To determine the altitude in feet when the atmospheric temperature ([tex]\( t \)[/tex]) is [tex]\(-27.5^\circ\)[/tex]F and the ground temperature ([tex]\( g \)[/tex]) is [tex]\(60^\circ\)[/tex]F, we follow these steps using the formula [tex]\( t = -0.0035a + g \)[/tex]:
1. Write down the given formula:
[tex]\[
t = -0.0035a + g
\][/tex]
2. Substitute the known values into the formula:
[tex]\[
-27.5 = -0.0035a + 60
\][/tex]
3. Isolate the term involving [tex]\( a \)[/tex] by subtracting [tex]\( 60 \)[/tex] from both sides:
[tex]\[
-27.5 - 60 = -0.0035a
\][/tex]
4. Simplify the left side:
[tex]\[
-87.5 = -0.0035a
\][/tex]
5. Divide both sides by [tex]\(-0.0035\)[/tex] to solve for [tex]\( a \)[/tex]:
[tex]\[
a = \frac{-87.5}{-0.0035}
\][/tex]
6. Carry out the division:
[tex]\[
a = 25000
\][/tex]
Therefore, the altitude when the atmospheric temperature is [tex]\(-27.5^\circ\)[/tex]F and the ground temperature is [tex]\(60^\circ\)[/tex]F is [tex]\(25,000\)[/tex] feet.
