1 Answer

Soccertrash · Answer 1 · 2022-01-10T19:49:26+0000

Answer:

y = 2.096 or
$y = (2\sqrt5+6)/(5)}$

Explanation:

Given

$y = (4)/(x) + \sqrt x + 0.2 - 5x$

x = (4)/(5)

Required

Find y

$y = (4)/(x) + \sqrt x + 0.2 - 5x$

Substitute
x = (4)/(5)

y = (4)/(4/5) + √(4/5) + 0.2 - 5 * 4/5

y = 5 + √(4/5) + 0.2 - 4

Collect like terms

y = √(4/5) + 5 + 0.2 - 4

$y = \sqrt{(4)/(5)} + 1.2$

Split the surd

$y = (\sqrt4)/(\sqrt5)} + 1.2$

$y = (2)/(\sqrt5)} + 1.2$

Rationalize

$y = (2\sqrt5)/(\sqrt5*\sqrt5)} + 1.2$

$y = (2\sqrt5)/(5)} + 1.2$

Take LCM and add

$y = (2\sqrt5+1.2*5)/(5)}$

$y = (2\sqrt5+6)/(5)}$

or solve as:

y = (2*2.24+6)/(5)}

y = (10.48)/(5)

y = 2.096

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