Answer:
1/ sqrt(1+ln^2(x)) * 1/(ln^2x +1) * 1/x
Step-by-step explanation:
f(x) = sin (tan^-1 (ln(x)))
u substitution
d/du (sin u) * du /dx
cos (u) * du/dx
Let u =(tan^-1 (ln(x))) du/dx =d/dx (tan^-1 (ln(x)))
v substitution
Let v = ln x dv/dx = 1/x
d/dv (tan ^-1 v) dv/dx
1/( v^2+1) * dv/dx
=1/(ln^2x +1) * 1/x
Substituting this back in for du/dx
cos (tan^-1 (ln(x)) * 1/(ln^2x +1) * 1/x
We know that cos (tan^-1 (a)) = 1/ sqrt(1+a^2)
cos (tan^-1 (ln(x)) * 1/(ln^2x +1) * 1/x
1/ sqrt(1+ln^2(x)) * 1/(ln^2x +1) * 1/x
We have three numbers to arrange so that 6 is 1/10 of the value of the other six.
Since position tells us whether we're talking about single, tens, hundreds, thousands (e.g. 25 is two times 10 plus five times 1) we know that the two sixes must be next to each other.
This leaves us with two options.
663 or 366.
In each of these cases the second 6 in the number is one tenth of the first 6.
If we look at the only other option: 636 we see that the second 6 is one hundredth of the value of the first 6.
37292827 the answer is that
After 5 years, value doubles.
Hence after 5 years, value is 250 x 2 = 500
After another 5 years, value doubles.
500 x 2 = 1000
Ans: $1000
