Plzz help will give Brainlest!!

In this problem we consider an equation in differential form Mdx+Ndy=0. (4x+2y)dx+(2x+8y)dy=0 Find My= 2 Nx= 2 If the problem is

zheka24 [161]

Answer:

$f(x,y)=2x^2+4y^2+2xy=C_1\\\\Where\\\\y(x)=\frac{1}{4} (-x\pm \sqrt{-7x^2+C_1} )$

Step-by-step explanation:

Let:

$M(x,y)=4x+2y\\\\and\\\\N(x,y)=2x+8y$

This is and exact equation, because:

$\frac{\partial M(x,y)}{\partial y} =2=\frac{\partial N}{\partial x}$

So, define f(x,y) such that:

$\frac{\partial f(x,y)}{\partial x} =M(x,y)\\\\and\\\\\frac{\partial f(x,y)}{\partial y} =N(x,y)$

The solution will be given by:

$f(x,y)=C_1$

Where C1 is an arbitrary constant

Integrate $\frac{\partial f(x,y)}{\partial x}$ with respect to x in order to find f(x,y):

$f(x,y)=\int\ {4x+2y} \, dx =2x^2+2xy+g(y)$

Where g(y) is an arbitrary function of y.

Differentiate f(x,y) with respect to y in order to find g(y):

$\frac{\partial f(x,y)}{\partial y} =2x+\frac{d g(y)}{dy}$

Substitute into $\frac{\partial f(x,y)}{\partial y} =N(x,y)$

$2x+\frac{dg(y)}{dy} =2x+8y\\\\Solve\hspace{3}for\hspace{3}\frac{dg(y)}{dy}\\\\\frac{dg(y)}{dy}=8y$

Integrate $\frac{dg(y)}{dy}$ with respect to y:

$g(y)=\int\ {8y} \, dy =4y^2$

Substitute g(y) into f(x,y):

$f(x,y)=2x^2+4y^2+2xy$

The solution is f(x,y)=C1

$f(x,y)=2x^2+4y^2+2xy=C_1$

Solving y using quadratic formula:

$y(x)=\frac{1}{4} (-x\pm \sqrt{-7x^2+C_1} )$

4 0

3 years ago

You have $20 to spend on taxi fare. The ride costs $5 plus $2.50 per mile. Write an inequality to determine how many miles you c

BARSIC [14]

Answer: Maximum 6 miles

Step-by-step explanation: In total you have $20.

Base fare of taxi is $5.

Per mile cost is $2.50.

Your total cost is where x is the number of miles. Since you're on a budget of maximum $20, the cost should be less than or equal to $20. We can write:

To find how many miles we can write, let's solve the inequality:

.

This means 6 is the maximum number of miles you can ride with $20.

4 0

3 years ago

6= 1 - 2n + 5<br> How can I solve this equation

bulgar [2K]

Answer:

Step-by-step explanation:

Simplifying

6 = 1 + -2n + 5

Reorder the terms:

6 = 1 + 5 + -2n

Combine like terms: 1 + 5 = 6

6 = 6 + -2n

Add '-6' to each side of the equation.

6 + -6 = 6 + -6 + -2n

Combine like terms: 6 + -6 = 0

0 = 6 + -6 + -2n

Combine like terms: 6 + -6 = 0

0 = 0 + -2n

0 = -2n

Solving

0 = -2n

Solving for variable 'n'.

Move all terms containing n to the left, all other terms to the right.

Add '2n' to each side of the equation.

0 + 2n = -2n + 2n

Remove the zero:

2n = -2n + 2n

Combine like terms: -2n + 2n = 0

2n = 0

Divide each side by '2'.

n = 0

Simplifying

n = 0

8 0

3 years ago

After multiplying each side of the equation by the LCD and simplify , the resulting equation is

Mamont248 [21]

The third option
Hope it helps

5 0

3 years ago

PLLLLEEEEAAASSSEEE HELP ME I REALLY NEED IT IT'S URGENT!!!!!

krok68 [10]

The answers would be

D
C
A
A

6 0

3 years ago