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4 years ago

^ question :)))))))))))

Mathematics

1 answer:

djyliett [7]4 years ago

6 0

Answer:

the second one

Step-by-step explanation:

420 minus 20 for every week "W" until the balance is at 240 dollars

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Consider the differential equation: (y^2+2*x)dx+(2*x*y-1)dy = 0. (a) show that the equation is exact by evaluating (\partial m)/

ruslelena [56]

The given ODE

$\underbrace{(y^2+2x)}_M\,\mathrm dx+\underbrace{(2xy-1)}_N\,\mathrm dy=0$

is exact if $\frac{\partial M}{\partial y}=\frac{\partial N}{\partial x}$ . It so happens that we have $\frac{\partial M}{\partial y}=2y=\frac{\partial N}{\partial x}$ , so it is indeed exact. For such an ODE, we're looking for a solution of the form $\Psi(x,y)=C$ , for which the differential is

$\mathrm d\Psi=\dfrac{\partial\Psi}{\partial x}\,\mathrm dx+\dfrac{\partial\Psi}{\partial y}\,\mathrm dy=0$

so we have the following system of PDEs that allow us to solve for $\Psi$ :

$\dfrac{\partial\Psi}{\partial x}=M=y^2+2x$

$\dfrac{\partial\Psi}{\partial y}=N=2xy-1$

In the first PDE, we can integrate both sides with respect to $x$ and recover $\Psi$ :

$\displaystyle\int\frac{\partial\Psi}{\partial x}\,\mathrm dx=\int(y^2+2x)\,\mathrm dx$

$\implies\Psi(x,y)=xy^2+x^2+f(y)$

Then differentiating this with respect to $y$ returns $N$ :

$\dfrac{\partial\Psi}{\partial y}=2xy+\dfrac{\mathrm df}{\mathrm dy}=2xy-1$

$\implies\dfrac{\mathrm df}{\mathrm dy}=-1$

$\implies f(y)=-y+C$

So the general solution to the ODE is

$\Psi(x,y)=xy^2+x^2-y+C=C$

or simply

$xy^2+x^2-y=C$

4 0

3 years ago

What is the approximate length of arc s on the circle below? Use 3.14 for pi . Round

evablogger [386]

Answer:

6.3

Step-by-step explanation:

Arc length is circumference

C = 2 * pi *r

We are finding a fraction of the total arc length

A circle is 360 degrees

45 degrees / 360 degrees = 1/8

Find the total arc length and multiply by the fraction of the circle

arc length = 2 * pi * r * 1/8

= 2 * 3.14 * 8 * 1/8

=6.28

Rounding to the nearest tenth

6.3

4 0

3 years ago

Read 2 more answers

Does anyone know the answer to this ?

nataly862011 [7]

Answer:

ABC and MNP are not congruent. ABC and EFG are not congruent. ABC and STU are congruent. EFG and MNP are congruent. EFG and STU are not congruent. STU and MNP are not congruent.

Step-by-step explanation:

4 0

3 years ago

What is the volume of the figure? Enter the answer in the box.

Annette [7]

Answer:

Add all the numbers together in each box the take those two numbers and multply them.

Step-by-step explanation:

10+9+9= 28

18+4+10= 32

32x28= 896

I hope that helps.

8 0

4 years ago

Read 2 more answers

PLEASE HELPPPP!!!!!!

Sloan [31]

Step-by-step explanation:

y=kx

say that y is the original prince and x is the sale price

15=k(10)

15/10=k

3/2=k

you can check with the next problem to check if it is the same

25=k(20)

25/20=k

5/4=k

so you take 5/4-3/2=-1/4 so the constant is -1/4

Hope that helps :)

8 0

3 years ago