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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.

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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181 questions
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The rate of change in the area of a circle sector

a circular clock of radius 5 inches .At time t minutes past noon, how fast is the area of the sector of the circle between the hour and minute hand increasing? I used implicit differentiation on the equation $A=\frac{(r²\theta)}{2}$ with r as a…
Saif DOGHRI
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Related rates of boat being pulled

I have the following related rates I am helping a student on, however, another tutor got $.9923$ and I get $1.007$. Here is my attempt and someone please just point out the silly mistake I might be making: Let $a$ be the height above the water of…
homosapien
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Variant of Sliding Ladder Related Rates Problem

We all know the related rates problem of a ladder sliding off a wall. In this we are told how fast the bottom or top is sliding and then asked to find how fast the other end of the ladder is moving at. My question is fairly similar. A ladder of…
WwW
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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 house. After $B$ turns at $A$'s house, he catches…
user978757
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Q:Related rates problem

Question: A person can swim from A to B (with current) in 40 minutes, and back (against current) in 45 minutes. How long does it take them to kayak from A to B if the return trip (B to A, against current) takes 15 minutes. Assume the speed of the…
user978757
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Related rates problem, swimming pool

I am having issues getting the correct answer for this question. I'll provide my attempted solution, as well as the book's answer. Question A swimming pool is 25 ft wide, 40 ft long, 3 ft deep at one end and 9 ft deep at the other, the bottom being…
Peatherfed
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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 listed) The problem: An airplane is flying 500…
Max Power
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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
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Related Rates Bikers

I was given the question: Bikes A and B are traveling on perpendicular roads. At the same time bike A is leaving the intersection at a rate of 2 feet per second and bike B is leaving the intersection at 3 feet per second. How fast in the distance,…
Joe Jackson
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Rates of Change Question help

I just wanted to check to see if I answered this question correctly :) any help would be much appreciated Q. Air is pumped into a spherical balloon such that the volume of the balloon is increasing at a rate of 3cm^2cm/sec. (i)Find the rate of…
user912758
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Can I get a hint for this rates of change question?

A ball of radius $24cm$ has its volume decreasing at a rate of three times its surface area per second. What is the time taken for the volume to be reduced to one-eighth of the initial size? Initial volume is $18432π$ and one with of this is…
user71207
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Related Rates question that I keep getting wrong?

I thought the acceleration would be cosx at x= pi/6, but that’s the wrong answer! Can someone help me here? It’s question three.
Flinn Bella
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Related Rates - Speed of his Shadow

I took an entire semester of calculus, and now, after suggestion by my professor, I'm applying for a calculus tutoring position. However, I've never been asked how to find a related rate using angles, and yet that's one of the questions for the…
Zack Jandali
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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.
Chong Siang Toh
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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 in 10 hours. When they work together, they can…
cricket900
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