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2 years ago

Please help, no links or you're getting reported

Mathematics

2 answers:

SOVA2 [1]2 years ago

6 0

The first graph slope is 4
The second graph slope is -1/3
The third graph slope is 3/4

Yuki888 [10]2 years ago

4 0

Answer:

Slope = y^2 - y^1 / x^2 - x^1

Graph n1

Slope = -5 - 1 / -6 - 2

Graph n2

Slope = -5 - 3 / 3 - 5

Graph n3

Slope = 3 - 0 / -4 - 5

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Show that (2xy3 + cos x)dx + (3x2 y2 − sin y)dy = 0 is exact, and find the solution. Find c if y(0) = π

Licemer1 [7]

We're looking for a solution of the form $F(x,y)=C$ . By the chain rule, this solution should have total differential

$\mathrm dF=\dfrac{\partial F}{\partial x}\,\mathrm dx+\dfrac{\partial F}{\partial y}\,\mathrm dy=0$

and the equation is exact if the mixed second-order partial derivatives of $F$ are equal, i.e. $\frac{\partial^2F}{\partial x\partial y}=\dfrac{\partial^2F}{\partial y\partial x}$ .

The given ODE is exact, since

$\dfrac{\partial(2xy^3+\cos x)}{\partial y}=6xy^2$

$\dfrac{\partial(3x^2y^2-\sin y)}{\partial x}=6xy^2$

Then

$\dfrac{\partial F}{\partial x}=2xy^3+\cos x\implies F(x,y)=x^2y^3+\sin x+f(y)$

$\dfrac{\partial F}{\partial y}=3x^2y^2-\sin y=3x^2y^2+\dfrac{\mathrm df}{\mathrm dy}$

$\dfrac{\mathrm df}{\mathrm dy}=-\sin y\implies f(y)=\cos y+C$

$\implies x^2y^3+\sin x+\cos y=C$

With $y(0)=\pi$ , we get

$\cos\pi=C\implies C=-1$

$\implies\boxed{x^2y^3+\sin x+\cos y=-1}$

6 0

3 years ago

HELLPPP! WILL MARK BRAINLISEST

Rina8888 [55]

Answer:77

Step-by-step explanation:

132 divided by 12(7+5) is 11

11*7=77 so theres 77 boys

4 0

3 years ago

a drawing of a surboard in a catalog shows it's length as 8 4/9 inches. find the actual length of surfboard if 1/2 inch length o

Delvig [45]

$\frac12 in -\frac38 ft \\
8\frac48 in - x\ ft\\
\\
\frac12x=\frac38 \cdot 8\frac49\\
\frac12x=\frac38 \cdot \frac{76}9\\
\frac12x=\frac{76}{24}\ /\cdot 2\\
x=\frac{76}{12}=6\frac13 ft\\\\
Answer:Actual\ lenght\ is\ 6\frac13ft.$