Question 815469
From "A varies directly to x" we get:
{{{A = k[1]*x}}}
(I'm using subscripts on the constants of variation because there are more than one and I want to name them as k's.)
From "x varies directly to t" we get:
{{{x = k[2]*t}}}<br>
We are looking for how A varies to t. So we do not want x in the equation. The second equation is already solved for x. Using this we can substitute into the first equation for x:
{{{A = k[1]*(k[2]*t)}}}
or
{{{A = k[1]*k[2]*t}}}
Since {{{k[1]}}} and {{{k[2]}}} are constants, so it their product. So if we let {{{k[3] = k[1]*k[2]}}} our equation becomes:
{{{A = k[3]*t}}}
which is an equation of direct variation. So A varies directly with t.