The chemist needs 381.6 milliliters for their experiment.
Answer:
c = 2.99m+ 6.85
Step-by-step explanation:
one time fee of 6.85
2.99 per movie rental
in other words you must pay 6.85
and 2.99 times the number of movies you watch
m = movies watched
c = cost
therefore
c = 2.99m+ 6.85
watching 13 movies at movie mania would mean that m (movies watched) would be 13
put that into the equation:
c = 6.85+ 2.99(13)
c = 6.85+ 38.87
c = 45.72
x*y' + y = 8x
y' + y/x = 8 .... divide everything by x
dy/dx + y/x = 8
dy/dx + (1/x)*y = 8
We have something in the form
y' + P(x)*y = Q(x)
which is a first order ODE
The integrating factor is
Multiply both sides by the integrating factor (x) and we get the following:
dy/dx + (1/x)*y = 8
x*dy/dx + x*(1/x)*y = x*8
x*dy/dx + y = 8x
y + x*dy/dx = 8x
Note the left hand side is the result of using the product rule on xy. We technically didn't need the integrating factor since we already had the original equation in this format, but I wanted to use it anyway (since other ODE problems may not be as simple).
Since (xy)' turns into y + x*dy/dx, and vice versa, this means
y + x*dy/dx = 8x turns into (xy)' = 8x
Integrating both sides with respect to x leads to
xy = 4x^2 + C
y = (4x^2 + C)/x
y = (4x^2)/x + C/x
y = 4x + Cx^(-1)
where C is a constant. In this case, C = -5 leads to a solution
y = 4x - 5x^(-1)
you can check this answer by deriving both sides with respect to x
dy/dx = 4 + 5x^(-2)
Then plugging this along with y = 4x - 5x^(-1) into the ODE given, and you should find it satisfies that equation.
The independent variable is the number of canvases and the dependent variable is the portraits
because she can’t make portraits if she doesn’t I have canvases so the number of portraits is decided on how many canvases she has
12–I think make sure thats right tho