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3 years ago

Pls I need help !!!!

Mathematics

1 answer:

harkovskaia [24]3 years ago

5 0

Answer:I have an answer a good answer

S H R E K I S L O V E

Step-by-step explanation:

Hail Shrek

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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

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

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

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3 years ago

Which is the BEST estimate for the surface area of the prism?

Advocard [28]

I think it may be 34ft^2

I hope that helps!

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3 years ago

A salesperson's weekly paycheck is 10% more than a second salesperson's paycheck. The two paychecks total $1525. Find the amount

Kaylis [27]

1525 ➗ 2 = 762.5
762.50 x 10% is 76.25
762.50 - 76.25 = 686.25
one paycheck is 762.50
the other is 686.25

I hope this helps.

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3 years ago

Pls answer this pls pls pls btw I go to cmm

Thepotemich [5.8K]

Answer:

Mile = length

Cup = Volume

Pound= Mass

Centimeter = length

Liter = volume

Gram = mass

pint = volume

yard=length

kilogram=mass

teaspoon=volume

millimeter=length

Step-by-step explanation:

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3 years ago

Measure the length of the top of your desk in centimeters.describe how you found the length

kobusy [5.1K]

Simply take a ruler with centimeters on it and measure your desk.Tell the teacher you counted how many centimeters.

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3 years ago