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3 years ago

The quadratic formula can be used to solve an equation only if the highest

Mathematics

1 answer:

Studentka2010 [4]3 years ago

6 0

i think it must be one or two

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Show that ( 2xy4 + 1/ (x + y2) ) dx + ( 4x2 y3 + 2y/ (x + y2) ) dy = 0 is exact, and find the solution. Find c if y(1) = 2.

fredd [130]

$\dfrac{\partial\left(2xy^4+\frac1{x+y^2}\right)}{\partial y}=8xy^3-\dfrac{2y}{(x+y^2)^2}$

$\dfrac{\partial\left(4x^2y^3+\frac{2y}{x+y^2}\right)}{\partial x}=8xy^3-\dfrac{2y}{(x+y^2)^2}$

so the ODE is indeed exact and there is a solution of the form $F(x,y)=C$ . We have

$\dfrac{\partial F}{\partial x}=2xy^4+\dfrac1{x+y^2}\implies F(x,y)=x^2y^4+\ln(x+y^2)+f(y)$

$\dfrac{\partial F}{\partial y}=4x^2y^3+\dfrac{2y}{x+y^2}=4x^2y^3+\dfrac{2y}{x+y^2}+f'(y)$

$f'(y)=0\implies f(y)=C$

$\implies F(x,y)=x^2y^3+\ln(x+y^2)=C$

With $y(1)=2$ , we have

$8+\ln9=C$

$\boxed{x^2y^3+\ln(x+y^2)=8+\ln9}$

8 0

3 years ago

An angle is double its complement. find the angle and the complement

Alona [7]

Complement means the other angle that will sum up to 90°

So:

x + 2x = 90°
3x = 90
x = 30°

So, it is 30° and 30 * 2°, or 60°

4 0

3 years ago

Read 2 more answers

The ordered pair (1, -2) is a solution to the system of linear equations.

vesna_86 [32]

Answer:

False

Step-by-step explanation:

2x + y = 0

Try (1, -2)

2(1) + (-2) = 0

2 + (-2) = 0

0 = 0

The solution works on the first equation.

-x + 2y = 5

-(1) + 2(-2) = 5

-1 - 4 = 5

-5 = 5

The solution does not work in the second equation.

Answer: False

3 0

3 years ago

Determine whether the relation is a function.

Alexxx [7]

Answer:

function

Step-by-step explanation:

every x value has only 1 y value

5 0

3 years ago

The temperature at the south pole was 6 degrees at 8am. At 3 pm it was -18 degrees. By how many degrees did the temperature drop

olga2289 [7]

Answer:

$24\°$

Step-by-step explanation:

we know that

To determine how many degrees drop the temperature, find out the absolute value of subtract the temperature at 8 am from the temperature at 3 pm.

$\left|-18-6\right|=24\°$

7 0

3 years ago