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3 years ago

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Gina mixed paint to make her favorite shade of purple. She filled up one third of the container with red paint. Then she filled

the remaining space with 4 Liters of blue paint.How many milliliters of paint did Gina mix

2 answers:

erma4kov [3.2K]3 years ago

7 0

6000 ml, that's lit how much. it's 1 third + 4 liters. So that equals out to 6. as two thirds of 6 is 4... you easily could have solved this on your own tbbhhhhh

ad-work [718]3 years ago

7 0

If the red is one third full, and it takes 4 more liters of blue, than there are 6 liters total to make the paint purple. Because if 4 liters is 2/3 then that makes the amount of red 2 liters.

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Problem 4: Solve the initial value problem

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$\implies \dfrac1{(y+1)(y-2)} = \dfrac{a(y-2)+b(y+1)}{(y+1)(y-2)}$

$\implies 1 = a(y-2)+b(y+1)$

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$\dfrac{y-2}{y+1} = e^{3x + C}$

$\dfrac{y-2}{y+1} = Ce^{3x}$

With the initial condition y(0) = 1, we find

$\dfrac{1-2}{1+1} = Ce^{0} \implies C = -\dfrac12$

so that the particular solution is

$\boxed{\dfrac{y-2}{y+1} = -\dfrac12 e^{3x}}$

It's not too hard to solve explicitly for y; notice that

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Then

$1 - \dfrac3{y+1} = -\dfrac12 e^{3x}$

$\dfrac3{y+1} = 1 + \dfrac12 e^{3x}$

$\dfrac{y+1}3 = \dfrac1{1+\frac12 e^{3x}} = \dfrac2{2+e^{3x}}$

$y+1 = \dfrac6{2+e^{3x}}$

$y = \dfrac6{2+e^{3x}} - 1$

$\boxed{y = \dfrac{4-e^{3x}}{2+e^{3x}}}$

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