How Do You Rearrange dS/dt = (n-x-rS)(L-1) to Solve for t?

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  • Thread starter BSLAHi
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In summary, "Rearranging Algebraic Calculus" is a mathematical technique used to manipulate algebraic equations and expressions in order to solve for a specific variable or simplify an equation. It is important to know how to rearrange algebraic equations because it is a fundamental skill in mathematics and is essential for solving various problems in fields such as physics, engineering, and finance. The basic steps for rearranging an algebraic equation are simplifying, isolating the variable, performing inverse operations, and checking the solution. A common example of rearranging an algebraic equation is solving for x in 3x + 5 = 20. Some common mistakes to avoid when rearranging algebraic equations include forgetting to perform inverse operations, simplifying
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BSLAHi
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Hello,

I have been given a general equation that is dS/dt = (n-x-rS)(L-1)
and it needs to be rearranged in order to for the subject to be t.

I have spent a while trying to find a way to attempt this but with no luck
so I will leave this here.

Thanking You,
BSLAHi
 
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  • #2
Hello BSLAHi.

You can separate the variables and integrate.
$$\frac{\mathrm dS}{\mathrm dt}\ =\ (n-x-rS)(L-1)$$
$\displaystyle\implies\ \int\frac{\mathrm dS}{n-x-rS}\ =\ \int(L-1)\,\mathrm dt$.
 

FAQ: How Do You Rearrange dS/dt = (n-x-rS)(L-1) to Solve for t?

What is Rearranging Algebraic Calculus?

Rearranging Algebraic Calculus is a mathematical process that involves manipulating algebraic equations to isolate a specific variable or term. It is often used to solve equations and simplify expressions.

Why is Rearranging Algebraic Calculus important?

Rearranging Algebraic Calculus is important because it allows us to solve complex equations and make sense of mathematical relationships. It also helps us to understand and analyze real-world problems and make informed decisions.

How do you rearrange algebraic equations?

To rearrange an algebraic equation, you can use properties of equality to move terms from one side of the equation to the other. This can involve adding, subtracting, multiplying, or dividing both sides by the same value.

What are some tips for rearranging algebraic equations?

Some tips for rearranging algebraic equations include: starting with the variable you want to isolate, simplifying both sides of the equation before rearranging, and keeping track of your steps to avoid mistakes.

Can Rearranging Algebraic Calculus be used in other branches of mathematics?

Yes, the principles of Rearranging Algebraic Calculus can be applied in other branches of mathematics, such as geometry, trigonometry, and calculus. It is a fundamental skill that is used in many areas of mathematics and science.

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