How Do You Rearrange the Equation v = sqrt(2kt/m) to Solve for M?

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To rearrange the equation v = sqrt(2kt/m) to solve for m, begin by squaring both sides to eliminate the square root, resulting in v^2 = 2kt/m. Next, multiply both sides by m to isolate m, yielding m = 2kt/v^2. Clarification on the equation's format is crucial, as misinterpretation can lead to different approaches. Proper use of parentheses is recommended to avoid confusion. The correct manipulation of the equation allows for accurate solving for m.
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Just need some help rearranging this equation to make M the subject, thanks

v = sqrt 2kt / m
 
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Start by squaring both sides.
 
sqrt v = sqrt 2kt / m
 
m = 2kt / v^2
 
jim the duke said:
Just need some help rearranging this equation to make M the subject,
v = sqrt 2kt / m
rock.freak667 said:
Start by squaring both sides.

jim the duke said:
sqrt v = sqrt 2kt / m
I see two mistakes in what you did:
1. rock.freak667 said to square both sides (not take the square root of both sides).
2. He said to do it to both sides, not just the left side.
 
jim the duke said:
Just need some help rearranging this equation to make M the subject, thanks

v = sqrt 2kt / m
If the problem is v= sqrt(2kt/m) then, yes, start by squaring both sides to get rid of the square root.

If the problem is v= sqrt(2kt)/m, which is the way I first interpreted it, start by multiplying both sides by m.

Please use parentheses to make your meaning clear!
 
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Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
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