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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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Can I use the slope of $\sqrt{N}$ to factor semiprimes? I get an equivalence if I try. How can I use related rates?

I need to make two definitions before I get to my question, which is at the bottom. Domain: is the X-axis (variable) Range: is the Y-axis $$f(Domain) = Range$$ I think semiprimes can be factored by ...
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Why do we need implicit diff for related rates problems?

Hello I am having to create a portfolio for my calc class. I am interested into the reason for implicit differentiation when trying to solve a related rates problem. I am sort of trying to find a ...
Ethan Barr's user avatar
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1 answer
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Help with a related rates and optimization problem

Hello this is a problem I am trying to work on that I'm stuck on. I got the general outline setup trying to use the pythagoras theorem but I'm aware that I want to find the x,y values to minimize the ...
Ethan Barr's user avatar
-1 votes
1 answer
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unsure about my mistake with this related rates problem.

I've seen solutions to this type of question on the site here, and have successfully solved some variants. But for some reason my solution to this particular problem doesn't jibe with what Mr. Sal ...
Chris Bedford's user avatar
5 votes
2 answers
78 views

Is this related rates solution correct, or a crazy coincidence?

One of my students arrived at a correct solution to a straightforward related rates problem, but I can't understand their method... Problem: an airplane flies at a constant altitude of 10km and speed ...
Michael Megliola's user avatar
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1 answer
25 views

What formula could calculate the speed of music playback in a variable length of time?

I am trying to create a patch in Max that records sound over a portion of a given length of time, then plays back the recording to fill out the remaining portion of time with the speed of playback ...
Joe Beribak's user avatar
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1 answer
38 views

How do I go from an infinite amount of instantaneous rates to an average rate?

I have a function that gives me rate at a point (the derivative) and I have a value for average rate that was experimentally calculated. How would I go about creating an expression to solve for a ...
DaBest Gamer's user avatar
2 votes
1 answer
53 views

Application of Differential Equations Logistics problem

Problem: The rate of change of the total number of sales, $dS(t)\over dt$, of a new product is proportional to $ S(t)\over t^2$, where $t$ is in years. If the saturation of the market is $50000$ units,...
TANK1_41's user avatar
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1 answer
44 views

Rate of change of ordinates and abscissae

The question that I am stuck at goes like this: On the curve $y^3=27x$, the absolute value of rate of change of ordinate is greater than the absolute value of rate of change of abscissa in the ...
Harikrishnan M's user avatar
-1 votes
2 answers
93 views

Related Rate Problem Involving Conical tank Formula. I do not understand why this is incorrect. [closed]

A right conical tank with the point oriented down, a height of 15 feet, and a radius of 4 feet has sprung a leak. How fast is the volume of water in the tank changing when the water is 2 feet high and ...
CompilingConfusion's user avatar
-1 votes
1 answer
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A relevant relentless reluctancy relating related rates?

I am reviewing some things in calculus, I have these two sample problems with their answers, that I tried to solve another way and got different results. I'd like to understand why what I made yielded ...
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Why does the derivative of Law of Cosines require radians?

The question I am solving says "2 sides of a triangle have lengths 9 ft and 18 ft. The angle between them is increasing at a rate of 2 degrees per minute. How fast is the length of the 3rd side ...
Data_Shark's user avatar
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74 views

Related Rates Problem - Water is being pumped into an inverted conical tank at an unknown constant rate.

Water is leaking out of an inverted conical tank at a rate of 0.015 m³/min. At the same time water is being pumped into the tank at a constant rate. The tank has height 13 meters and the diameter at ...
Val's user avatar
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3 votes
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Related rates ---not use chain rules?

Here is the question:Two people start from the same point at the same time. One walks north at 2 mi/h and the other walks west at 4 mi/h. How fast is the distance between them changing after 30 ...
elainehxw's user avatar
6 votes
3 answers
971 views

To find rate of change of area of triangle when rate of change and value of length of base and height are 3cm/min, 5cm/min and 8cm,10cm respectively.

I am trying understand very simple related rates problem (area of triangle on youtube): The base of a right triangle is increasing at 3cm/min while the height of the triangle is increasing at a rate ...
Michal's user avatar
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1 answer
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Two rates of change

Two mice (say $A$ and $B$) eat a piece of food. The rate of consumption for $A$ is proportional to amount of food left(Proportionality constant = $2$) and rate of consumption for $B$ is proportional ...
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Finding the rate of sliding of an inclined ladder.

The foot of a ladder 50 ft. long rests on horizontal ground, and the top of the ladder rests against the side of a pyramid which makes an angle of 120° with the ground. If the foot of the ladder is ...
Barry's user avatar
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Related rates problem with cube and its space diagonal - what did I do wrong?

Problem: The volume of a cone is increasing at a rate of 6 cubic units per second. When the volume of the cube is 81 cubic units, at what rate is the longest diagonal of the cube is increasing? Here's ...
ada's user avatar
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3 votes
1 answer
209 views

Related Rates: Shadow of Ball Problem

A light is at the top of a pole $50$ft high. A ball is dropped from the same height from a point $30$ft away from the light. How fast is the shadow of the ball moving along the ground $1\over 2$ ...
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Length between to moving points

Point A moves along the x-axis at the constant rate of a ft/s while point B moves along the y-axis at the constant rate of b ft/s. Find how fast the distance between them is changing when A is at the ...
Camelot823's user avatar
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1 vote
1 answer
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Finding an expression for the rate of change of a spherical container [closed]

Hi all I was wondering how I would find an expression for the rate of change of a spherical container which is being filled up with a liquid. I am aware that I must use Derivatives as the liquid is ...
JulianAlvarez's user avatar
-1 votes
1 answer
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Two masons laying bricks

I'm having trouble solving a puzzle in Swedish. I've translated it to English: Two masons work on a project. One mason can complete the project alone in 8 hours, while the other can complete it alone ...
cricket900's user avatar
0 votes
1 answer
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Instant rate of growth of a spherical balloon

I am having trouble with a problem involving a spherical balloon, and I was hoping someone could help me out. The problem is as follows: "Air is blown into a spherical balloon so that its volume ...
cricket900's user avatar
-1 votes
1 answer
44 views

Related Rate Does Not Stay Constant

If a right triangle with hypotenuse of length $26$ has a leg of length $10$; and this leg (of length 10) is constantly incremented at a speed of $4$ units per second (let "seconds" be ...
Camelot823's user avatar
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Related Rates Result Not Precise

If I have a ladder of length $24$ feet leaned against a wall, with the foot of the ladder being $10$ feet away from the wall; and a man pulls the foot of the ladder away from the wall at $4$ feet per ...
Camelot823's user avatar
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4 votes
1 answer
392 views

What did I do wrong in this simple related rates problem?

The question is A street light is mounted at the top of a 15-ft-tall pole. A man 6 ft tall walks away from the pole with a speed of 5 ftys along a straight path. How fast is the tip of his shadow ...
iwjueph94rgytbhr's user avatar
0 votes
1 answer
54 views

Related Rate of conical tank without height given

So I am in a calculus 2 class and am stuck on a question as I don't think I have enough information. Can someone please help me with my next step so I can solve this. A conical tank is filled at a ...
Morgan Rose's user avatar
2 votes
2 answers
231 views

Multiple Solutions? Suppose ${x^2}+{y^2} = 45$ and $x=2y$ ... find $\frac{dy}{dt}$

Suppose ${x^2}+{y^2} = 45$ and $x=2y$ for positive values of $x$ and $y$ find $\frac{dy}{dt}$ when $\frac{dx}{dt}=2$ I am new to implicit differntiation and related rates. When I attempted to solve ...
Theodore Veteto's user avatar
1 vote
1 answer
89 views

Related rates problem - how a beam from a laser moves across the wall

The problem: Let $\theta$ be the angle between the laser and the horizontal line which is at a 90 degree angle at the wall(see drawing). The laser point moves at a pace of 1cm/sec vertically on the ...
Lars's user avatar
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1 answer
171 views

How long to quadruple

How long does it take to quadruple your money at 4.5% interest rate? I've already used the Rule of 144, divided 144 by 4.5 and got 32 and it was marked incorrect.
Sid's user avatar
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0 answers
27 views

A minimum/maximum problem using the point of inflection

If I had an equation $F(t)$ = $t$ $e^{\frac{-t}{10}}$ that modelled the concentration of a chemical with respect to time (where $t$ represented time in minutes). If I wanted to find the time when the ...
George Orwell's user avatar
-2 votes
1 answer
39 views

What rate is the radius changing for a sphere? [closed]

I just thought of this question and wondered if there was a nice way to solve it. Question: The volume of a sphere is $100$ cubic metres and is losing $2\mathrm m^3/\mathrm s$. At what rate is the ...
htq's user avatar
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1 vote
1 answer
600 views

What is the underlying mathematics behind law of mass action?

When calculating reaction rates of of a chemical reaction, what is the reason taking product of concentration of chemicals (i. e. V+ = k[A][B]) instead addition (e.g. k[A] + k[B])? Does this related ...
Dendrobium's user avatar
1 vote
1 answer
48 views

Given a list of angular rates and timestamps, how do you correctly obtain the angles?

There are 5 dynamic angular rates ω_k (°/s) for 5 different time epochs t_k. For each time epoch, the respective angle ...
Mino's user avatar
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0 votes
2 answers
162 views

Maximum of a utility function

I was practising some related rates problems and I came across this particularly difficult question. The question goes like this: Suppose Peyam's utility function is given by: $U(\theta)=\frac{\mu C}{\...
Joshua Ayitevie's user avatar
1 vote
0 answers
49 views

Why would one have to assume that the rate of evaporation has to be proportional to the surface area?

The problem states the following: A container in the shape of a right circular cone with vertex angle a right angle is partially filled with water. A. Suppose water is added at a rate of 3 cu.cm/sec. ...
Sam C.'s user avatar
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0 votes
2 answers
183 views

Basic Question: Differentiating Related Functions (Calculus)In [closed]

In case anyone else is searching for an answer in the future: The question contained an assumption. There is no rule dictating different processing of the 2 variables based on the variable whose ...
Hal's user avatar
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0 answers
76 views

Determine the formula that represents the volume of water in a bowl

The inner surface of a bowl is the shape formed by rotating completely about the y-axis the area bound by the curve y=${x^2}$—2, the x-axis, the y-axis and the line y=3. (i) find the volume of the ...
Theo's user avatar
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0 votes
0 answers
19 views

Connected rates of change with Area and feta (Further math question)

Question about the rate of change in delta A Hi can anyone explain to me how to do section b of this question? This question is about arcs length, area of sectors and connected rates of change.
Tintin's user avatar
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-1 votes
1 answer
61 views

Finding rate of pouring water in inverted conical cone with water loss [closed]

Question: Water is dripping from a filter in the shape of an inverted right circular cone at a rate of $\rm5\ cm^3/s$. The altitude of the filter is $\rm10\, cm$ and its base radius is $\rm 5\ cm$.At ...
user1039203's user avatar
2 votes
1 answer
279 views

Related Rates - Volume of a spherical balloon

A weather balloon rises through the air at a rate of $500 \ \text{m}/\text{min}$. Every $1000 \ \text{m}$, the decrease of air pressure outside the balloon causes its radius to increase by $8 \ \text{...
VL12345's user avatar
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0 answers
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GRE related rates problem [duplicate]

$\textbf{Problem}:$ A square pyramid of side length $100$cm and height of $100$cm is melting at a consistent rate such that all of the ice less than $y$ cm from the surface melts after $y$ hours. (...
homosapien's user avatar
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3 votes
2 answers
221 views

Using related rates, why can we ignore dimensions and consider rates of change, when in seemingly identical situations, we must consider both?

So I was preparing a lesson on related rates for the calc 1 class I am a TA for and I realized that the two problems below in the photo are basically identical: Given a right triangle, x, x', y, y' ...
Ethan Shade's user avatar
2 votes
1 answer
129 views

Average rate of water dripping from a cylindrical bucket

Water drips out of the bottom of a cylindrical bucket that is initially full. The rate of dripping is proportional to the height of water column in the bucket. If the rate of dripping at half height ...
S.S's user avatar
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0 votes
1 answer
79 views

Area of Triangle decreasing as one of its acute angles decreases in measure

A right triangle has a hypotenuse length of $26''$. If one of the acute angles is decreasing at the rate of $10^\circ$ per second, how fast is the area of the triangle decreasing when this acute angle ...
Jon Loredo's user avatar
1 vote
1 answer
214 views

Related Rates question filling up conical paper cup. [closed]

So this is just from some college exam and I was trying to do it and got stuck on this question because I've never really encountered related rates before. I read up a bit about related rates but ...
tommyk's user avatar
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0 answers
235 views

Related Rates with negative rates of change

If a car is moving towards an object and you get the rate of change to be -30 mph, I know that you don't say that the speed of the car is negative, it just means that the distance between the car and ...
Solar-powered Ants's user avatar
0 votes
1 answer
92 views

Calculating the velocity of a car towards another car

I have a Car1 traveling (not directly) towards another Car2, both cars can freely drive away from each other (making the velocity from Car1 to Car2 negative) What I know of the cars is the velocity, ...
JareBear's user avatar
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0 votes
1 answer
479 views

Rate of change of the area of a triangle

The sides of a triangle measuring 40 m, 32 m, and 16 m increase at the rates of 2 m/s, 5 m/s and 3 m/s, respectively. How fast is the area of the triangle changing? a. 138.42 m^2/s b. 113.69 m/s c. ...
frequency24's user avatar
1 vote
1 answer
50 views

Distance between an ice cream truck and a smoothie truck with related rates

$A$ and $B$ walk back and forth along the path between their houses at uniform rates, with $B$ walking faster. One evening, they leave home at the same time and pass each other 55 meters from $A$'s ...
user978757's user avatar