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Suppose x, y, and s are differentiable functions of t that are related by the equation s^2 = 3x +...

Question:

Suppose {eq}x, y, {/eq} and {eq}s {/eq} are differentiable functions of {eq}t {/eq} that are related by the equation {eq}s^2 = 3x + y^2 {/eq}. If {eq}\frac{\mathrm{d}x}{\mathrm{d}t} = 2 {/eq} and {eq}\frac{\mathrm{d}y}{\mathrm{d}t} = 4 {/eq}, then find {eq}\frac{\mathrm{d}s}{\mathrm{d}t} {/eq} when {eq}x = 8 {/eq} and {eq}y = 5 {/eq}.

Related Rates:

The related rates problem is any problem in which we are given one or more rates and asks us to find another. In other words, we can say the problem that asks us to relate some rates are related rate problems. We relate rates by differentiating an equation that contains the variables involved.

Answer and Explanation: 1

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Given:

  • {eq}s^2 = 3x + y^2 {/eq}.
  • {eq}\dfrac{\mathrm{d}x}{\mathrm{d}t} = 2 {/eq}
  • {eq}\dfrac{\mathrm{d}y}{\mathrm{d}t} = 4 {/eq}

We have to find...

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Related Rates: The Draining Tank Problem

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Chapter 15 / Lesson 4
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The draining tank problem considers how quickly water would drain from a receptacle. This lesson explores the formulas which mathematicians would use to solve this problem, including the use of related rates.


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