Can someone answer this correctly for my sister please​

It looks like the given differential equation is

(3x² + y²) y + (y² - x²) x dy/dx = 0

Multiply both sides by 1/x³ to get

(3 + y²/x²) y/x + (y²/x² - 1) dy/dx = 0

(Note that in order to do this, we must have x ≠ 0, which means that if a solution exists, it would have to be on either (-∞, 0) or (0, ∞).)

Now substitute z = y/x, or y = xz, from which we get dy/dx = x dz/dx + z. Making this replacement and simplifying yields a separable equation:

(3 + z²) z + (z² - 1) (x dz/dx + z) = 0

(3 + z²) z + (z² - 1) x dz/dx + (z² - 1) z = 0

(z² - 1) x dz/dx = -(2z³ + 2z)

x dz/dx = (2z³ + 2z)/(1 - z²)

(1 - z²)/(2z (z² + 1)) dz = dx/x

Integrate both sides. On the left, split up the expression into partial fractions.

[tex]\dfrac{1-z^2}{z(z^2+1)} = \dfrac az + \dfrac{bz+c}{z^2+1}[/tex]

[tex]\dfrac{1-z^2}{z(z^2+1)} = \dfrac{a(z^2+1)+(bz+c)z}{z(z^2+1)}[/tex]

[tex]1-z^2 = (a+b)z^2 + cz + a[/tex]

for which we find a = 1, b = -2, and c = 0:

[tex]\dfrac{1-z^2}{2z(z^2+1)} = \dfrac12 \left( \dfrac1z - \dfrac{2z}{z^2+1} \right)[/tex]

Integrating and simplifying yields

1/2 ∫ (1/z - 2z/(z² + 1)) dz = ∫ dx/x

1/2 (ln|z| - ln(z² + 1)) = ln|x| + C

1/2 ln|z / (z² + 1)| = ln|x| + C

ln(√(z/(z² + 1))) = ln|x| + C

exp[ln(√(z/(z² + 1)))] = exp[ln|x| + C]

√(z/(z² + 1)) = exp[ln|x|] exp[C]

√(z/(z² + 1)) = Cx

z/(z² + 1) = Cx²

Replacing z = y/x then gives us an implicit solution of

(y/x) / (y²/x² + 1) = Cx²

xy / (y² + x²) = Cx²

y / (y² + x²) = Cx

y = Cx (y² + x²)

Cxy² - y + Cx³ = 0

though we can solve for y explicitly (assuming x > 0) using the quadratic formula to end up with

y = (1 + √(1 - Cx⁴))/(Cx)

(the other solution only differs by the sign on the square root)

Answer:

120

Step-by-step explanation:

trough dependent sarcasm

[tex]xy =-21~~.....(i)\\\\x+ y=20~~....(ii)\\\\\text{From equation (i):}\\\\xy = -21 \implies y = -\dfrac{21}x~~.....(iii)\\\\\text{Substitute y in equation (ii):}\\\\x - \dfrac{21}x = 20\\\\\implies x^2 -20x -21= 0\\\\\implies x^2 - 21x + x-21=0\\\\\implies x(x-21) +(x-21) =0\\\\\implies (x+1)(x-21)=0\\\\\implies x = -1 ~~\text{or}~~ x =21\\\\\text{Substitute x in equation (iii):}\\\\y = 21 ~~ \text{or}~~ y = -1\\\\\text{Hence,}~ (x,y)=(21,-1) ~~ \text{or}~~ (x,y) = (-1,21)[/tex]

6(2/9)

4(2/3)

18/54

8/12

=18/54

=8/12

u divided all

Let the number should be duvided be X

Given number = 6 2/9

⇛ (6×9+2)/9

⇛ (54+2)/9

⇛ 56/9

On dividing 56/9 by X then the result

= (56/9)/X

= 56/9X

According to the given problem

The result = 4 2/3 = 14/3

⇛ 56/9X = 14/3

⇛ 9X×14 = 56×3

⇛ 9X = 56×3/14

⇛ 9X = 4×3

⇛9X = 12

⇛X = 12/9

=⇛X = 4/3 or 1 1/3

Answer↓

The required number is 4/3 or 1 1/3

Check↓

On dividing 6 2/9 by 1 1/3

⇛ 6 2/9 ÷ 1 1/3

⇛ (56/9)÷(4/3)

⇛ (56/9)×(3/4)

⇛ (56×3)/(9×4)

⇛ 14/3

⇛4 2/3

Verified.

Answer: Slope formula: m = y2 - y1/ x2 - x1

2 - (-2)/ 1 - 0

2 + 2/1

4/1

Slope = 4

Would appreciate brainly <3

Answer:

Expression: -7 + 8f - 2b - f + 3b + 6

# of Terms: 6

Like Terms: 8f and f, -2b and 3b, and -7 and 6

Coefficients: 8, 1, -2, and 3

Constants: -7 and 6

Expression: -11x + 4 + 8x - 4 + 3x

# of Terms: 5

Like Terms: -11x, 8x, and 3x & 4 and -4

Coefficients: -11, 8, and 3

Constants: 4 and -4

Step-by-step explanation:

The coefficient is the number in front of the variable.

The variable is any letter that you may see in an expression.

Terms are the numbers and variables, that are separated by the different signs.

Like terms are the terms that share the same variable/exponent.

Constants are the terms without variables.

Hope this helps you :)

Sorry if it's somehow wrong.

[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$500\\ r=rate\to 1.25\%\to \frac{1.25}{100}\dotfill &0.0125\\ t=years\dotfill &3 \end{cases} \\\\\\ I = (500)(0.0125)(3)\implies \boxed{I = 18.75}[/tex]

Answer:

1 1/2

Step-by-step explanation:

because when you divide 7.5 by 5 you get 1.5

Answer:

both is 48

Step-by-step explanation:

Answer:

4 better inbox

Step-by-step explanation:

Answer:

-320 i guess

Step-by-step explanation:

51*-2*3-21+7=-320

Answer:

7.9000000÷96

=0.0822916667

Answer:

Its a

Step-by-step explanation:

9514 1404 393

Answer:

  102

Step-by-step explanation:

87 more than 15 is ...

  15 +87 = 102

Louie had 102 iPads before Cassandra tool some.

Answer:

Step-by-step explanation:

y = mx + b for line through (7, 4) and perpendicular to -5x + 9y = - 71

perpendicular lines have negative reciprocal slopes

-5x + 9y = - 71

9y = 5x - 71

y = (5/9)x - 71/9

so a perpendicular line will have slope -9/5

y = (-9/5)x + b

plug in our desired point

4 = (-9/5)7 + b

4 = -63/5 + b

20/5 = -63/5 + b

b = 83/5

y = (-9/5)x + 83/5

5y = -9x + 83

Step-by-step explanation:

1/33

1/3 is 0.33333....

1/30 is 0.03333...

1/300 is 0.003333...

and so on.

that was in the initial thought.

in oder to interrupt the 1/3=0.3333... series and interlace the 3s with 0s, I had to divide by 10, but also by further 10% (in total 11) of that to create a 0.0303 sequence.

I initially thought that I would have to add then 10% of that and then 10% if that, but no, the one step is sufficient.

so, it turned out to be 1/3 / 11 = 1/33.

Answer:

12 meters sq

Step-by-step explanation:

area= length x width

area= 3x4

area=12 meters sq

Answer:

1. 7

2. 8

3. 17 cars

4. 6 guppies

5. 54

6. 15 pencils

Step-by-step explanation:

Have a great day! Feel free to mark as brainliest! :)

Answer:

8y⁴+25y³+60y²+10y+7

Step-by-step explanation:

8y⁴+y³+y²+24y³+3y²+3y+56y²+7y+7

8y⁴+25y³+60y²+10y+7

Answer:

8y^4+25y^3+60y^2+10y+7

Step-by-step explanation:

(y^2+3y+7)(8y^2+y+1)

We are going to multiply the first term, y^2, by the whole second part (8y^2+y+1)

8y^4+y^3+y^2

now we multiply the 2nd term, 3y, by the whole second part (8y^2+y+1))

24y^3+3y^2+3y

now we do the same to the last term, 7.

56y^2+7y+7

now we need to add all three of our products together

(8y^4+y^3+y^2)+(24y^3+3y^2+3y)+(56y^2+7y+7)

adding like terms:

8y^4+y^3+24y^3+y^2+3y^2+56y^2+3y+7y+7

we get:

8y^4+25y^3+60y^2+10y+7

Answer:

-2x - 2

Step-by-step explanation:

-2(x + 1)

Therefore, the answer is -2x - 2.

Answer:

-2x - 2

Step-by-step explanation:

Simplify:

-Chetan K

Answer:

B.52 is the answer i think for the total number of kids

Answer:

No

Step-by-step explanation:

yes it is

for it to not be a function it would need to have a curve or somthing that make it go somehwere else

Answer:

15.625

Step-by-step explanation:

old number = 288

new number = 243

percent decrease = (old - new / new ) * 100

= (288 - 243 / 288) * 100

= 45 / 288  * 100

= 15.625

Answer:

15.6 (rounded)

Step-by-step explanation:

I took the test

Answer:

3/4x - 5 = x

= -3/10 -> -0.15

2 Decimal places = 0.150

Answer:

helooo

Step-by-p explanation:

Answer:

A. 26

Step-by-step explanation:

substitute the number in for the variables (letters).

[tex]m + 5n \\ \\ 1 + 5(5) \\ 1 + 25 \\ 26[/tex]