Question

Inverse of t = (120r)/(r+120)

Answer 1

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Answer:

r = 120t/(120 -t)

Explanation:

Given t = f(r), solve for r.

`t(r+120)=120r \qquad\text{multiply by $r+120$}\\\\rt+120t=120r \qquad\text{eliminate parentheses}\\\\rt-120r=-120t \qquad\text{subtract $120t+120r$}\\\\r(t-120)=-120t \qquad\text{factor}\\\\r=(-120t)/(t-120) \qquad\text{divide by $t-120$}\\\\\boxed{r=(120t)/(120-t)} \qquad\text{negate numerator and denominator}`