2 years ago

Which point can be used to find f(3)

1 answer:

3 0

Commonly the horizontal axis represent the x-axis. So, you need the point that means x = 3 (positive 3), so, it is the point A.

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kotykmax [81]

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2 years ago

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

$8+\ln9=C$

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

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2 years ago

jenyasd209 [6]

[b.3] ^_^
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3 years ago

tangare [24]

1)5/24
2)1 and 1/3 im not sure
3)1 and 1/3
4)1/7

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ivolga24 [154]

Answer:

Step-by-step explanation:

vertical angles congrunet (angleFJH + angle GJI)

& (angleHFJ + angle JGI congruent)

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2 years ago