Question

What is vaule of y when x=4'5

Answer 1

Answer:

$y = 2.096$ or $y = \frac{2\sqrt5+6}{5}}$

Step-by-step explanation:

Given

$y = \frac{4}{x} + \sqrt x + 0.2 - 5x$

$x = \frac{4}{5}$

Required

Find y

$y = \frac{4}{x} + \sqrt x + 0.2 - 5x$

Substitute $x = \frac{4}{5}$

$y = \frac{4}{4/5} + \sqrt{4/5} + 0.2 - 5 * 4/5$

$y = 5 + \sqrt{4/5} + 0.2 - 4$

Collect like terms

$y = \sqrt{4/5} + 5 + 0.2 - 4$

$y = \sqrt{\frac{4}{5}} + 1.2$

Split the surd

$y = \frac{\sqrt4}{\sqrt5}} + 1.2$

$y = \frac{2}{\sqrt5}} + 1.2$

Rationalize

$y = \frac{2\sqrt5}{\sqrt5*\sqrt5}} + 1.2$

$y = \frac{2\sqrt5}{5}} + 1.2$

Take LCM and add

$y = \frac{2\sqrt5+1.2*5}{5}}$

$y = \frac{2\sqrt5+6}{5}}$

or solve as:

$y = \frac{2*2.24+6}{5}}$

$y = \frac{10.48}{5}$

$y = 2.096$