Related rates Definition and 371 Threads

A water tank has the shape of an inverted circular cone with base radius 2 m and height 4 m. If water is being pumped into the tank at a rate of 2 m^3/ min, find the rate at which the water level is rising when the water is 3 m deep. The answer to this question is $$\frac{8}{9\pi}$$But I got a...

Since it's the summer, I might as well take advantage of all the math helpers on the site :cool: (yay!) I'm pretty rusted when it comes to related rates, so it'd be great if someone checked my work :D Problem: A rectangle has two sides along the positive coordinate axes and its upper right...

Hey guys, I need some more help for this problem set I've been working on. I'm doubting some of my answers and I'd appreciate some help. This is only for question 1. Ignore 2. Question: For the first one, drawing out the question clearly tells us that we are working with a 90 degree...

Hey guys, I've two more word problem questions this time. Question: So for the first one, I know that y=T-Ts where Ts = 20. Thus, if T(0) = 90, then T'(70) = -1 T'(t) = k (T-Ts) k= -1/50 (via substitution) Now, we must find y. y'(t) = ky and y(t) = T(t) - Ts y(0) = 90- 20 y(0) = 70...

Hey guys, I want to make sure I am on the right track with this problem: The radius of a sphere is increasing at a rate of 4 cm/s. How fast is the volume increasing when the radius is 40 cm? (Recall the formula relating the area A and radius r of a sphere: A = 4πr^2.) So, I use the...

For problem: See Attachment I've never done a problem of this sort and it's proving to be much more difficult compared to the other problems I have had assigned to me. I'm not entirely sure which formulas to use but I've been playing with the following: Length of Arc = r\theta A = \pir^2 C =...

Homework Statement If a snowball melts so that its surface area decreases at a rate of 10 cm^2/min, find the rate at which the diameter decreases when the diameter is 11 cm.Homework Equations I don't know what i am doing wrong.The Attempt at a Solution A=4(pi)r^2 dA/dt=...

Water is leaking from a trough at the rate of 0.8 l/s. The trough has a trapezoidal cross section, where the width at the bottom is 55 cm, at the top is 85cm, and the height is 25 cm. The length of the trough is 3 m. Find the rate at which the height is changing when the depth of water is 11 cm.

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Here are the questions: I have posted a link there to this thread so the OP can view my work.

Homework Statement A particle is moving along the graph of y=sqrt(x). At what point on the curve are the x-coordinate and the y-coordinate of the particle changing at the same rate? Homework Equations y = sqrt(x) y' = 1/(2sqrt(x)) The Attempt at a Solution The solution to the...

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Homework Statement A large container has the shape of a frustum of a cone with top radius 9 metres , bottom radius 2 metres , and height 7 metres. The container is being filled with water at the constant rate of 4.2 cubic meters per minute. At what rate is the level of water rising at the...

The base of a pyramid-shaped tank is a square with sides of length 12 feet, and the vertex of the pyramid is 10 feet above the base. The tank is filled to a depth of 4 feet, and 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...

Homework Statement I've worked through both parts of this question twice in what I assume is the correct manner, but I'm receiving an unexpected result from part B. The question is as follows: Sand is dumped such that the shape of the sandpile remains a cone with height equal to twice...

Homework Statement http://i.minus.com/jbxIzu0P7sTqP0.png Homework Equations V(sphere) = 4/3(pi)(r^3) V = 36pi in^3 dr = -0.2 in dV = ? The Attempt at a Solution I basically solved for the radius, and took the derivative and plugged in the value of the radius and the...

Homework Statement The circumference of a circle is increasing by 4 inches per second. What is the rate of change of the diameter with respect to time if the radius is 2 inches? Homework Equations C = 2∏r = ∏d. The Attempt at a Solution dC/dt = 4 = ∏dd/dt. dd/dt = 4/∏ Is this it? It...

Homework Statement Grit, which is spread on roads in winter, is stored in mounds which are the shape of a cone. As grit is added to the top of a mound at 2 cubic meters per minute, the angle between the slant side of the cone and the vertical remains 45º. How fast is the height of the mound...

Homework Statement A potter forms a piece of clay into a cylinder. As he rolls it, the length, L, of the cylinder increases and the radius, r decreases. If the length of the cylinder is increasing at 0.1 cm per second, find the rate at which the radius is changing when the radius is 1 cm and...

Homework Statement The spherical head of a snowperson is melting under the HOT sun at the rate of -160 cc/h (cubic centimetres per hour.) Find the rate at which the radius is changing when the radius r=16. Use cm/h for the units. (The volume of a sphere is given by V= 4π⋅r^3/3.) I have...

Homework Statement http://i6.minus.com/jErr8PMddiofz.png Homework Equations V of cone = pi/3 (r^2)h The Attempt at a Solution I'm assuming this is correct and that dh/dt = 0.2 ft/min I basically substituted a value of h in for the radius so I wouldn't be doing multi-var...

Homework Statement http://i.minus.com/jz5YbMhv91p6K.png Homework Equations Volume is the area of the base (or cross section) times height. The Attempt at a Solution The base is a triangle. The area of a triangle is (0.5)(base length)(height). In this case that's 0.5*20*15, or...

(a) The half-life of morphine in the bloodstream is 3 hours. Suppose that there's initially 0.4 mg of morphine in the system, how long does it take until there's only 0.01 mg of morphine remaining in the bloodstream? (b) Suppose that there is initially x0 (0 is a subscript) grams of Kool-Aid...

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Homework Statement http://i4.minus.com/jboxzSadIJVVoi.jpg Homework Equations Product rule; implicit differentiation. Volume of cylinder, V = pi(r^2)(h) The Attempt at a Solution dV/dt = 0 = pi[2r(dr/dt)(h) + (dh/dt)(r^2)] Solve the equation after plugging in r = 5; h = 8, and dh/dt =...

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Homework Statement A street light is at the top of a pole that is 18 feet tall. A woman 6 ft tall walks away from the pole with a speed of 4 ft/sec along a straight path. How fast is the length of her shadow moving when she is 35 ft from the base of the pole?Homework Equations a^2 + b^2 = c^2...

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1. Assume that the radius r of a sphere is expanding at a rate of 50 cm/min. The volume of a sphere is V= 4/3 πr^3 and its surface area is 4πr^2.Determine the rate of change of volume when r = 13 cm [b]2. I tried d/dr=8*13*50*pi [b]3. 5200pi but is wrong

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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 200ft of the string has been let out? Homework Equations - The Attempt at a Solution I've tried two different...

Homework Statement A girl enters a ramp with a speed of 30ft/s. The ramp has 4ft in height and 15ft in length. Calculate the speed at which she comes out of the ramp. Homework Equations - The Attempt at a Solution I was thinking of just using cosθ=x/z, and just plugging in the...

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Here is the question: I have posted a link there to this topic so the OP can see my work.

Here is the question: I have posted a link there to this topic so the OP can see my work.

Here is the question: I have posted a link there to this topic so the OP can see my work.

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I have an oil spill that spills out at a rate of 100 ft per second. I need to find the rate of change of the radius at 800ft. The problem I thought would have been set up like this... A=∏rsquared 100ft per second= 2∏r, but this isn't correct, it is actually... 100ft per second - 2∏r...

Homework Statement Suppose that during the first year after its hatching, the weight of a duck increases at a rate proportional to its weight. The duck weighed 2 pounds when hatched, and 3.5 lbs at age 4 months. How many lbs will it weight at 6 months? A) 4.2 lbs B) 4.6 lbs C) 4.8 lbs D)...

This is an extra credit question in my class. We didn't get any picture or diagram, so my assumptions might be as good as yours. 1. Problem Consider a room where the walls can close in on each other. The room has a height of 9 feet, width of 12 feet and a length of 20 feet. For simple terms...

Here is the question: Here is a link to the question: Calculus Homework Question - related rates help? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Here is the question: Here is a link to the question: This is a calculus I question in the section about related rates.? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 1.0 ft/s, how fast is the angle between the ladder and the ground changing when the bottom of the ladder is 8 ft from the wall? [b]So, I'm having a difficult time figuring...

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Here is the question: Here is a link to the question: A security camera is centered 50 ft above a 100 foot hallway... Related Rates Question! HELP? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Here is the question: Here is a link to the question: Please help with differential equations problem solving.? - Yahoo! Answers I have posted a link there to this topic so the OP may find my response.

Here is the question: Here is a link to the question: Calculus related rates question, Help please!? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

I've tried these problems but I just can't wrap my head around them. Thanks to anyone that can help me out here. I have a couple more problems similar to these to solve, but if I can get to understand these then I'll have no problem with the others. Here are some diagrams I drew...

Homework Statement If theta increases at a constant rate of 3 radians per minute, at what rate is x increasing in units per measure at the instant when x equals 3 units? The Attempt at a Solution I drew the triangle and I came to the conclusion that I needed to use 5sin(theta)=x...

Homework Statement A liquid is being filtrated by a filter with a cone form. The filtring tax is 2cm^3/min. The cone has 16cm height, 4 cm radius. The volume V is given by pi*r^2*y/2 where y is the height, r the radius. Discover a formula that relates the tax of variation of the liquid...