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4 years ago

I’ll give out brainliest just please help me out ((trigonometry))

Mathematics

1 answer:

Delicious77 [7]4 years ago

5 0

Answer:

Step-by-step explanation:

I am so sorry what grade is this?

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Find general solutions of the differential equation. Primes denote derivatives with respect toÂ x.

zepelin [54]

Answer:

$\mathbf{3x^2y^3+2xy^4=C}$

Step-by-step explanation:

From the differential equation given:

$6xy^3 +2y ^4 +(9x^2y^2+8xy^3) y' = 0$

The equation above can be re-written as:

$6xy^3 +2y^4 +(9x^2y^2+8xy^3)\dfrac{dy}{dx}=0$

$(6xy^3 +2y^4)dx +(9x^2y^2+8xy^3)dy=0$

Let assume that if function M(x,y) and N(x,y) are continuous and have continuous first-order partial derivatives.

Then;

M(x,y) dx + N (x,y)dy = 0; this is exact in R if and only if:

$\dfrac{{\partial M }}{{\partial y }}= \dfrac{\partial N}{\partial x}}} \ \ \text{at each point of R}$

relating with equation M(x,y)dx + N(x,y) dy = 0

Then;

$M(x,y) = 6xy^3 +2y^4\ and \ N(x,y) = 9x^2 y^2 +8xy^3$

So;

$\dfrac{\partial M}{\partial y }= 18xy^3 +8y^3$

$\dfrac{\partial N}{\partial y }$

Let's Integrate $\dfrac{\partial F}{\partial x}= M(x,y)$ with respect to x

Then;

$F(x,y) = \int (6xy^3 +2y^4) \ dx$

$F(x,y) = 3x^2 y^3 +2xy^4 +g(y)$

Now, we will have to differentiate the above equation with respect to y and set $\dfrac{\partial F}{\partial x}= N(x,y)$ ; we have:

$\dfrac{\partial F}{\partial y} = \dfrac{\partial}{\partial y } (3x^2y^3+2xy^4+g(y)) \\ \\ = 9x^2y^2 +8xy^3 +g'(y) \\ \\ 9x^2y^2 +8xy^3 +g'(y) =9x^2y^2 +8xy^3 \\ \\ g'(y) = 0 \\ \\ g(y) = C_1$

Hence, $F(x,y) = 3x^2y^3 +2xy^4 +g(y) \\ \\ F(x,y) = 3x^2y^3 + 2xy^4 +C_1$

Finally; the general solution to the equation is:

$\mathbf{3x^2y^3+2xy^4=C}$

5 0

3 years ago

Find the probability that either event a or b occurs if the chance of a occurring is .5, the chance of b occurring is .3, and ev

Evgesh-ka [11]

Then the probability is
P(a)+P(b)-P(a&b)
0.5+0.3-0.5*0.3=0.8-0.15=0.65

7 0

4 years ago

Please help me !! Simplify 5 - (-1)

sergiy2304 [10]

Answer:

Step-by-step explanation:

5+1

a negative and a negative make a positive.

6 0

3 years ago

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Need help with this problem

Alika [10]

Answer: B) 86°

Step-by-step explanation:

The angles of a triangle always add to equal 180.

So let's call the third angle x and add the other two angles with it.

32+62+x=180

94+x=180

Now we solve for x

Subtract 94 from both sides

94-94+x=180=94

x=86

3 0

3 years ago

Can someone please help me

Olegator [25]

For a given x, the value on the blue line is about 1/2 the value on the black line. The appropriate choice is
y = (1/2)x

3 0

4 years ago

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