Answer :
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]
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]
