The length equals √123=11.09 inches
Therefore the statement "The length of the photo frame is between the 11 inches and 12 inches." is true.
Check if the equation is exact, which happens for ODEs of the form

if
.
We have


so the ODE is not quite exact, but we can find an integrating factor
so that

<em>is</em> exact, which would require


Notice that

is independent of <em>x</em>, and dividing this by
gives an expression independent of <em>y</em>. If we assume
is a function of <em>x</em> alone, then
, and the partial differential equation above gives

which is separable and we can solve for
easily.




So, multiply the original ODE by <em>x</em> on both sides:

Now


so the modified ODE is exact.
Now we look for a solution of the form
, with differential

The solution <em>F</em> satisfies


Integrating both sides of the first equation with respect to <em>x</em> gives

Differentiating both sides with respect to <em>y</em> gives


So the solution to the ODE is


Inequality, because want to know when we'll make a profit.

Profit: Let's See When 280d equals 52000

So, after 190 days Julianne will make a profit
1 lb is equal to 16 oz, therefore 16 * 7 is 112oz then add 1/2 lb which is 8oz so the final answer is 120 oz