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Explications étape par étape:
To make k the subject of the first formula \( w = km \), divide both sides by \( m \):
\[ \frac{w}{m} = k \]
So, the subject of the formula becomes \( k = \frac{w}{m} \).
To make e the subject of the second formula \( b = a \sqrt{1 - e^2} \), first isolate the square root term:
\[ \frac{b}{a} = \sqrt{1 - e^2} \]
Then, square both sides to eliminate the square root:
\[ \left(\frac{b}{a}\right)^2 = 1 - e^2 \]
Now, isolate \( e^2 \):
\[ e^2 = 1 - \left(\frac{b}{a}\right)^2 \]
Finally, take the square root of both sides to solve for \( e \):
\[ e = \sqrt{1 - \left(\frac{b}{a}\right)^2} \]
So, the subject of the second formula becomes \( e = \sqrt{1 - \left(\frac{b}{a}\right)^2} \).