F(2)=3 divide by 2x-5

Mathematics

1 answer:

Margaret [11]3 years ago

8 0

Answer:

$f(2) = \frac{3}{2x - 5}$

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An ordinary Fair die is a cube with the number 1 through 6 on the sides (represented by painted spots). imagine that such a die

aleksandrvk [35]

Event A Answer: $\frac{5}{12}$

Step-by-step explanation:

sum greater than 7 leaves are the following combinations for 8, 9, 10, 11, and 12:

8 = 26, 35, 44, 51, 62 (5 possibilities)

9 = 36, 45, 54, 63 (4 possibilities)

10 = 46, 55, 64 (3 possibilities)

11 = 56, 65 (2 possibilities)

12 = 66 (1 possibility)

This is a total of 15 possibilities out of 36 total: $\frac{15}{36}$ = $\frac{5}{12}$

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Event B Answer: $\frac{1}{2}$

Step-by-step explanation:

sum is an even number means both dice are odd or both dice are even. That results in the following combinations:

11 13 15

22 24 26

31 33 35

42 44 46

51 53 55

62 64 66

This is a total of 18 possibilities out of 36 total: $\frac{18}{36}$ = $\frac{1}{2}$

7 0

3 years ago

Find Integrating Fector: ylogy dx + ( x-logy )dy=0

12345 [234]

Rewrite the ODE as

$y\log y\,\mathrm dx+(x-\log y)\,\mathrm dy=0\iff y\log y\dfrac{\mathrm dx}{\mathrm dy}+x=\log y$
$\dfrac{\mathrm dx}{\mathrm dy}=\dfrac1{y\log y}x=\dfrac1y$

so that it is now linear in $x$ . An integrating factor would

$\mu(y)=\exp\left(\displaystyle\int\frac{\mathrm dy}{y\log y}\right)=e^{\log(\log y)}=\log y$

Multiply both sides by $\mu(y)$ to get

$\log y\dfrac{\mathrm dx}{\mathrm dy}=\dfrac1yx=\dfrac{\log y}y$
$\dfrac{\mathrm d}{\mathrm dy}[x\log y]=\dfrac{\log y}y$
$x\log y=\displaystyle\int\frac{\log y}y\,\mathrm dy$
$x\log y=\dfrac12\log^2y+C$
$x=\dfrac12\log y+\dfrac C{\log y}$