Melody

That is in radians.

-cos(2 radians)

im x → 1, ((sin(x+1))-(sin2x))/(x-1)

\(\displaystyle \lim_{ x → 1} \; \frac{sin(x+1)-sin2x}{x-1}\\ \mbox{This is the indeterminate form of 0/0 so use l'hopital's rule}\\ =\displaystyle \lim_{ x → 1} \; \frac{cos(x+1)-2cos2x}{1}\\ =\displaystyle \lim_{ x → 1} \; cos(x+1)-2cos2x\\ = cos(2)-2cos2\\ =-cos(2)\)

Thanks Spawn  LOL

30*(1.06)^5

30*(1.06)^5 = 40.146767328

40 words

Yes it would take a while LOL 

d2 + 7/3d = 2

Need to find the nature of its roots.

\(d^2+\frac{7}{3}d=2\\ d^2+\frac{7}{3}d-2=0\\ \mbox{It is easiest to multiply this by 3 to get rid of the fraction}\\ 3d^2+7d-6=0\\ \)

Now the nature of the roots is determined by the discriminant.  That it the bit under the square root in the quadratic formula.

The symbol for the discriminant is a triangle.

\(\triangle=b^2-4ac\\ \triangle=7^2-4*3*-6\\ \triangle=49+72\\ \triangle=121\\ \)

Now 121 is a perfect square so this means there will be two rational roots :)

If you want more explanation then ask for it :)

Actually it is probably more than that because sometimes the bag as 20 b***s and sometimes it has 21 b***s.

I was only looking at the combinations of 21 b***s ://

There are going to be a lot of (wipe out)  stars in this answer!     LOL

Hi guest.  It is mind blowing!

Here is something else that might b**w you mind.Say your mum gives you 1c allowance for the first week of January.

That is pretty useless you say - might as well throw it away!

BUT

then each week after that she gives you double as much as she geve you last times.

So in week 2 you get 2c

week3         4c

week 4        8c

You have still only got a total of 1+2+4+8 = 15c

week 5       16c

week 6        32c

week 7       64c

week 8       $1.28

week 9       $2.56

by the time you get to the end of the year - week 52 you will get     2^51 approx    2.2518*10^15 cents

That is     week 52          $ 22,518,000,000,000

How is that for mind blowing :)

Hi NavySealFleetAdmiral  Welcome to web2.0calc  forum      

Your question looks interesting :)

When mineral deposits formed a coating 1 mm think on the inside of a pipe, the area through which which can flow was reduced by 20%. Find the original inside diameter of the pipe.

Let the original radius be r

\(Original \;Area =\pi r^2\\ Reduced\; Area =\pi(r-1)^2\\ 100\%-20\%=80\%\\ 80\%\;of\;\pi r^2=\pi(r-1)^2\\ 0.8*\pi r^2=\pi(r^2-2r+1)\\ 0.8 r^2=r^2-2r+1\\ 0.2r^2-2r+1=0\\ r^2-10r+5=0\\ r=\frac{10\pm\sqrt{100-20}}{2}\\ r=\frac{10\pm\sqrt{80}}{2}\\ r=\frac{10\pm 4\sqrt{5}}{2}\\ r=5\pm 2\sqrt{5}\\ r\approx 5\pm 4.47\\ BUT\;r>1\\ r\approx 9.47\;mm\\ \)

Check:    0.8*pi*9.47^2 = 225.3926852858567108

pi*8.47^2 = 225.3806844019199977

Yes close enough :)

Three of the sides are recatngles.  You work out the area for each of those.

The two ends are matching triangles so you work out the area for one of those and double it.

Now add the areas for the 5 sides all together and you have the surface area :)