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3 years ago

A six-sided number cube is rolled twice.

Mathematics

1 answer:

Kitty [74]3 years ago

4 0

Answer:

1/6

Step-by-step explanation:

Probability is a chance of an event taking place.

Probability = (favorable outcome)/(total outcome)

There are 3 even sides in a dice.

P(even) = 3/6 = 1/2

There are 2 numbers that are greater than 4 in a dice.

P(x>4) = 2/6 = 1/3

P(even and x>4) = 1/2 × 1/3 = 1/6

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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

$8+\ln9=C$

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

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3 years ago

How many ways can you make 35?

Ksju [112]

35 é divisível por 5 e 7
5 e 7 são números primos, logo, 35 pode ser escrito...
5*7, 7*5, 35*1

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3 years ago

Read 2 more answers

F( y ) = y + y 2 - 3

ExtremeBDS [4]

F(y) = y + y^2 - 3

f(-2) = -2 + (-2^2) - 3
f(-2) = -2 + 4 - 3
f(-2) = -1

f(-4) = -4 + (-4^2) - 3
f(-4) = -4 + 16 - 3
f(-4) = 9

f(0) = 0 + 0^2 - 3
f(0) = -3

f(2) = 2 + 2^2 - 3
f(2) = 2 + 4 - 3
f(2) = 3

f(4) = 4 + 4^2 - 3
f(4) = 4 + 16 - 3
f(4) = 17

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3 years ago

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pentagon [3]

Answer:

Hope it helps plz give BRAINLIES! :D

Step-by-step explanation:

$80

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Elodia [21]

The answer would be 3

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