Sure, let's go through the solution of the given equation step by step:
You need to solve the equation:
[tex]\[ \frac{3}{4} w + \frac{1}{6} w^2 = \frac{4}{5} z^3 \][/tex]
1. Identify the terms:
- On the left side of the equation, you have the terms [tex]\(\frac{3}{4} w\)[/tex] and [tex]\(\frac{1}{6} w^2\)[/tex].
- On the right side of the equation, you have the term [tex]\(\frac{4}{5} z^3\)[/tex].
2. Convert the fractions to decimals for simplicity:
- [tex]\(\frac{3}{4}\)[/tex] equals approximately 0.75.
- [tex]\(\frac{1}{6}\)[/tex] equals approximately 0.1667.
- [tex]\(\frac{4}{5}\)[/tex] equals 0.8.
3. Rewrite the equation using these decimals:
[tex]\[ 0.75w + 0.1667w^2 = 0.8z^3 \][/tex]
Now, the equation in simplified numerical form is:
[tex]\[ 0.1667w^2 + 0.75w = 0.8z^3 \][/tex]
This equation states that the sum of [tex]\(0.1667w^2\)[/tex] and [tex]\(0.75w\)[/tex] is equal to [tex]\(0.8z^3\)[/tex].
This completes the detailed step-by-step conversion and verification of the given equation. The resultant equation is:
[tex]\[ 0.1667w^2 + 0.75w = 0.8z^3 \][/tex]
Thus, we have verified that:
[tex]\[ \frac{3}{4} w + \frac{1}{6} w^2 = \frac{4}{5} z^3 \][/tex]
can be rewritten as:
[tex]\[ 0.1667w^2 + 0.75w = 0.8z^3 \][/tex]
