Question

Given x varies inversely with y and xy=2, what is the value of x when y=1?

Answer 1

Answer:

x = 2

Step-by-step explanation:

Given that x varies inversely as y then the equation relating them is

x = $\frac{k}{y}$ ← k is the constant of variation

To find k use the condition xy = 2, thus

k = xy = 2

x = $\frac{2}{y}$ ← equation of variation

When y = 1, then

x = $\frac{2}{1}$ = 2

Answer 2

In an Inversely proportional relationship increasing one variable will decrease the other variable. The value of x when the value of y is 1 is 2.

What is the directly proportional and inversely proportional relationship?

Let there are two variables p and q

Then, p and q are said to be directly proportional to each other if

p = kq

where k is some constant number called the constant of proportionality.

This directly proportional relationship between p and q is written as

p∝q where that middle sign is the sign of proportionality.

In a directly proportional relationship, increasing one variable will increase another.

Now let m and n be two variables.

Then m and n are said to be inversely proportional to each other if

$m = \dfrac{c}{n} \\\\ \text{or} \\\\ n = \dfrac{c}{m}$

(both are equal)

where c is a constant number called the constant of proportionality.

This inversely proportional relationship is denoted by

$m \propto \dfrac{1}{n} \\\\ \text{or} \\\\n \propto \dfrac{1}{m}$

As visible, increasing one variable will decrease the other variable if both are inversely proportional.

Given that x varies inversely with y. Therefore, we can write the function as,

x ∝ 1/y

x = k/y

where k is the constant of proportionality.

Now, given that the value of xy is 2. Therefore, we can write,

x = k/y

xy = k

2 = k

Therefore, the function is x=k/y.

Further, the value of x when y=1 is,

x = k/y

x = 2 / 1

x = 2

Learn more about Directly and Inversely proportional relationships:

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