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Solve for [tex]\( r \)[/tex].

[tex]\[ \frac{f}{r^2} + a = n + k \][/tex]

A. [tex]\( \pm \sqrt{\frac{f}{n+k-a}} \)[/tex]

B. [tex]\( \pm \sqrt{\frac{f}{nk-a}} \)[/tex]

C. [tex]\( \pm \sqrt{\frac{nk-a}{f}} \)[/tex]

D. [tex]\( \pm \sqrt{\frac{n+k-a}{f}} \)[/tex]



Answer :

GinnyAnswer
Let's solve for [tex]\( r \)[/tex] in the given equation:

[tex]\[ \frac{f}{r^2} + a = n + k \][/tex]

To isolate [tex]\( r \)[/tex], let's follow these steps:

1. Subtract [tex]\( a \)[/tex] from both sides:

[tex]\[ \frac{f}{r^2} = n + k - a \][/tex]

2. Isolate [tex]\( r^2 \)[/tex] by multiplying both sides by [tex]\( r^2 \)[/tex]:

[tex]\[ f = (n + k - a)r^2 \][/tex]

3. Divide both sides by [tex]\( (n + k - a) \)[/tex]:

[tex]\[ r^2 = \frac{f}{n + k - a} \][/tex]

4. Take the square root of both sides to solve for [tex]\( r \)[/tex]:

[tex]\[ r = \pm \sqrt{\frac{f}{n + k - a}} \][/tex]

The solutions for [tex]\( r \)[/tex] are:

[tex]\[ r = \pm \sqrt{\frac{f}{n + k - a}} \][/tex]

Given the provided choices, the correct answer is:

[tex]\[ \boxed{\pm \sqrt{\frac{f}{n+k-a}}} \][/tex]

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