Answer
a. $K= \frac{5(F-32)}{9}+273.15$
b. $k\approx 355.37$
Work Step by Step
a.
The given formula is
$\Rightarrow F=\frac{9}{5}(K-273.15)+32$
Subtract $32$ from each side.
$\Rightarrow F-32=\frac{9}{5}(K-273.15)+32-32$
Simplify.
$\Rightarrow F-32=\frac{9}{5}(K-273.15)$
Multiply each side by $\frac{5}{9}$.
$\Rightarrow \frac{5(F-32)}{9}=\frac{5}{9}\cdot \frac{9}{5}(K-273.15)$
Simplify.
$\Rightarrow \frac{5(F-32)}{9}=K-273.15$
Add $273.15$ to each side.
$\Rightarrow \frac{5(F-32)}{9}+273.15=K-273.15+273.15$
Simplify.
$\Rightarrow \frac{5(F-32)}{9}+273.15=K$
b.
Substitute $180$ for $F$ in the above equation.
$\Rightarrow \frac{5(180-32)}{9}+273.15=K$
Subtract.
$\Rightarrow \frac{5(148)}{9}+273.15=K$
Simplify.
$\Rightarrow 82.22+273.15\approx K$
$\Rightarrow 355.37\approx K$
