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http://www.wolframalpha.com/input/?i=sqrt(i)

Subtract 12 from each side

will get \(\sin \left(2x\right)+2\left(2\cos \left(x\right)-3\sin \left(x\right)\right)-12=0\)

Use the identity \(\sin \left(2x\right)=2\cos \left(x\right)\sin \left(x\right)\)

\(\left(2\cos \left(x\right)-3\sin \left(x\right)\right)2+2\cos \left(x\right)\sin \left(x\right)-12=0\)

\(2\left(2\cos \left(x\right)+\cos \left(x\right)\sin \left(x\right)-3\sin \left(x\right)-6\right)\)

\(=2\left(\sin \left(x\right)+2\right)\left(\cos \left(x\right)-3\right)\)

solving each part equivalent to 0

\(\sin \left(x\right)+2=0\:\:\:\mathrm{or}\:\:\:\cos \left(x\right)-3=0\)

sinx cannot be -2

and cos x cannot be 3 

hence , no answer in R

(-1)^(1/4)=

0.70710678118654752440084... +
0.70710678118654752440084... i

Hello Max,

you may find this interesting to read

(1, -7) is a solution of infinitely many equations.

Examples: \(y=\frac{x-15}{2}\\ y=\frac{2x-23}{3}\\ y=x^2-5x-2\\ y= (x-8)(x^2+8x+64)\)

\(\frac{d^3}{d^5}=\frac{\frac{d^3}{d^3}}{\frac{d^5}{d^3}}= \frac{1}{d^2}\)

I don't get it. Is it a maths joke?

Maths, firstly, was used for counting. But for quicker counting, people invented addition and subtraction. Human beings are always greedy, and they invented multiplication and division for faster addition and subtraction. Then people started to be curious about questions like ' What is the ratio of perimeter of circle and the diameter?' and 'What is the length of the diagonal of the square?' , then they invented pi and square roots, those people, who were interested in maths questions, is now called mathematicians......

Math is a subject that is very important in life. 

You learn how to count and see how many of a thing there will be if something happens.

It's easier to describe if you just start learning. 

Have Fun!

I will let the 3 vertices be A(1, 1), B(8, 1) and C(5, 5)

I will let AB be the base of the triangle.

AB = 8 - 1 = 7

The height of the triangle = 5 - 1 = 4

Area = 7 x 4 / 2 = 14

and I think the last time I logged into the forum is 9-7-2016

I mean 'more than 2 days' with 'long'

Solve for x : x = 5 - y

Solve for y : y = 5 - x 

Which one do you want? It is because I can't solve both variables with only 1 equation.

has it?  I didn't realize.  I thought you were here very often :)

Anyway it is good that you are here now :)

100 - 12y

200 + 10 + | r 2 = 210 + | r 2.

I can not recognize the last bit of the question

Hi Melody :D It has been long since my last login 

\(\frac{7}{6}\times \frac{8}{7} \times ...... \times \frac{40}{39}= \frac{40}{6}= \frac{20}{3}\)

The numerator of the n-th fractions just cancels out with the denominator of the (n+1)-th fractions

7/6 x 8/7 x 9/8 x 10/9 x 11/10 x 12/11 x 13/12 x 14/13 x 15/14 x 16/15 x 17/16 x 18/17 x 19/18 x 20/19 x 21/20 x 22/21 x 23/22 x 24/23 x 25/24 x 26/25 x 27/26 x 28/27 x 29/28 x 30/29 x 31/30 x 32/31 x 33/32 x 34/33 x 35/34 x 36/35 x 37/36 x 38/37 x 39/38 x 40/39

The numerator is  40!/6!   and the denominator is  39!/5!

\(\frac{40!}{6!}\div \frac{39!}{5!}\\ =\frac{40!}{6!}\times \frac{5!}{39!}\\ =\frac{40}{6}\times \frac{1}{1}\\ =6\frac{4}{6}\\ =6\frac{2}{3}\\ \)

You use 7 through 40 divided by 6 through 39. The common factors are 7 through 39. You are left with merely 40/6 which equals 6 and 2/3.

0.0059 - (- 0.0096)

= 0.0155

I can't edit either.

Not many people can I don't know why.

I wanted you to do exactly as you have done.

I have deleted your earlier post to try and limit confusion :)

Thanks Melody

Very nicely done Omar :)