Question

Make M the subject of the formula

Q

`q = (d)/(2\pi) √(f - hm) / m`
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Answer 1

The rearranged formula for m in terms of Q, d, F, h, and r is
`\( m = (4Q^2)/(d^2(4F-4hr)) \)`.

To make M the subject of the formula Q, you need to rearrange the equation to isolate M on one side. You can do this by following these steps:

Divide both sides by d/2 to get rid of the fraction on the right side. This gives you Q/(d/2) = sqrt(F-hr)*m

Square both sides to get rid of the square root on the right side. This gives you (Q/(d/2))^2 = (F-hr)*m

Divide both sides by (F-hr) to isolate m on the right side. This gives you (Q/(d/2))^2/(F-hr) = m

Simplify the expression on the left side by using the exponent rule (a/b)^2 = a2/b2. This gives you Q2/(d2/4)/(F-hr) = m

Simplify the expression further by multiplying the numerator and denominator by 4. This gives you 4Q2/d2/(4F-4hr) = m

Finally, swap the sides to make m the subject of the formula. This gives you m = 4Q2/d2/(4F-4hr)

Therefore, the rearranged equation is m = 4Q2/d2/(4F-4hr).