All Answers 358108 Answers

You're welcome. When did the operational ancient fossil come? 

and huereka!

Thanks Dragon.  :)

Write the fraction that you want, and then, click the equal button on the calculator. It will give the precise decimal. 

Thanks Dragon.   :)

I guss so. And later on, you can learn more difficult expressions with algebra.

You're welcome.

You're welcome. I always forget. But I remember that I have to write the sticky topic thing.

$$2+2=4$$

You are addin one extra.

When I read the Wnd of Day Wrap, I bet that it would be one of the best.

Yes. If geno3141 takes it too hard, her will spend his power, and be upset, depressed etc.

So, Rom is from Rome.

Let the width be w

the length is  2w-11.75  inches

Perimeter = 2l+2w

$$\\102.5=2(2w-11.75)+2w\\\\
102.5=2[(2w-11.75)+w]\\\\
51.25=2w-11.75+w\\\\
63=3w\\\\
w=21 \;\;inches\\\\
l=2*21-11.75\\\\
l=30.25\;\;inches\\\\
check\\\\
P=2(30.25+21)=102.5\;\;inches\\\\
$all looks good$$$

@@ End of Day Wrap       Wed 1/10/14        Sydney, Australia      Time 10:20 pm      ♬  

Hi all,

Lots of great answers today from Alan, Rosala, NathanDeAlien, CPhill, NinjaDevo, LyleandBrittany, Geno3141, DragonSlayer554, Radio, A sassy ninja, AngelicaMarrufo, Sru, Pyramid and Kitty

Again, i was absent most of the day so I have not answered very many.  Most have received some kind of an answer and that it absolutely the best we can do.  

Now for some interest posts:

1) MacLaurin Series Expansion  (Thanks Alan)

between x=0 and x=6?

$$\\V=\pi \int_0^6\;(5(sin(4x))^2dx\\\\
V=25\pi \int_0^6\;sin^2(4x)dx\\\\
--------------------\\\\
cos(8x)=cos^2(4x)-sin^2(4x)\\\\
cos(8x)=1-sin^2(4x)-sin^2(4x)\\\\
cos(8x)=1-2sin^2(4x)\\\\
(cos(8x)-1)/-2=sin^2(4x)\\\\
sin^2(4x)=\frac{1-cos(8x)}{2}\\\\
--------------------\\\\$$

$$\\SO\\
V=25\pi \int_0^6\;sin^2(4x)dx\\\\
V=25\pi \int_0^6\;\frac{1-cos(8x)}{2}dx\\\\
V=12.5\pi \int_0^6\;1-cos(8x)dx\\\\
V=12.5\pi\left [\;x-\frac{sin(8x)}{8}\right]_0^6\\\\
V=12.5\pi\left [\left(\;6-\frac{sin(48)}{8}\right)-\left(\;0-\frac{sin(0)}{8}\right)\right]\\\\
V=12.5\pi \left(\;6-\frac{sin(48)}{8}\right)\\\\$$

sin(48)=-0.768254661     (remember that it is 48 radians)

$${\mathtt{12.5}}{\mathtt{\,\times\,}}{\mathtt{\pi}}{\mathtt{\,\times\,}}\left({\mathtt{6}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{0.768\: \!254\: \!661}}}{{\mathtt{8}}}}\right) = {\mathtt{239.390\: \!610\: \!267\: \!802\: \!800\: \!8}}$$

$$So I get $ 239\;units^3\qquad $(To the nearest whole number)$$$

The general idea is that we help you solve it.    

Only if N=1 or P=0

Thank you BumbleBee.  I know that I can rely on you to protect our wonderful magical realm.  

It gives 19.34615385 because that is an estimate of the answer.  (there are too many digits to display them all)

No calc will give you 9.333333333333333333333333333333333333333 because that is not the answer.  

Thurs 2/10/14

1) Dragons 'opinion' of us all.   (Thanks Dragon)

I immediately recognise 25,24,7 as being a pythagorean triad.  (Not that you need to use this)

Draw the triangle, in the number plane (the radius it the hypotenuse, the centre of he circle is the origin.)

the y value is positive so theta is in the 1st or 2nd quadrant.

$$\theta = arcsine(24/25)\qquad or \qquad \theta = 180-arcsine(24/25)$$   

arc sin is the same as inverse sin.

$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}^{\!\!\mathtt{-1}}{\left({\frac{{\mathtt{24}}}{{\mathtt{25}}}}\right)} = {\mathtt{73.739\: \!795\: \!291\: \!688^{\circ}}}$$       

  OR

$${\mathtt{180}}{\mathtt{\,-\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}^{\!\!\mathtt{-1}}{\left({\frac{{\mathtt{24}}}{{\mathtt{25}}}}\right)} = {\mathtt{106.260\: \!204\: \!708\: \!312}}$$

$$sin \theta = 24/25

cos \theta = \pm 7/25

tan \theta = \pm 24/7$$

Dragon is the champion of Camelot!  What would we do without our Slayer??

Kitty is our Princess.  Every magic realm needs its princess.  

-----------------------------------

OR you can make it just one fraction by finding a common denominator.  Hint , it will be 7*5=35

Not quite Pyramid,    

You have to simplify by adding like terms.

5x+4x-8x=1x =x

-68+34=-34

so the answer is       x-34       

Hi Alan,

I don't know about this stuff so I am just using your formula and a bit of logic (most likely incorrect)

"If α is the linear coefficient of thermal expansion then

 α = change in length/(original length*temperature change)"

$$\\11\times 10^{-6}=\frac{\triangle l_s}{23.89\times 195}\\\\
\triangle l_s = 11\times 10^{-6}\times23.89\times 195 \\\\$$

$${\mathtt{11}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{\left(-{\mathtt{6}}\right)}{\mathtt{\,\times\,}}{\mathtt{23.89}}{\mathtt{\,\times\,}}{\mathtt{195}} = {\mathtt{0.051\: \!244\: \!05}}$$

$$\\\alpha_R=\frac{\triangle l_s+(24.01-23.89)}{23.89*195}\\\\
\alpha_R=\frac{0.05124405+0.12}{4658.55}\\\\$$

$${\frac{\left({\mathtt{0.051\: \!244\: \!05}}{\mathtt{\,\small\textbf+\,}}{\mathtt{0.12}}\right)}{{\mathtt{4\,658.55}}}} = {\mathtt{0.000\: \!036\: \!759\: \!088\: \!128\: \!3}}$$

$$\\\alpha_R=3.7\times 10^{-5} $ per degree celcius$ \qquad \\
$(correct to 2 significant figures)$$$

Is this correct?

n is the POSITION OF THE N'TH TERM.

IN THE SEQUENCE   3,5,7,9,11,.....

The second term is 5

the 5th term is 11

the n'th  term could be written as 2n+1

In this context n cannot be 0.  What is the 0th term?  It does not make sense!