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9sec^2 (x)  tan(x)   -  12tan (x)   = 0       re-write as

9tan (x) sec^2 (x)  - 12 tan (x)   =   0

Factor out the greatest common factor,   3tan(x)

3tan (x)  [ 3 sec^2 (x)  - 4  ]  = 0

6 which is equal to 4

Oh sorry, I've seen this wrong. I am sorry! asinus

We need to find the radius

Circumference  = 2 * 3.14 * radius

 7.85  =  2 * 3.14 * radius                divide both sides by  2 * 3.14  =  6.28

[7.85 / 6.28 ] m   =  radius

And the area, A, is given by :

A  =  3.14 * radius^2    =   3.14 * [ 7.85 / 6.28]^2   ≈  4.91 m^2

Actually, the guest is correct....this graph is symmetric around the y axis  and will = 0 at

pi/2 + n*pi      radians......where n is an integer.......

See the graph below :

Hi Guest, your solution for coshx * cosx = 0 is not correct.

There are only four results, not infinitely many.

Greeting! asinus

Oh sorry, I've seen this wrong.

Your solution for coshx * cosx = 0 is correct.
 

I am sorry! asinus

I probably did read the question incorrectly!  I read it as the sum of the weights of the first 12 elephants plus half of that of  their right-hand neighbours must equal 6000kg. It didn't make sense to me to assume the 6000 was shared between only two elephants.  Even so, the answer I gave isn't unique.

Perhaps the guest who asked the question might provide some clarification.

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Just use the caret key ... 

Example :

6 ^ 3   = 216

The area of the smaller triangle to the larger triangle  will  be  (2/5)^2  =  4/25  =  4 : 25

the answer is 4

the answer is 5

Let the sum of all ages = A

And let N be the number of family members.......then we have two equations

A  =  20N      

A - 40  = 15(N - 1)   →  A  =  15(N-1) + 40   

Setting these equal, we have

20N  =   15(N-1) + 40

20N  = 15N + 25

5N  = 25

N  = 5

Thus.....we have  2 adults and 3 children

Let the number of children =C

Let the sum total of the whole family's ages =S

S/(C+2)=20..........................(1)

(S-40) /(C+1) =15.................(2), solve for C, S

C = 3 children in the family

S =100 - The family combined ages.

( sqrt  [x + 1]  +  sqrt [ 1 - x])  / sqrt [x]      we can write

sqrt [x + 1] / sqrt [x]      +  sqrt [ 1 - x ] / sqrt [x]

The domain of the first  is  (0, infinity)  while the domain of the second is (0, 1]

The intersection of these domains  is  (0,1]  so this interval is where the function is defined

See the graph, here :  https://www.desmos.com/calculator/dea2cd3jnp

Happy Birthday Melody!!

Recently, I was visiting your riotous birthday party of 2015.  (There wasn’t a birthday party on the forum for 2016, for some reason). It seems like that party it’s still going on.

0.03584229  =  3.584229 x 10^-2

Here is another simple solution:

Will write all the numbers as 6 digits as follows:

000001, 000002, 000003...........999997, 999998, 999999.

Since we have 1,000,000 numbers, each of which is 6 digits, then:

Total number of INDIVIDUAL DIGITS =6 x 1,000,000 =6,000,000 digits.

Now, the average VALUE of each digit is:[0+1+2+3+4+5+6+7+8+9=45] / 10 =4.5

Therefore the total VALUE of the 6,000,000 digits will be:

6,000,000 x 4.5 =27,000,000. And will add 1 for the last of digit of 1,000,000 itself and will have:

27,000,000 + 1 =27,000,001 - Total Value of ALL digits from 1 to 1,000,000.

(36x+53y)+(-5x+33y)   combine like terms

36x - 5x   + 53y  +  33y  =

31x  +  86y

coshx*cosx=0  x=?

\(cos\ x =0\\x=\frac{\pi}{2}+\pi\cdot n\\n \in ℤ\)

\(cosh\ x=\frac{1}{2}(e^x+e^{-x})>0\\ for \ x\in \Re\)    no solution

\(solution:\)

\(coshx \cdot cosx=0\\x_1=\frac{\pi}{2} \\x_2=\frac{\pi}{2}+\pi\\x_3=-\frac{\pi}{2}\\x_4=-(\frac{\pi}{2}+\pi) \)

\(x=\frac{\pi}{2}+\pi\cdot n\)     Thank you! C.

\( for\ n \in ℤ\)

  !

By simple inspection:

u = 39 and 89

Average =[39+89] / 2 =64

Спасибо большое вам!!!

Alan: Did you misread the question? Or am I reading it wrong?. It says:

"It is known that if one adds the weight of any elephant to half of the weight of its neighbor to the right one obtains 6000 kg" It sounds to me that the 6,000 kg is shared between TWO elephants only. No?. Of course, the question could have many answers. I think they have some crucial information missing. Note, that a newly-born baby elephant can weigh between 200 -300 kg, while a full-grown bull elephant can weigh up to 6 metric tonnes, or 6,000 kg, at least the African species.

As follows:

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