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Ipatiy [6.2K]
2 years ago
5

Help I will give brainless

Mathematics
1 answer:
Reptile [31]2 years ago
4 0

Answer:

1) -4       2)-3        3) -2     4) -1    5) 0

Step-by-step explanation:

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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

so

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

8 0
3 years ago
Adult tickets for the movie theater cost $9. Child tickets cost $5.25. Write an expression for the total cost of a group of adul
sammy [17]

Answer:

Step-by-step explanation:

9a + 5.25c

5 0
3 years ago
Sharon drops a rubber ball from a height of 160 feet. Every bounce sends the
spayn [35]

Answer:

140 feet

Step-by-step explanation:

If the first time she dropped the ball was from 160 feet then the second time she dropped the ball is would bounce back up 80 feet.  The third time it would bounce 40 feet.  And the 4th time it would bounce 20 feet

So the total distance the ball traveled from the first time it hit the ground is 140 feet

I'm not 100% sure I understand the question but I tried

7 0
3 years ago
4. Suppose 11 out of 17 students said they were attending the football game. How many students out of 875 would you expect to at
SCORPION-xisa [38]

We have to basically multiply:

11/17 x 475

And simplifying that we get

307.35

And since there can't be .35 person

So out final answer is 307

pls pls brainlist

6 0
3 years ago
-1/2 times -2/3 times -6/7=
fenix001 [56]

Answer:

Exact Form:  −2/7

Decimal Form: -0. 285714

8 0
3 years ago
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