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\(x=\sqrt{84}\)
\(\text{which also equals }\)

\(x=2\sqrt{21}\)

\(\text{We first convert the negative square roots to complex numbers:}\)

\((6+8i)(3-4i)= 2(3+4i)(3-4i)= 2(9+16)= 50\)

PQXRS = 68 - X = 56

I know what cs is lololol

bro im talking about FUSION

That's hydrogen, helium, carbon, oxygen, neon, magnesium, iron, 

and I left Cs for you to look up.  Gotta let you do something. 

You can find a "table of elements" on the internet. 

_.

tbh its a chem problem

what does it mean by smudges?  

It's a method of hacking a passcode by examining the screen for the smudges left on the screen above the digits by oily fingers.  The idea is that when the legitimate user taps in the passcode, the digits he touched will be smudged.  So that reveals which digits are in the passcode, therefore narrowing down the possible combinations.  

.

x>=-3<=1

[-3, 1]

why is it out of 12 and not 14. like C(14,2)

\displaystyle \int [ln(x)]^2 dx

\(\displaystyle \int [ln(x)]^2 dx\\ =\displaystyle \int [ln(x)] [ln(x)] dx\\ u=lnx\qquad v'=lnx\\ u'=\frac{1}{x}\qquad v=?\\~\\ ---------------------\\ \displaystyle \int [ln(x)] dx\\ =\displaystyle \int 1*[ln(x)] dx\\ p=lnx\qquad q'=1\\ p'=\frac{1}{x}\qquad q=x\\ so\\ \displaystyle \int 1*[ln(x)] dx\\ =xlnx-\int \frac{1}{x}*x\;dx\\ =xlnx-\int 1\;dx\\ =xlnx-x\\~\\ \text {So v=xlnx-x}\\~\\ ----------------\\ \)

Going back to the beginning

\(\displaystyle \int [ln(x)]^2 dx\\ =\displaystyle \int [ln(x)]  [ln(x)] dx\\ \qquad u=lnx\qquad v'=lnx\\ \qquad u'=\frac{1}{x}\qquad v=xlnx-x\\~\\ =uv-\int vu' dx \;\;+c \)

And you can finish it 

LaTex:

\displaystyle \int [ln(x)]^2 dx\\
=\displaystyle \int [ln(x)]  [ln(x)] dx\\
u=lnx\qquad v'=lnx\\
u'=\frac{1}{x}\qquad v=?\\~\\
---------------------\\
\displaystyle \int [ln(x)] dx\\
=\displaystyle \int 1*[ln(x)] dx\\
p=lnx\qquad q'=1\\
p'=\frac{1}{x}\qquad q=x\\
so\\
\displaystyle \int 1*[ln(x)] dx\\
=xlnx-\int \frac{1}{x}*x\;dx\\
=xlnx-\int 1\;dx\\
=xlnx-x\\~\\
\text {So v=xlnx-x}\\~\\
----------------\\

Hi Solviet,

You are still here.

the reason you are not on the leaderboard is becasue you have not posted anything for over a month.

If you make a post you will reappear   :)

Have you forgotten your password?

Lets see

a)  4 people  are chosen from 14       

   That is just 14 choose 4 = 14C4  = 1001     (it is not really choose, C stands from combinations)

   You say you get that?

b)   2 of the candiates do not want to go together.

        ok  Let's say those 2 are BOTH chosen

        Then there will be 2 chosen out of the remaining 12  which is    12C2  = 66

        BUT those are the combinations that are NOT allowed so the number of possible combinations will be

          14C4 - 12C2   = 1001 - 66 = 935

Does that help?

is it possible to explain b and c. I don't get why "choosing 4 from 12 " and "choosing 2 from 12"?

Thanks in advance.

\(\newcommand{\dint}{\displaystyle\int} \begin{array}{rcl} \dint (\ln x)^2 \,dx &=& x(\ln x)^2 - \dint x\,d\left((\ln x)^2\right)\\ &=& x(\ln x)^2 - \dint x\cdot \dfrac{2\ln x}{x}\,dx\\ &=& x(\ln x)^2 - 2\dint \ln x\,dx\\ &=& x(\ln x)^2 - 2\left(x\ln x - \dint x\,d(\ln x)\right)\\ &=& \cdots \end{array}\)

I will leave the rest to you.

As you said, a smoot is 67 inches. 

168 acres is equivalent to 168 * 43560 square feet, which is equivalent to 168 * 43560 * 144 square inches.

Dividing by 67^2 gives around 235000 square smoots.

2y = 2f(x) is just y = f(x), so the point is (9, 7).

By Vieta's formula, \(\text{product of roots} = \dfrac{-k}3\).

But since one zero is the reciprocal of the other, product of roots is 1.

Therefore, \(\dfrac{-k}3 = 1\). That means k = -3.

If x is a positive even integer then so is 9x -2, so the smallest odd number greater than this must be 9x-2+1 = 9x-1

Similarly, 8x+3 must be an odd number, so the largets odd number less than this must be 8x+3-2 = 8x + 1

Can you finish from here?

For 

a) How many ways are there of choosing 4 from 14

b) How many ways of choosing 4 from 14 less how many ways of choosing 2 from 12

c) How many ways of choosing 4 from 12 plus how many ways of choosing 2 from 12.

(In general:  How many ways of choosing m from n is given by:  \(\frac{n!}{(n-m)!\times m!}\) )

But the answes are already there, arn't they?

Without the repetitions of the 8 digis, you have the following permutations:

For the first 2 pairs, there are: 4 x 4 ==16 permutations. For the nest 2 pairs, there are: 3 x 3 ==9 permutations

So, the total beginning with digit will be: 16  x  9 ==144

144 x 8 digits ==1,152 permutations

beats me how you can measure an AREA using a kitchen scale.

The answer is 7288