Rewrite 2/11 and 1/7 so that they have a common denominator

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:

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:

1.5

Step-by-step explanation:

12 / 8 = 1.5

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: (x+2)^2 -11

Step-by-step explanation:

X^2 +4x -7

Half the middle term, add it to x and put them into a bracket and square it

(X+2) ^2 -7

Square the second term to get 4 and then take that away from 7. (We do this because if we had the extra 4, our answer when’s we multiplied out of the brackets wouldn’t be x^2 +4x -7.)

(X+2)^2 -7 -4

Now simplify the whole numbers outside the bracket

(X+2) ^2 -11

Answer:

7.9000000÷96

=0.0822916667

Answer:

Emily receives $1,750 less after the shift

Step-by-step explanation:

Answer:

9x² - 12x + 4

Step-by-step explanation:

(3x - 2)² = (3x - 2)(3x - 2)

Each term in the second factor is multiplied by each term in the first factor , that is

3x(3x - 2) - 2(3x - 2) ← distribute both parenthesis

= 9x² - 6x - 6x + 4 ← collect like terms

= 9x² - 12x + 4

Answer:

both is 48

Step-by-step explanation:

Answer:

− 1.875

Step-by-step explanation:

Do you want an explanation?

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.

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:

x-intercepts: (1,0), (−2,0) and (2,0)

y-intercept: (0,4)

The graph is rising and crosses 3 times the x-axis and 1 time the y-axis as shown above.

Answer:

the first one is true

Step-by-step explanation:

√36>5 = 6>5

7<√10 = 7<3.162

√9>√25 = 3>5

Therefore, the first one is correct

Answer:

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

Answer:

120

Step-by-step explanation:

trough dependent sarcasm

Answer:

Step-by-step explanation:

So at 55 miles per hour you go 12 miles in a little over 13 minutes.

.

Hope this helps you to understand the problem and how to use the formula to solve it.

Distance = Speed * Time

.

You might be able to understand this by thinking, "If I go at 60 miles per hour for 2 hours,

how far do I travel?" The answer is:

.

Distance = 60 miles per hour* 2 hours = 120 miles

.

In the problem you are told that the distance to be covered is 12 miles. The speed is 55 miles

per hour. Put these into the equation and you get:

.

12 miles = 55 miles per hour * Time

.

You can then solve for the Time by dividing both sides of this equation by 55 to get:

.

12/55 = Time

.

So it takes 12/55 hours to go 12 miles. The fraction 12/55 converts to a decimal by dividing

55 into 12 to get 0.218181818 of an hour. Since an hour has 60 minutes, you can convert

the answer to minutes by multiplying 60 by 0.218181818 to get about 13.09 minutes.

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.

The difference between the two is 4,5

Answer:

60

Step-by-step explanation:

Perimeter = 2l + 2w

57x2 = 114

234 - 114 = 120

120 / 2 = 60

Answer:

PLEASE MARK ME AS BRANLIEST!!!!!

Step-by-step explanation:

a1 = first term; an= an-1 + d a1 = the first term in the sequence an = the nth term in the sequence an-1 = the term before the nth term n = the term number d = the common difference.

{10, 15, 20, 25, 30, 35, } first term = 10, common difference = 5 recursive formula: a1= 10; an= an-1 + 5

f(n) = f(n-1) + 12

f(1) = 7

f(2) = (7-1) + 12 = 18

f(3) = (18-1) + 12 = 29

f(4) = (29-1) + 12 = 40

f(5) = (40-1) + 12 = 51

7, 18, 29, 40, 51

Answer:

Its a

Step-by-step 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]

Answer:

All closed.

Addition, subtraction as well as multiplication of polynomials result into another polynomial. Therefore, the set of polynomials is closed under addition, subtraction and multiplication.

Open polynomial set is (x² + x - 4) - (x² + x + 8)

Closed polynomial sets are (2 - x)(1 + 3x) and (5b - 3c)(7b - 3c)

A polynomial is an expression consisting of variables and their coefficients, operations of addition, subtraction, multiplication, and positive-integer powers of variables are involved in polynomial. If the result of a polynomial set applying different operations is polynomial then it is closed under that operation.

Given, polynomial sets

(x² + x - 4) - (x² + x + 8)

Applying subtraction operation

x² + x - 4 - x² - x - 8

Subtracting like terms

-12

The result is integer, it is open polynomial set

(2 - x)(1 + 3x)

Applying multiplication operation

2 - x - x - 3x²

= 2 - 2x - 3x²

The result is polynomial, it is closed polynomial set

(5b - 3c)(7b - 3c)

Applying multiplication operation

35b² - 15bc - 21bc + 9c²

= 35b² - 36bc + 9c²

The result is polynomial, it is closed polynomial set

Hence, (x² + x - 4) - (x² + x + 8) is an open polynomial set

(2 - x)(1 + 3x) and (5b - 3c)(7b - 3c) are closed polynomial sets.

Learn more about polynomials here:

https://brainly.com/question/11536910

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[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]