Question
1.6.1 Change the formula to make \( d \) the subject: \[ w=\frac{2 m}{d^{2} v} \]
Ask by Boone Deleon. in South Africa
Feb 21,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( d = \sqrt{\frac{2m}{wv}} \)
Solution
We start with the equation:
w = (2m) / (d²v).
Step 1: Multiply both sides by d²v to eliminate the fraction:
w · d²v = 2m.
Step 2: Solve for d² by dividing both sides by wv:
d² = (2m) / (wv).
Step 3: Take the square root of both sides to solve for d:
d = √[(2m) / (wv)].
Thus, the formula rearranged to make d the subject is:
d = √((2m) / (wv)).
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Simplify this solution Mind Expander
To make \( d \) the subject of the formula, we start by multiplying both sides by \( d^2 v \) to eliminate the fraction. This gives us: \[ w \cdot d^{2} v = 2m \] Next, we can divide both sides by \( w \cdot v \): \[ d^2 = \frac{2m}{w \cdot v} \] Finally, we take the square root of both sides to solve for \( d \): \[ d = \sqrt{\frac{2m}{w \cdot v}} \]
