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3 years ago

What are the answers to these i put them in the picture

Mathematics

1 answer:

tekilochka [14]3 years ago

8 0

The problem to number 1 is a inequality, so
x-2<-7
x<-5
since it is < it will have open dot.
Answer: C

2. x/3>-3
x>-9

Answer: D

3. 5p+26<72
5p<46
p<9.2

Answer: C

4. -3w+3>=18
-3w>=15
x<=-5

5. 15x-21>= 12x+18
x>=13
Answer A

6: |3x|=15
Absolute values positive so {-5,5}
Answer: B
7: |2x-3|=5
x=4,-1
Answer: C

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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

Use the interactive protractor to determine the measure of the angle. what is manglejhg? 70° 75° 110° 115°

DanielleElmas [232]

Using the interactive protractor, the measure of the angle JHG is 115°

<h3>How to determine the measure of the angle?</h3>

The image that completes the question is added as an attachment.

The question requests that we determine the measure of JHG using a protractor.

To do this, we set one end of the protractor at 0°.

Then, we take the measurement of the other end

Using the interactive protractor, the other end stops at 115°

Hence, the measure of the angle JHG is 115°

Read more about angles at:

brainly.com/question/24839702

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5 0

2 years ago

The difference of a number divided by 7 and 9 is equal to 2. use the variable C what the unknown

bogdanovich [222]

Given that the number is C.
The number divided by 7 is C/7
Difference means we will subtract 9 from C/7.
Therefore, the equation will be:
C/7 - 9 = 2 (multiply all terms by 7 to get rid of the fraction)
C - 63 = 14
C = 14 + 63 = 77

5 0

3 years ago

The graph below shows the numbers of cups of kiwi juice that are mixed with different numbers of cups of lemon-lime soda to make

Leya [2.2K]

Answer:

4:1

Step-by-step explanation:

4 cups of kiwi juice for every cup of lemon lime soda

6 0

3 years ago

Read 2 more answers

Estimate 5.9* 3.4 find the answer please help

zvonat [6]

Since it says ESTIMATE:
round 5.9 to 6 and 3.4 to 3
6* 3 = 18
The estimate would be LETTER C 18

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3 years ago