Given the relationship \( b = \frac{a_1}{h} \), we know that when \( h = 5 \), \( b = 8 \). Using this information, we can solve for \( a_1 \):
\[ 8 = \frac{a_1}{5} \]
Multiplying both sides by 5 gives:
\[ a_1 = 8 \times 5 = 40 \]
Now that we have \( a_1 = 40 \), we can find \( b \) when \( h = 4 \):
\[ b = \frac{a_1}{h} = \frac{40}{4} = 10 \]
Now, let's find \( b \) when \( h = \frac{1}{4} \):
\[ b = \frac{a_1}{h} = \frac{40}{\frac{1}{4}} \]
Dividing by a fraction is the same as multiplying by its reciprocal:
\[ b = 40 \times 4 = 160 \]
Thus, the answers are:
- When \( h = 4 \), \( b = 10 \)
- When \( h = \frac{1}{4} \), \( b = 160 \)