2 years ago

What is the volume of a box that will hold exactly 567 of these cubes with 1/3 inch sides?

1 answer:

8 0

Let’s find the volume of the small cubes.
1/3^3
1/27
Now multiply this by 567
567•(1/27)
21
The volume of the box is 21 inches cubed.

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fredd [130]

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$\dfrac{\partial\left(4x^2y^3+\frac{2y}{x+y^2}\right)}{\partial x}=8xy^3-\dfrac{2y}{(x+y^2)^2}$

so the ODE is indeed exact and there is a solution of the form $F(x,y)=C$ . We have

$\dfrac{\partial F}{\partial x}=2xy^4+\dfrac1{x+y^2}\implies F(x,y)=x^2y^4+\ln(x+y^2)+f(y)$

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With $y(1)=2$ , we have

$8+\ln9=C$

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2 years ago