Melody

simplify the square root of 144g to the power if 8

\((\sqrt{144g})^8\\ =(\sqrt{144}*\sqrt{g})^8\\ =(12*\sqrt{g})^8\\ =12^8*(\sqrt{g})^8\\ =12^8*(g^{1/2})^8\\ =12^8*g^{(1/2)*8}\\ =429\;981\;696\;g^{4}\\\)

arc tan is the same as inverse tan

just hit [2nd] [atan] 

I assume that IS the derivate and you just want the equation solved

\(0 = {{\pi x(10(\sqrt{225-x^2}+15)-x^2})\over{\sqrt{225-x^2}}}\\ 0 =\frac{{\pi x(\sqrt{10\sqrt{225-x^2}+15)}+x)(\sqrt{10\sqrt{225-x^2}15)}-x})}{{\sqrt{225-x^2}}}\\ x=0\:\;\:or\;\;(\sqrt{10\sqrt{225-x^2}+15)}+x)=0\;\;or\;\;(\sqrt{10\sqrt{225-x^2}+15)}-x)=0\\ x=0\:\;\:or\;\;(\sqrt{10\sqrt{225-x^2}+15)}=-x\;\;or\;\;(\sqrt{10\sqrt{225-x^2}+15)}=+x\\ x=0\:\;\:or\;\;10\sqrt{225-x^2}+15=x^2\\ x=0\:\;\:or\;\;\sqrt{225-x^2}=\frac{(x^2-15)}{10}\\ x=0\:\;\:or\;\;225-x^2=\frac{(x^4-30x^2+225)}{100}\\ x=0\:\;\:or\;\;225-x^2=\frac{(x^4-30x^2+225)}{100}\\ x=0\:\;\:or\;\;22500-100x^2=x^4-30x^2+225\\ x=0\:\;\:or\;\;x^4+70x^2-22275=0\\ \)

\(x=0\:\;\:or\;\;x^4+70x^2-22275=0\\ x ^2= {-b \pm \sqrt{b^2-4ac} \over 2a}\\ x ^2= {-70 \pm \sqrt{4900+4*22275} \over 2}\\ x ^2= {-70 \pm \sqrt{94000} \over 2}\\ x ^2\approx {-70 \pm306.6 \over 2}\\ x ^2\approx {-70 \pm306.6 \over 2}\\ x ^2\approx 118.3\\ x\approx \pm10.9\\~\\ so\;I\; get\;\\~\\ x=0\;\;or\;\;x\approx \pm10.9\)

You probably should check those 2 approx answers though.   ://

Mmm I do not think it is right.  

I am not sure I am answering the right question anyway.://

x=0 is definitely a solu​tion to the question that I answered.  ://

Just like this

6*6^2*tan(pi/6)

But make sure you set the units to radians.  There is a toggle button for this on the bottom left of the calculator.

How would I prove that "tan(x+1)2 = (1+sin(2x))/cos2x" ?

It is not clear what you want me to prove....

\(tan(x+1)^2 = \frac{1+sin(2x)}{cos2x}\\ or\\ tan(x+1)^2 = \frac{1+sin(2x)}{cos^2x}\\\)

The symbol for power on the net is ^

ex       3^2=9

Could you please rewrite your question clearly.

0<x<1, 2x<y<3x, xy/5<z<5xy

You are told x is between 0 and 1

I seperated the rest into 4 different constraints

2x<y

y>2x

The smallest 2x can be (not quite) is 0 so y>0

y<3x

The limit for 3x is 3 so y has to be smaller than 3

0<y<3

xy/5<z

z>xy/5

the lower limit for x is 0 and the lower limit for y is 0 so 

xy>0

xy/5>0

z>0

z<5xy

The upper limit of xy is 1*3=3

so the upper limit of 5xy is 15

z<15

0<z<15

limit constraints

0<x<1

0<y<3

0<z<15

NO

\(\frac{2}{5}\times 2 = \frac{4}{5}\\ 1\frac{4}{3}\;\mbox{is not even a proper mixed numeral - the little number has to be on the top of the fraction.}\)

-14  +63 =  +63  -14    = 63-14 =   ???

No,

mm stands for millimetres and m stands for metres

There are 1000mm in a metre

So that means there are 1000^2 mm^2 in a metre^2

and there are 1000^3 mm^3 in a metre^3

so

\(1,000,000,000 mm^3=1m^3\\ or\\ 1mm^3=10^{-9}m^3\)

Hi MWizzard :)

You lost me here

23.1406926328 = i√ i5

you wanted

\(\sqrt[i]{-1}=\ {(-1)}^{1/i}\\ Where\; did\; your\; i^5 \;come\; from?\;\;i^5=i \;\;but\;so\;what?\)

I might be missing something ://