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3 years ago

What happens to the volume of a rectangular prism when the length and width are double and the height is tripled

Mathematics

1 answer:

Andrei [34K]3 years ago

3 0

The volume goes up by a factor of 2 * 2 * 3 = 12 times.

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Show that (2xy3 + cos x)dx + (3x2 y2 − sin y)dy = 0 is exact, and find the solution. Find c if y(0) = π

Licemer1 [7]

We're looking for a solution of the form $F(x,y)=C$ . By the chain rule, this solution should have total differential

$\mathrm dF=\dfrac{\partial F}{\partial x}\,\mathrm dx+\dfrac{\partial F}{\partial y}\,\mathrm dy=0$

and the equation is exact if the mixed second-order partial derivatives of $F$ are equal, i.e. $\frac{\partial^2F}{\partial x\partial y}=\dfrac{\partial^2F}{\partial y\partial x}$ .

The given ODE is exact, since

$\dfrac{\partial(2xy^3+\cos x)}{\partial y}=6xy^2$

$\dfrac{\partial(3x^2y^2-\sin y)}{\partial x}=6xy^2$

Then

$\dfrac{\partial F}{\partial x}=2xy^3+\cos x\implies F(x,y)=x^2y^3+\sin x+f(y)$

$\dfrac{\partial F}{\partial y}=3x^2y^2-\sin y=3x^2y^2+\dfrac{\mathrm df}{\mathrm dy}$

$\dfrac{\mathrm df}{\mathrm dy}=-\sin y\implies f(y)=\cos y+C$

$\implies x^2y^3+\sin x+\cos y=C$

With $y(0)=\pi$ , we get

$\cos\pi=C\implies C=-1$

$\implies\boxed{x^2y^3+\sin x+\cos y=-1}$

6 0

3 years ago

Please answer this question <br> Show your work also

DedPeter [7]

Answer:

t = -14

Step-by-step explanation:×

I did 4+3 which equals 7.

Now I know I need t/-2 to equal 7.

Next, I did 7×2 which equals 14.

When you divide 2 negative numbers you get a positive number.

So -14 ÷ -2 = 7

So t = -14

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3 years ago

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How would the graph change if the b value in the equation is decreased but remains greater than 1? Check all that apply.

Harrizon [31]

Answer:

The graph will begin on a lower point on the y-axis.

The y-values will continue to increase as x increases.

Step-by-step explanation:

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4 years ago

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What is 1/10th of 0.08?

erastovalidia [21]

It is 0.008. Thanks (:

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4 years ago

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2. If a= 2, b= 3 and c= 3,evaluate: i) a+ 2b ii) a+b+c

scoundrel [369]

Answer:

$i)a + 2b = 2 + 2(3) = 2 + 6 = 8 \\ ii)a + b + c = 2 + 3 + 3 = 2 + 6 = 8$

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2 years ago

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