Melody

Hint:

the integral is lnx =   the integral of (1*lnx)  

do that first.

You need to use integration by parts twice.

I have not done it, I don't have time at present, but that is how I would proceed.

Please present your questions properly.

ok

367^367^367   mod11

= 367^(367^367)    mod11

= 4^(4^4)                mod11

= 4^ 256                 mod11

= 4^ 3                     mod11

=  64                      mod11

=   9                       mod11

If this were my question, the first thing I would do is expand it out.

Have you done that?  What did you get?

The answerer got it with a little computer program that they wrote.

I can never remember whether

2^3^4    means     2^(3^4)      or      (2^3)^4

Just do it one bit at a time.

Let f(x) = (x - 1)/(x + 1). Compute f(f(f(5))).

f(5)=(5 - 1)/(5 + 1) = 4/6  =  2/3

\(f(f(5)) = f(\frac{2}{3}) \\ =\frac{ (\frac{2}{3}-1) }{ (\frac{2}{3}+1) }\\~\\ =\frac{ \frac{-1}{3} }{ \frac{5}{3} }\\~\\ =\frac{-1}{5}\\~\\ f(f(f(5)) )=f( f(\frac{2}{3}))=f(\frac{-1}{5}) \\ etc\)

you need to check what i have done and then finish it.

Who cares where you got it.

It is  YOUR homework.

If you want others to do YOUR homework for free then go to some planet where it is legal and buy a few slaves.

You might find it easier if you swap the z for an x and the swap it back at the end

\((4-z)(z+7) ≥ 2\\ (4-x)(x+7) ≥ 2\\ -x^2 -3x +28 \ge 2\\ -x^2 -3x +26 \ge 0\\ x^2+3x -26 \le 0\\ \)

 \(y=x^2+3x-26\\ \text{Is a concave up parabola}\)

So it will be less than 0 between the roots.  Draw it to see what i mean

Use the quadratic formula to find the roots

etc

2/3 of the way from 6 to 12 would be 10.  Agreed?

2/3(12-6) = 2/3 (6) = 4          6+4=10      That is how to find it more formally.

so

Given R(-6,19)  and S(15,-5), what are the coordinates of the point on segment RS two-thirds of the distance from R to S?

the x value will be    -6  +  2/3(15 - -6) 

and you can find the y value