Questions tagged [related-rates]

In differential calculus, related rates problems involve finding a rate at which a quantity changes by relating that quantity to other quantities whose rates of change are known.

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Solving mathematical economics problem

kindly I'm stuck in this problem instead of many attempts through net present value and other discounted cash flow methods, some one could give me a detailed information and answers on this problem : (...
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Could someone please provide a solution to part A of a rates of change question [closed]

Rates of change question from a mathematics textbook about a dissolving pill. Having a hard time understanding the working and thought process of part (a) of the question. Any insight would be ...
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implicit differentiation related rates, rate of an angle

A particle moves along the graph of $y=x^2$ over the plane xy at a constant velocity of 10cm/s. Let θ denote the angle between the x-axis and the line that goes from the origin to $P(x,x^2)$. find ...
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What is the technique of solving the following? Area of circle is increasing 3 times as fast as its radius in centimeters. What is the radius? [closed]

I have a general idea that it is solved by using derivatives, but I am having a hard time converting text into equations? Problem: Area of expanding circle is increasing 3 times as fast as its radius ...
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Growth rate of subscribers

This must be a trick question. I have cracked my brains trying different methods, but still can't figure out.
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How fast is the angle of elevation changing?

Here is the situation We need to find $\dfrac{ d \alpha }{d t }$ In vectorial notation, we write the speed of the drone as $$ V = (20 \cos 30, 20 \sin 30) = (10 \sqrt{3}, 10) $$ Let's say $t$ ...
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Related rates calculus: how is $\frac{x}{y} \frac{dx}{dt} = \frac{dy}{dt}$?

Hello, in this problem the person wrote dy/dt the same as x/y times dx/dt. I don't get how this works. Wouldn't you get (xdx)/(ydt)? Also in this question I posted: Related Rates Calculus - Confused ...
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Related Rates Calculus - Confused About What dx/dt, dy/dt and dx/dy mean

Hello, I am confused as to how they got 5y in this problem when they multiplied dx/dy by dy/dt in the fourth line. I am also confused as to what dx/dt and dx/dy and dy/dt mean.
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Find the ratio between the radius and the height

A coffee filter has the shape of an inverted cone. Water drains out of the filter at a rate of 10 cm$^3$/min. When the depth of water in the cone is 8 cm, the depth is decreasing at 2 cm/min. What is ...
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increments and differentiation to determine related rates

In an isosceles triangle with sides 20 inches long and a vertex angle of $60^\circ$, the angle is closing in at $2^\circ/min$. At what rate should the sides be changing to keep the area of the ...
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Solving problem using related rates yields incorrect result

I've been trying for a while to figure out what I did wrong on this problem, help would be appreciated. "A 25-ft ladder is leaning against a wall. If we push the ladder toward the wall at a rate of 1 ...
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How to convert a rate involving radians to something that can be applied to a straight direction in a related rates problem.

I can do related rates problems a little bit, but I've been given one that requires me to use a rate of $\frac{-\pi}{6}$ radians per second to figure out how fast a plane is going. Since I assume that ...
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Please check my work finding related rates

I have completed a word problem involving related rates, and gone over it myself. However, this is the first relative rates problem I've ever done, and I would appreciate it if people would check my ...
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Related rates, my answer differs from the book, misprint or me?

Did my answer go wrong or does the book have a misprint?(there have been some inconstancies between the definitions used in the chapters and answer key, like two different authors, though only one is ...
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Does Implicit Differentiation Depend on the Form of the Equation?

I stumbled across a related rates problem which involved using implicit differentiation: A rock is initially dropped at height h a horizontal distance d from a street lamp that's H tall. The lamp ...
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Related Rates change in theta

I have come at this a few different ways and I just can't seem to figure out how to get the correct answer for this. The question is: A fisherman is reeling in a fish at a rate of 20 centimeters per ...
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Related Rates: rate of change of the distance between two objects [closed]

A boat starts off $172$ miles directly west from the city. It travels due south at a speed of $30$ miles per hour. After travelling $126$ miles, how fast is the distance between the boat and city ...
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t what rate is his distance from second base decreasing when he is halfway to first base?

A baseball diamond is a square with side $90ft$. A batter hits the ball and runs toward first base with a speed of $24ft/s$. a)At what rate is his distance from second base decreasing when he is ...
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How fast is the length of his shadow on the building decreasing when he is 4 m from the building

A spotlight on the ground shines on a wal 12 m away. If a man 2m tall walks from the spotlight toward the building at a speed of 1.6m/s, how fast is the length of his shadow on the building decreasing ...
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How fast is the height of the water in a cylindrical tank increasing?

A cylindrical tank with radius $5m$ is being filled with water at a rate of $3m^{3}/\min$. How fast is the height of the water increasing. The radius $r=5m$ The rate of water is $\dfrac{dV}{dt}=3m^{...
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How fast is the area of the rectangle increasing?

The length of a rectangle is increasing at a rate of 8 cm/s and its width is increasing at a rate of 3 cm/s . When the length is 20 cm and the width is 10 cm, how fast is the area of the rectangle ...
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Related Rates of Change Ship

A ship is 5 km east and 7 km North of a lighthouse. It is moving North at a rate of 12 $kmh^{−1}$ and East at a rate of 16 $kmh^{−1}$. At what rate is its distance from the lighthouse changing? ...