Let's examine the given equation and the values provided:
Given:
[tex]\[ 1.78 x^5 - 20 x^7 + 169 x^3 \][/tex]
We have specific terms to evaluate:
[tex]\[ a = 1.78 x^5 \][/tex]
[tex]\[ b = -20 x^7 \][/tex]
[tex]\[ c = 169 x^3 \][/tex]
### Working through each term:
1. Term involving [tex]\( x^5 \)[/tex]:
[tex]\[ a = 1.78 x^5 \][/tex]
From the given data, the coefficient of [tex]\( x^5 \)[/tex] is 1.78.
2. Term involving [tex]\( x^7 \)[/tex]:
[tex]\[ b = -20 x^7 \][/tex]
The coefficient of [tex]\( x^7 \)[/tex] is -20, indicating this term is subtracted in the equation.
3. Term involving [tex]\( x^3 \)[/tex]:
[tex]\[ c = 169 x^3 \][/tex]
The coefficient of [tex]\( x^3 \)[/tex] is 169.
### Summary:
- The coefficient of [tex]\( x^5 \)[/tex] is 1.78.
- The coefficient of [tex]\( x^7 \)[/tex] is -20.
- The coefficient of [tex]\( x^3 \)[/tex] is 169.
Thus, the detailed coefficients of each term in the polynomial are:
[tex]\[
\begin{array}{c}
a = 1.78, \\
b = -20, \\
c = 169
\end{array}
\][/tex]
