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Stels [109]
2 years ago
13

To rewrite the expression ab+a+b+1, Jozelle first writes (ab+a) + (b+1). What property justifies this?

Mathematics
1 answer:
rodikova [14]2 years ago
7 0

Answer:

I believe it is associative property of addition or commutative

Step-by-step explanation:

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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 Fare 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
Sally opens a lemonade stand and sells 2x cups of lemonade for x number of days.Each cup of lemonade sells for y dollars.Sally w
lina2011 [118]

Answer:

2xy/2 = money for 1 charity

Step-by-step explanation:

2 lemonades for each day (x) = 2x

amount of money made = 2xy = no of lemonades sold x profit of 1 lemonade

two charities = 2xy/2 = total profit divided by no of charities

8 0
3 years ago
I give ten points and brainliest if you say hi
patriot [66]

Answer:

Hi hope you have a wonderful and blessed day!!!!

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
melissa purchased a car at the price of 20,540 with a down payment of 3,900 and financed the rest paying 8.6% interest compounde
DaniilM [7]

Answer:

$478.06

Step-by-step explanation:

let's first start out by figuring out the present value of the loan

((20540*1.0825)+955+57)-3900

Which gives me a value of 23246.55

I'm then going to assume that the 8.6% is a nominal interest rate meaning that the effectively monthly rate is equal to .086/12=.0072

Which means we have

23246.55=X(a angle 60 at .0072) (i'm using annuities to solve this if you don't know what this is just ask)

Solve this and get $478.06

6 0
3 years ago
Please help me asap, pleaseee :/<br><br><br> ty ty :D
weeeeeb [17]

7x+8y=32

Just do pemdas

6 0
2 years ago
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