Sure, let's solve the given problem step-by-step.
Given:
[tex]\[ R^2 = X^2 + Y^2 \][/tex]
We need to rewrite the formula for [tex]\( Y \)[/tex].
Step 1: Start with the given formula:
[tex]\[ R^2 = X^2 + Y^2 \][/tex]
Step 2: Isolate [tex]\( Y^2 \)[/tex] on one side of the equation. To do this, we need to subtract [tex]\( X^2 \)[/tex] from both sides of the equation:
[tex]\[ R^2 - X^2 = Y^2 \][/tex]
Step 3: To solve for [tex]\( Y \)[/tex], take the square root of both sides of the equation. Remember, when we take the square root, we consider the principal (non-negative) root:
[tex]\[ Y = \sqrt{R^2 - X^2} \][/tex]
So the correct answer is:
[tex]\[ \text{c. } Y = \sqrt{R^2 - X^2} \][/tex]
Thus, the formula for [tex]\( Y \)[/tex] in terms of [tex]\( R \)[/tex] and [tex]\( X \)[/tex] is:
[tex]\[ Y = \sqrt{R^2 - X^2} \][/tex]
Therefore, the correct option is:
c. [tex]\( Y = \sqrt{R^2 - X^2} \)[/tex]
