Related rates Definition and 371 Threads

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...

Hi, I am terrible when it comes to doing these questions. I was wondering if you guys have any tips on how to do these questions. Like for example, just say there's a question like the following: Water is poured into a reservoir in teh shape of a cone 6ft. tall with a radius of 4ft. If...

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...

A balloon is 200 ft. off the ground and rising vertically at the constant rate of 15 ft/sec. An automobile passes beneath it traveling along a straight road at the constant rate of 45 mph or 66 ft/sec. How fast is the distance between them changing 1 sec. later? i know how to do related...

Question: Ohm's law for electrical circuits states that V=IR, where V is voltage, I is current in amperes, and R is the resistance in ohms. Suppose that V is increasing at the rate of 1 volt/sec while I is decreasing at the rate of 1/3 amp/sec. Let t denote time in seconds. a)what is the value...

Hi, I have no clue on how to work these problems out. Due tomorrow, please help! Thanks. http://img.photobucket.com/albums/v299/p4nda/RelatedRates.jpg

Hi, Is this a question on related rates? If so, can anyone help me do this question? I have no clue on even how to start it out. A clock has an hour hand 4cm long and a minute hand 8cm long. How fast is the distance between the tips of the hands changing at 2:00?

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 2m3/min, how fast is the water level rising when the water is 0.5m deep? Answer is 0.77m/min. Sorry for not posting this in the...

Grain is emptying from the bottom of a funnel-shaped hopper at a rate of 1.2m3/min. If the diameter of the top of the hopper is 5m and the sides make an angle of 30o with the vertical, determine the rate at which the level of grain in the hopper is changing, when it is half the height of the...

Hi guys, I'm completely stuck here when doing related rates questions. Here is the question, and following the setup I have so far. -------------------------------------------------------------------------------------------------------------------------------- Water is leaking out of an...

So I'm doing my homework and I get stuck (again) on this problem: Okay what I first did was gather all my given information. That includes all the given dimensions of the pool and dv/dt to be the 1/4 cubic feet per minute. I just need guidance through this problem or where to start... so if...

i don't really understand when you differentiate both sides of an equation to, for example, time. like, if you have tan(x)=y/50, you would get sec^2(x)dx/dt=1/50*(dy/dt) so does that mean when you differentiate both sides you find the derivative of the whole term and then multiply it by...

Ive been searching on the net and found some good sites but found nothing to help me with these questions. Could you please explain how to get the answer? 1. A spherical water tank has a radius of 15m. If water is pumped in at a rate of 10m3/minute, find how fast the level in the tank is...

On the final exam that I just took, the last problem went like this: A spotlight is shining on a building. It is 36 feet away from the building. A man that is 6 feet tall is walking toward the building. Calculate the rate of change in the length of his shadow if he is walking toward the...

Hello here's the problem: Each of the two sides of a triangle are increasing at the rate of 1/2 foot per second, and the included angle is decreasing 2 degrees per second. Find the rate of change of the area when the sides and included angle are respectively 5ft., 8ft., and 60 deg...