3 years ago

Which is M = 9pn solved for p

Mathematics

1 answer:

prohojiy [21]3 years ago

7 0

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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

2 years ago

A square has a perimeter of 28 inches. Find the area of the square.

sasho [114]

Answer:

A = 49 in^2

Step-by-step explanation:

The perimeter of a square is found by

P = 4s where s is the side length

28 = 4s

Divide each side by 4

28/4 = 4s/4

7 =s

We want to find the area

A = s^2 where s is the side length

A = 7^2

A = 49 in^2

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2 years ago

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Whats your favorite dog breed...?

Anni [7]

Answer:

husky mix of germany shepherd

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2 years ago

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Twice the difference of a number and seven

levacccp [35]

The difference of a number and seven is x - 7. So twice that, would be:

2(x - 7)

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2 years ago

This is the graph of f(x). What is the value of f(3)? A. 8 B. 6 C. 3 D:5

Andreyy89

Since we can find that the graphs Y value is by a factor of 2 looking at the graph we can find
f(3)=8

4 0

2 years ago