To express the air temperature ([tex]\( t \)[/tex]) in terms of Gnarly's speed ([tex]\( a \)[/tex]), we start with the given equation:
[tex]\[ a = 12 - 0.035t \][/tex]
Our goal is to solve this equation for [tex]\( t \)[/tex]. Let's break it down step by step:
1. Rewrite the equation to isolate the term involving [tex]\( t \)[/tex]:
[tex]\[ 12 - 0.035t = a \][/tex]
2. Subtract 12 from both sides to move the constant term to the right side:
[tex]\[ -0.035t = a - 12 \][/tex]
3. Now, multiply both sides of the equation by [tex]\(-1\)[/tex] to remove the negative sign:
[tex]\[ 0.035t = 12 - a \][/tex]
4. Finally, divide both sides by 0.035 to solve for [tex]\( t \)[/tex]:
[tex]\[ t = \frac{12 - a}{0.035} \][/tex]
So, the air temperature [tex]\( t \)[/tex], in terms of Gnarly's speed [tex]\( a \)[/tex], is given by:
[tex]\[ t = \frac{12 - a}{0.035} \][/tex]
This is the expression that relates the air temperature to Gnarly's speed.
