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Aleksandr-060686 [28]

3 years ago

14

Factor the polynomial completely using the X method. x2 + 13x – 48 What is the four-term polynomial and factored form of the po

lynomial?

2 answers:

Orlov [11]3 years ago

7 0

Answer:

Answer is C on EDG: x^2 + 16x - 3x - 48 = (x+16)(x-3)

Step-by-step explanation:

cestrela7 [59]3 years ago

3 0

The factored form comes from breaking each term up x2 = x times x
-48 has numerous possibilities for two factors but the to factors that multiply and get -48 while adding to get +13 are +16 and -3 so the answer in factored form is (x + 16) (x -3)

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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

-144 is -1 x 2a x 3b what is the sum of a+b?

BigorU [14]

-144= -1×2a×3b
144=2a×3b
144= 6ab
24= ab

a,b could b any two factors that have a product of 24
For example a,b could = 6,4 or 8,3 or 24,1

Answer:
This question is tricky because it could have multiple answers: for example is a,b= 6,4 then a+b= 10, but if a,b=24+1=25. So, the answer is that the sum of a+b varies depending on which 2 factors of 24 a and b are equal to. Does this make sense?

7 0

3 years ago

Pls help!!!!!!!!!!!1

Sloan [31]

Answer:lol it's -3

Step-by-step explanation: it's 3 because you had dirt 45.50 in your account and then you have to get books and those books will cost $3 more which means that you don't have that money since it indicates that in the problem which means that it would be -3 because you don't have the money so that's why I think it's negative 3.

6 0

3 years ago

Click on the picture to look at some equivalent fractions. Look at them closely. Can you see a relationship of any kind between

Vera_Pavlovna [14]

when you simplify 2/4 it equals 1/2. Making them both equal the same.

2/3 when you double the numbers to make a bigger fraction you make 4/6.

2x2 = 4/ 3x3= /6 = 4/6

3/9 simplified is 1/3. Three goes into three one time, making the top one and three goes into 9 three times making the bottom 3.

When 9/12 is rounded down it is equivalent to 3/4

5 0

3 years ago

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What is the area of parallelogram ABCD?<br>

Andrej [43]

Answer:

15

Step-by-step explanation:

6 0

3 years ago

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