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0.017455064928

As according to the Hitchhiker's guide to the galaxy, after God created the world and all life, his last words to humanity were, "Sorry for the inconvenience." As thus, he decided to create a meaning to live, the pursuit to find the meaning of life. However, to make the hunt last longer, he made the answer so blatantly complicated and yet so pointless that nobody would even think that this is the meaning to life.

          After hundreds of millenia, a computer was built by a group of aliens to find what exactly the meaning to life was. However, the computer could not crack it even a little. It then decided to spend another century to build a giant supercomputer, one complex enough to find the meaning of life. After another century, the supercomputer is built. It determines that the meaning of life is not a cause, a reason, an action or person, it is actually the number:

42

I went to the beach, drove back home, and my mom gave me a mini orchid plant.

living

Life = 42

The first derivative

        1-5x

 y = -------- 

        3x+2

\(\boxed{Quotient Rule\\ y'=\frac{vu'-uv'}{v^2}}\\~\\ y'=\frac{-5(3x+2)-3(1-5x)}{(3x+2)^2}\\ y'=\frac{-15x-10-3+5x}{(3x+2)^2}\\ y'=\frac{-10x-13}{(3x+2)^2}\\ \)

From the diagram  x = sqrt(11^2 -4^2) =10.24

So the area of the shaded triangles (there are two)  =  2  x  (1/2 x 4 x 10.24)  =  40.96

Angle theta = arcsin 10.24/11 = 68.58

2 x theta =137.15   (central angle)

Total cross sectional area = pi r ^2 = pi 11^2 =  380.13

SECTOR area =  137.15/360 x  380.13 = 144.82 sqft

SECTOR - triangles = SEGMENT area = 144.82 - 40.96 = 103.86 sqft

How full is it ? 

  (Total area - SEGMENT area )/ Total area =  (380.13-103.86)/380.13 = 72.67 % full

thank you so much!! :3

A map has a scale 6.5 in=32 miles.  How far apart are two cities that are 97.5  inches apart on the map?

\(\begin{array}{|rcll|} \hline && 97.5\ in. \times \frac{32\ \text{miles} }{6.5\ in.} \\ &=& 97.5 \times \frac{32 }{6.5 } \ \text{miles} \\ &=& 480 \ \text{miles} \\ \hline \end{array} \)

The two cities are 480 miles far apart.

324/1000

Simplify

81/250

\(\sqrt[3]{-64}\) = -4

10 + -4 = 10-4 = 6

Identify the highest common factor of 9 and 30.

\(\begin{array}{lcll} \text{Factors of } 9 &:& 1, {\color{red}3}, 9 \\ \text{Factors of } 30 &:& 1, 2, {\color{red}3}, 5, 6, 10, 15, 30 \\ \end{array} \)

\(\begin{array}{rcll} 3 \text{ is the Greatest Common Factor } \end{array}\)

Set up the long addition

519628

+761943

-----------

Calculate 8 + 3, which is 11.

Since 11 is two-digit, we carry the first digit 1 to the next column.

      1

519628

+761943

----------

         1

Calculate 2 + 4, which is 6. Now add the carry digit of 1, which is 7.

      1

519628

+761943

-----------

        71

Calculate 6 + 9, which is 15.
Since 15 is two-digit, we carry the first digit 1 to the next column.

1    1

519628

+761943

----------    

      571

Calculate 9 + 1, which is 10. Now add the carry digit of 1, which is 11.
Since 11 is two-digit, we carry the first digit 1 to the next column.

11  1

519628

+761943

-----------

1571

Calculate 1 + 6, which is 7. Now add the carry digit of 1, which is 8.

11  1

519628

+761943

-----------

81571

Calculate 5 + 7, which is 12.
Since 12 is two-digit, we carry the first digit 1 to the next column.

1 11 1

519628

+761943

281571

Bring down the carry digit of 1.

1 11 1

519628

+761943

1281571

Therefore, 519628 + 761943 = 1281571.

12815711281571

-sinx=12/13

\(\begin{array}{|rcll|} \hline -\sin(x) &=& \frac{12}{13} \\ \sin(x) &=& -\frac{12}{13} \\ x_1 &=& \arcsin(-\frac{12}{13}) + z\cdot 360^{\circ} \quad & | \quad z \in Z \\ \mathbf{x_1} &\mathbf{=}& \mathbf{-67.3801350520^{\circ} + z\cdot 360^{\circ}} \\\\ \sin(x)=\sin(180^{\circ}-x) &=& -\frac{12}{13} \\ 180^{\circ}-x_2 &=& \arcsin(-\frac{12}{13}) + z\cdot 360^{\circ} \quad & | \quad z \in Z \\ x_2 &=& 180^{\circ}- \arcsin(-\frac{12}{13}) + z\cdot 360^{\circ} \\ x_2 &=& 180^{\circ}- (-67.3801350520^{\circ}) + z\cdot 360^{\circ} \\ \mathbf{x_2} &\mathbf{=}&\mathbf{ 247.380135052 + z\cdot 360^{\circ}} \\ \hline \end{array} \)

0.346 recurring as a fraction?

\(\begin{array}{|rcll|} \hline 1000\cdot 0.\overline{346} &=& 346.\overline{346} \\ 1\cdot 0.\overline{346} &=& 0.\overline{346} \\\\ 1000\cdot 0.\overline{346} - 1\cdot 0.\overline{346} &=& 346.\overline{346}-0.\overline{346} \\ 999\cdot 0.\overline{346} &=& 346 \\ 0.\overline{346} &=& \frac{346}{999} \\ \mathbf{ 0.346\ recurring } &\mathbf{=}& \mathbf{ \frac{346}{999} }\\ \hline \end{array}\)

0.2 recurring as a fraction?

\(\begin{array}{|rcll|} \hline 10\cdot 0.\bar{2} &=& 2.\bar{2} \\ 1\cdot 0.\bar{2} &=& 0.\bar{2} \\\\ 10\cdot 0.\bar{2} - 1\cdot 0.\bar{2} &=& 2.\bar{2}-0.\bar{2} \\ 9\cdot 0.\bar{2} &=& 2 \\ 0.\bar{2} &=& \frac{2}{9} \\ \mathbf{ 0.2\ recurring } &\mathbf{=}& \mathbf{ \frac{2}{9} }\\ \hline \end{array} \)

find factors x^2+y^6 =x^2 + y^6. It has NO FACTORS!!

0.222222222222....=2/9

.346346346.......=346/999.

If powers are allowed then:

19^9^5 =1.32246... x 10^75,509

x = y = z = 1.

16 /1/4 

=16 *4 (reciprocal)

=64

hi Rosala, it is really good to see you here :))

My husband gave me some roses.  That was pretty cool :))