Let's break down the problem step-by-step:
Step 1: Calculate [tex]\( a^2 - b^2 \)[/tex]
Given:
- [tex]\( a = 2 \)[/tex]
- [tex]\( b = -3 \)[/tex]
First, calculate [tex]\( a^2 \)[/tex] and [tex]\( b^2 \)[/tex]:
[tex]\[ a^2 = 2^2 = 4 \][/tex]
[tex]\[ b^2 = (-3)^2 = 9 \][/tex]
Now, find [tex]\( a^2 - b^2 \)[/tex]:
[tex]\[ a^2 - b^2 = 4 - 9 = -5 \][/tex]
Step 2: Consider the divisor [tex]\(\delta \)[/tex]
Assume [tex]\(\delta = 1\)[/tex]:
[tex]\[ \frac{a^2 - b^2}{\delta} = \frac{-5}{1} = -5 \][/tex]
Step 3: Incorporate the mixed number [tex]\(-3 \frac{4}{6}\)[/tex]
Convert the mixed number into an improper fraction and make calculations:
[tex]\[ -3 \frac{4}{6} = -3 + \frac{4}{6} \][/tex]
[tex]\[ -3 \frac{4}{6} = -3 + \frac{2}{3} \][/tex]
Convert [tex]\(\frac{4}{6}\)[/tex] into a decimal:
[tex]\[ \frac{4}{6} = 0.66667 \][/tex]
So:
[tex]\[ -3 + 0.66667 = -2.33333 \][/tex]
Step 4: Solve the division by [tex]\( \frac{9}{5} \)[/tex]
Given the expression:
[tex]\[ -2.33333 \div \frac{9}{5} \][/tex]
This is equivalent to:
[tex]\[ -2.33333 \times \frac{5}{9} \][/tex]
Let's multiply:
[tex]\[ -2.33333 \times \frac{5}{9} = -1.2963 \][/tex]
Therefore, the value of the entire expression is:
[tex]\[ \boxed{-1.2963} \][/tex]
