , r = 2.5 . We...

The angle of elevation of the Sun is decreasing at a rate of 0.25 rad/h. How fast is the shadow cast by a 400-ft-tall building increasing when the angle of elevation of the Sun is π/6? I thought about using the special triangle to find exact values for trig functions at π/6 but I don't know...

An object is dropped from rest from a height of 200 ft, 300 feet horizontally across from a 200 ft tall light tower. The object's height above the ground at any given time, t, in seconds, is h= 200 - 16t^2 feet. Exactly 2 seconds after it is dropped, what is the rate at which the shadow is...

Hello. I really need help on my math homework. Please anybody help me. I would really appreciate it. These 2 problems have to do with related rates and they are too advanced for me... I just need to be shown the way and I could get it I just need to know how to start... thank you. Problem 1...

Sand is falling onto a cone-shaped pile at the rate of 9pi cubic feet per minute. the diameter of the base is always 3 times the height of the cone. At what rate is the height of the pile changing when the pile is 12 feet high. work: dV/dt=+9 ft^3/min d=3h then r=3h/2 dr/dt=(3/2)...

I'm in AP Calculus BC and I've had no trouble with any of Calc I or II (I self studied it all previously), but this one related rates problem that seemed relatively simple got me. (This is also in the Schaum's Outline Calculus book if anyone has that. My teacher gave it to us on a worksheet of...

[SOLVED] Related Rates Problem Here is the problem word for word: "Angela Lansbury displayed her athletic prowess by skydiving out of a hovering helicopter 100ft away from a cliff. However, the chutes fail and she plummets to certain disaster. If her position, in feet, is given by...

At a rate of 10ft^3/min, water is pouring into a conical cistern that is 16ft deep and 8ft in diameter at the top. But the cistern has developed a small leak. At the same time the water is 12ft deep, the water level is observed to be rising at 1/3 ft/min. How fast is the water leaking out? i...

A lamp is located on the ground 10 m from a building. A man 1.8 m tall walks from the light toward the building at a rate of 1.5 m s⁻¹. What is the rate at which the man's shadow on the wall is shortening when he is 3.2 m from the building ? Give your answer correct to two decimal places...

This is the problem as it appears in the text. "As a spherical raindrop evaporates, its volume changes at a rate proportional to its surface area A. If the constant of proportionality is 3, find the rate of change of the radius r when r=2." My first question is does the constant of...

Hi, I'm having doubt about whether or not I'm approaching two related rates of change problems correctly... Below is my working: 1) The diagram represents a trough. (It's drawn like a cylinder, except the ends are right, isosceles triangles) The trough is 1.5m long. Water is being poured...

am i doing this right? A cylindrical tank with a radius of 5 ft and a height of 20ft is filled with a certain liquid chemical. A hole is punched in the bottom. At that moment the chemical drains ut of the tank at the rate of 2ft^3/min. At what rate is the height of liquid in the tank changing...

Thoughts: V=\frac{1}{3}\pi r^{2}h=\frac{1}{3}\pi (\frac{4}{5}h)^{2}h \frac{dV}{dt}=\frac{16}{25}\pi h^{2}\frac{dh}{dt} Now I replace \frac{dV}{dt} with 0.1-0.001h^2. This is where I am stuck. Any suggestions? Thanks.

Im going through odd number related rate problems in preparation for an exam tmmrw. The correct answer is \frac{10}{\sqrt{133}}. There is something wrong with the relation I construct; first the problem: The diagram they give is similar to an isocelles triangle with PQ running 12 ft down the...

Given, "if a snowball melts so that its surface area decreases at a rate of 1 cm^2/min, find the rate at which the diameter decreases when the diameter is 10 cm." \frac{dD}{dt} = \frac{dD}{dA} \frac{dA}{dt} were D is my diameter, A is (surface) area and t is time. I relate D to A by, A =...

Hello, I'm having some troubles with some more rates questions and was wondering if someone could help me out. A construction worker pulls a 5m plank up the side of a building under construction by means of a rope tied to the end of a plank. The opposite end of the plank is being dragged...

Hi Again, I am doing a question on related rates that I have become stuck on. The height (h) of an equilateral triangle is increasing at a rate of 3cm/min. How fast is the area changing when h is 5cm? I know that the area of a triangle is bh/2, but after that I am stuck :redface: I...

I was wondering if anyone has a set of related rates questions, online or even to scan for me or something so i can practice doing some..i found a small handful on the net, but i wanted a bit more to practice from..thanks a bunch :)

A balloon is in the shape of a cylinder with hemispherical ends of the same radius as that of the cylinder. The balloon is being inflated at the rate of 261 (pi) cubic inches per minute. At the instant the radius of the cylinder is 3 inches, the volume of the balloon is 144 (pi) cubic inches...

Hello all Just had questions on related rates: 1. The radius of a circle is growing by \frac{dr}{dt} = 7 . How fast is the circumference growing? Ok so C = 2\pi r and \frac{dC}{dr} = 2\pi \frac{dr}{dt} = 2\pi(7) = 14\pi 2. #1 has some amazing implications. Suppose you want to put a...

Hello all Just came across a few questions on related rates and would like some verification on whether I am doing these correctly: 1. Let \theta be an acute angle in a right triangle, and let x and y, respectively be the sides adjacent and opposite of \theta . Suppose that x and y vary...

Ok. This is the question I got from a friend of the family. There is a conically shaped bin in which sand is poured in at a rate of 2.4 m3 per minute. The sand escapes out the bottom of the conically shaped bin at 0.8 m3 per minute. The opening at the top has a radius of 5 m and the opening...

Hello all I need help with the following question Two ships A and B are sailing away from the point O along routes such that angle AOB = 120 degrees. How fast is the distance between them changing if, at a certain instant OA = 8 mi. OB = 6 ,i., ship A is sailing at the rate of 20 mi/hr...

if a raindrop is a perfect sphere,and it accumulates moisture at a rate proportional to its surface area. Show that the radius increases at a constant rate. I know surface area of sphere = 4 * pi * r^2 dV/ dr = 4 * pi * r^2 I am not sure where to go from here Any help is appreciated...