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3 years ago

A. 67 B. 135 C. 75 D. 150

Mathematics

1 answer:

dolphi86 [110]3 years ago

6 0

The awnser is B because 33% is 1/3 of 100% so if you do 45×3=135

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Determine the values of the constants r and s such that i(x, y) = x rys is an integrating factor for the given differential equa

garri49 [273]

$\underbrace{y(7xy^2+6)}_{M(x,y)}\,\mathrm dx+\underbrace{x(xy^2-1)}_{N(x,y)}\,\mathrm dy=0$

For the ODE to be exact, we require that $M_y=N_x$ , which we'll verify is not the case here.

$M_y=21xy^2+6$
$N_x=2xy^2-1$

So we distribute an integrating factor $i(x,y)$ across both sides of the ODE to get

$iM\,\mathrm dx+iN\,\mathrm dy=0$

Now for the ODE to be exact, we require $(iM)_y=(iN)_x$ , which in turn means

$i_yM+iM_y=i_xN+iN_x\implies i(M_y-N_x)=i_xN-i_yM$

Suppose $i(x,y)=x^ry^s$ . Then substituting everything into the PDE above, we have

$x^ry^s(19xy^2+7)=rx^{r-1}y^s(x^2y^2-x)-sx^ry^{s-1}(7xy^3+6y)$
$19x^{r+1}y^{s+2}+7x^ry^s=rx^{r+1}y^{s+2}-rx^ry^s-7sx^{r+1}y^{s+2}-6sx^ry^s$
$19x^{r+1}y^{s+2}+7x^ry^s=(r-7s)x^{r+1}y^{s+2}-(r+6s)x^ry^s$
$\implies\begin{cases}r-7s=19\\r+6s=-7\end{cases}\implies r=5,s=-2$

so that our integrating factor is $i(x,y)=x^5y^{-2}$ . Our ODE is now

$(7x^6y+6x^5y^{-1})\,\mathrm dx+(x^7-x^6y^{-2})\,\mathrm dy=0$

Renaming $M(x,y)$ and $N(x,y)$ to our current coefficients, we end up with partial derivatives

$M_y=7x^6-6x^5y^{-2}$
$N_x=7x^6-6x^5y^{-2}$

as desired, so our new ODE is indeed exact.

Next, we're looking for a solution of the form $\Psi(x,y)=C$ . By the chain rule, we have

$\Psi_x=7x^6y+6x^5y^{-1}\implies\Psi=x^7y+x^6y^{-1}+f(y)$

Differentiating with respect to $y$ yields

$\Psi_y=x^7-x^6y^{-2}=x^7-x^6y^{-2}+\dfrac{\mathrm df}{\mathrm dy}$
$\implies\dfrac{\mathrm df}{\mathrm dy}=0\implies f(y)=C$

Thus the solution to the ODE is

$\Psi(x,y)=x^7y+x^6y^{-1}=C$

4 0

3 years ago

The parent function is the simplest form but doesnt contain

In-s [12.5K]

The answer you are looking for is "A Constant Slope",.

-I hope this is the answer you are looking for please feel free to post your questions here on brainly at any time.

3 0

3 years ago

5(-2/3) this is it and I don’t know it

erma4kov [3.2K]

Answer:

4 1/3

Step-by-step explanation:

hope this helps!

4 0

3 years ago

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Help me please! Math homework. I’m in 7th grade, and I lost all my brain cells

maria [59]

Answer:

A) 32, 40, 48, 56, 64, 72, 80

B) y-axis goes 4, 8, 12

x-axis goes 4, 8, 12, 16, 20

3 0

3 years ago

1/3 cup of flour is used to make 5 dinner rolls.

Radda [10]

Divide.

1/3 / 5

Or multiply by the reciprocal of 5:

1/3 * 1/5 = 1/15

Therefore 1/15 cup of flour is used to make 1 dinner roll.

We can set up a proportion:

5/1/3 = x/5 2/3

Multiply 5 2/3 to both sides:

28 1/3 / 1/3 = x

85 = x

So 85 rolls can be made with 5 2/3 cups of flour.

3 0

3 years ago

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