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< how i can calculate tanh > 

If you have a scientific calculator, it should have hyperbolic functions on it.  I just checked mine, and the keys are on the main screen.  If you don't see it on yours, tap the "2nd" key and see if it shows up then.  Other than that, I have no ideas. 

_.

Sorry, but there's no problem to calculate! Could you please include it?

The point of intersection is (12/7, 69/28).

7^2005 = 2.6397951619824450567257574123295e+1694

If you raise 7 to power of 2005 you get the above number, which is 1695 digits long! And the last 10 digits of it are ..........6,088,416,807.

20! mod 12^8 = 0

can you explain a little bit more how you got that?

thanks

Simplify the following:
sqrt(sqrt(56) sqrt(126))

sqrt(126) = sqrt(9×14) = sqrt(3^2×14):
sqrt(sqrt(56) sqrt(3^2 14))

sqrt(3^2 14) = sqrt(3^2) sqrt(14) = 3^(2/2) sqrt(14) = 3 sqrt(14):
sqrt(sqrt(56)×3 sqrt(14))

sqrt(56) = sqrt(8×7) = sqrt(2^3×7):
sqrt(sqrt(2^3 7) 3 sqrt(14))

sqrt(2^3 7) = sqrt(2^3) sqrt(7) = 2 sqrt(2) sqrt(7):
sqrt(2 sqrt(2) sqrt(7)×3 sqrt(14))

sqrt(2) sqrt(7) = sqrt(2×7):
sqrt(2 sqrt(2×7) 3 sqrt(14))

2×7 = 14:
sqrt(2 sqrt(14)×3 sqrt(14))

2 sqrt(14)×3 sqrt(14) = 2×14×3:
sqrt(2×14×3)

2×14 = 28:
sqrt(28×3)

28×3 = 84:
sqrt(84)

sqrt(84) = sqrt(4×21) = sqrt(2^2×21):
sqrt(2^2 21)

sqrt(2^2 21) = sqrt(2^2) sqrt(21) = 2^(2/2) sqrt(21) = 2 sqrt(21): 

2 sqrt(21)

The difference between a number and its reciprocal is 3. What are the possible values of the number?

Hello Guest!

\(a-\frac{1}{a}=3\\ \frac{a^2-1}{a}=3\\ a^2-1=3a\\ a^2-3a-1=0\)

\(a=1.5\pm\sqrt{1.5^2+1}\)

\({\color{blue}a_1}=1.5+1.803=\color{blue}3.303\\ {\color{blue}\frac{1}{a_1}}=\color{blue}0.303 \)

\({\color{blue}a_2}=1.5-1.803=\color{blue}-0.303\\ {\color{blue}\frac{1}{a_2}}=\color{blue}-3.303\)

  !

  !

Write an equation of a line that is parallel to 2x-3y=0 that passes through the point (-3,-1)

Hello Guest!

\(2x-3y=0\)

is identical

\(y=\frac{2}{3}x\)

\(m=\frac{2}{3}\)

\(f(x)=m(x-x_1)+y_1\)

\(f(x)=\frac{2}{3}(x-(-3))+(-1)=\frac{2}{3}x+2-1\)

\(y=\frac{2}{3}x+1\)

  !

7^2005 % 10^10 =6088416807  - The tens digit is "zero".

 6 + 9 + 13.5 + 20.25 + 30.375 =79.125 

My bad/..... I'm stuck on this too

Find the largest integer n for which 12^n evenly divides 20!.

How did you get [343! / 7^57] mod 7 = 6? Why does it equal 6?

N=1991*1993*1995*1997*1999. What is the sum of the hundreds, tens and units digits of N?

=3160183 6203377055. [0 + 5 + 5] = 10

1) You said 17 is incorrect

3.55687428E14

That is 17!.

I am quite confused as how that is a factor of...

80325.

its 17....

Ok then, tell us the answer.

Well 1 is wrong!

9! is already 360 K or so, no point of going further.

Dragon did not try to solve this problem, not even sure he gave it more than 6 seconds of thought.

I agree with your answer, guest.

Hi tacobell, I think that Violynx is correct.

An integer can have any number of digits, just so long as it's a whole number, i.e., no fractional component.  If that's what you mean.  If you're remarking why did I stop at 8! it was because dividing by 8! gives a quotient ~ 1.99 so there's no point in dividing by any larger numbers. 

_.

Had you actually tried to solve this question instead of trying to get others to do your work, you would not assume "oh well it is probably a 2 digit number"

For your information, a "two digit number" factorial, the least being 10!, is in the millions.