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no such thing as the time barrier

Extrapolate the right-most line. For every 2 units reduction in y it increases by 3 units in x.

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75 → 25*3 → 5^2*3

so 2sqrt(75) → 2sqrt(5^2*3) → 2*5sqrt(3) → 10sqrt(3)

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When is your birthday asinus ?

Thanks for the birthday list!

1/2 + 1 + 1/4

\(\frac{1}{2}+1+\frac{1}{4}=\frac{2}{4}+\frac{4}{4}+\frac{1}{4}=\frac{7}{4}\color{blue}=1\frac{3}{4}\)

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Let the numbers be a and b where b is bigger than a

a+b = 12    (1a)            b=12-a   (1b)

b+5a=32    (2)

Sub    b=12-a    into (2)

12-a +5a =  32

12 +4a     = 32

        4a    = 20

          a   =  5

b=12-a = 12-5  =7

2040 - 2017 = 23 years

Present population = 128 M

Future population =?

FP = 128 x [1 + R]^N

FP =128 x 0.998^23

FP =128 x 0.955....

FP =122.24 Million - expected Japan's population in 2040.

Two friends of mine practically live on bananas. Both like the daiquiri form, and one truly prefers it.

 I like bananas but they sometimes disagree with my carnivorous K9-DNA, making me nauseated.

There is a unique tip-top mind on here, represented by a unique artistic flower.  My banana-loving friend finds her presence refreshing and her intelligence inspiring.  I do too.    

How are you getting the 13?

From your graph, I suggest the following:

1. (-inf, -4) U (-2, 3) U (4, 13)

2. (-4, -2) U (3, 4) U (13, inf)

3. (-3, -1) U (0, 2)

4. (-5, -3) U (-1, 0) U (2, 4) U (4, inf)

5. (-5, -1) U (-1, 1)

6. (1, 3)

7. (-inf, -5) U (3, 4) U (4, inf)

8. (-inf, -5)

cos 180° = -1  and sin 180° = 0 so your expression reduces to just 3

or you could write 3 + 0i if you insist!

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Raise both sides to the power 4

287^4 = (F^0.25)^4

287^4 = F^(0.25*4)

287^4 = F

F = 6784652161

Wow Guest, you must eat a lot of really healthy food, like maybe bananas...just as an example.... to keep your brain in tip-top condition 

(tanx + 1)^2 cosx          expand

(tan^2x + 2tanx + 1) cosx

(tan^2x + 1  + 2tanx) cos x      re-order inside the parentheses

........... tan^2x + 1   = sec^2x ..........

(sec^2x + 2tanx) cosx          put everything in terms of sine, cosine        

( 1/cos^2x   +  2 sinx / cos x )  cosx        

 Distribute the cosx acroos the terms in the parentheses

( 1/cos x  +  2 sin x)

secx  + 2sinx