Question

A quantity h varies directly with w and inversely with pIf h = 2, w = 4, and p = 6What is the constant of variation?

Answer 1

Answer:

Value of constant of variation is $k=3$

Step-by-step explanation:

Let 'k' be the constant of variation.

According to first condition, h varies directly with w. That is,

$h\propto w$

According to second condition, h varies inversely with p. That is,

$h\propto \dfrac{1}{p}$

Combining both conditions,

$h\propto \dfrac{w}{p}$

Now to remove proportionality sign use constant of variation k,

$h=k\dfrac{w}{p}$

Given that, h = 2, w = 4 and p = 6. Substituting the value,

$2=k\dfrac{4}{6}$

Multiplying both side of equation by $\dfrac{6}{4}$

$\dfrac{6}{4}\times 2=k$

Simplifying,

$\dfrac{12}{4}=k$

$3=k$

Therefore value of constant of variation is $k = 3$