To find the value of [tex]\( y \)[/tex] when [tex]\( x = \frac{4}{5} \)[/tex], let’s break the expression [tex]\( y \)[/tex] into its constituent parts and calculate each step-by-step.
The given formula for [tex]\( y \)[/tex] is:
[tex]\[ y = \frac{4}{x} + \sqrt{x + 0.2} - 5x \][/tex]
1. Calculate [tex]\( \frac{4}{x} \)[/tex]:
[tex]\[ x = \frac{4}{5} \][/tex]
[tex]\[
\frac{4}{x} = \frac{4}{\frac{4}{5}} = 4 \cdot \frac{5}{4} = 5
\][/tex]
2. Calculate [tex]\( \sqrt{x + 0.2} \)[/tex]:
[tex]\[
x = \frac{4}{5} = 0.8
\][/tex]
[tex]\[
x + 0.2 = 0.8 + 0.2 = 1
\][/tex]
[tex]\[
\sqrt{x + 0.2} = \sqrt{1} = 1
\][/tex]
3. Calculate [tex]\( 5x \)[/tex]:
[tex]\[
x = \frac{4}{5} = 0.8
\][/tex]
[tex]\[
5x = 5 \cdot 0.8 = 4
\][/tex]
4. Combine all the terms to find [tex]\( y \)[/tex]:
[tex]\[
y = \frac{4}{x} + \sqrt{x + 0.2} - 5x
\][/tex]
[tex]\[
y = 5 + 1 - 4 = 2
\][/tex]
Therefore, the value of [tex]\( y \)[/tex] is:
[tex]\[
y = 2
\][/tex]
