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KengaRu [80]
3 years ago
6

Write the expression in exponential form.

Mathematics
1 answer:
omeli [17]3 years ago
3 0
(3 root a)^2 hope this helps
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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
Please help i have no idea what it means and the test is tomorrow.
Anarel [89]

Answer:

H. 2

Step-by-step explanation:

√(1 − cos² x) / sin x + √(1 − sin² x) / cos x

Use Pythagorean identity.

sin² x + cos² x = 1

So:

1 − cos² x = sin² x

and

1 − sin² x = cos² x

Substitute:

√(sin² x) / sin x + √(cos² x) / cos x

sin x / sin x + cos x / cos x

1 + 1

2

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3 years ago
What's the answer to this problem
Anna71 [15]
Um I think if you multiply the amount of hersheys by the ribbon you would get youre answer
Hoped i helped i couldn't see the number of ribbons
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How do you solve break even problems?
Mandarinka [93]
A break even problem is found when you calculate starting a buisieness
so lets ssay you have to buy 3 coppy machines and each machine costs 2000 dollars,
the people who want to use your coppy machines have to pay $0.40 per page
so you have spent 6000 dollars already
when you break even, it is when your earnings equals your expenditure (how much you earned equals how much you paid)
8 0
3 years ago
Question 2
SCORPION-xisa [38]
Where are the choices
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