If y varies inversely as x and y = 5 when x = 10, how do you find y when x = 2?

Question

If y varies inversely as x and y = 5 when x = 10, how do you find y when x = 2?

2 Answers

Impact of this question

38981 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-08-07T13:00:27

$y = 25$ $y=25$

Explanation:

$y = \frac{k}{x}$ $y=k/x$ ;where $x$ $x$ and $y$ $y$ are variables and $k$ $k$ is constant
or
$5 = \frac{k}{10}$ $5=k/10$
or
$k = 5 (10)$ $k=5(10)$
or
$k = 50$ $k=50$
So Equation becomes $y = \frac{50}{x}$ $y=50/x$
When $x = 2$ $x=2$
$y = \frac{50}{2}$ $y=50/2$
or
$y = 25$ $y=25$

Answer 2 · 2016-08-07T13:07:15

The equation is $y = \frac{50}{x}$ $y=50/x$

At $x = 2; y = 25$ $x=2;" "y=25$

Explanation:

There is a relationship between $y and x$ $y" and "x$

Mathematically this is written as $y . α . \frac{1}{x}$ $y color(white)(.)alpha color(white)(.) 1/x$

The $α$ $alpha$ is stating that a relationship exists but as yet it is not totally defined

,~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Let $k$ $k$ be the constants of variation

Write $y . α . \frac{1}{x}$ $y color(white)(.)alpha color(white)(.) 1/x$ as: $y = k \times \frac{1}{x} \to y = \frac{k}{x}$ $" "y=kxx 1/x" " ->" " y=k/x$

You find the value $k$ $k$ by substituting the values for the known condition $(x, y) \to (10, 5)$ $(x,y)->(10,5)$

Thus we have:

$y = k \times \frac{1}{x} \to 5 = \frac{k}{10}$ $y=kxx 1/x" " ->" "5=k/10$

Multiply both sides by 10

$10xx5=cancel(10)xxk/(cancel(10))$

$=>k=50$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
So the equation is:

$y=50/x$

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Thus at $x=2$ we have:

$y=50/2=25$

Science

Math

Humanities

... and beyond

If y varies inversely as x and y = 5 when x = 10, how do you find y when x = 2?

2 Answers

Explanation:

Explanation:

Related questions

Impact of this question