All Answers 358460 Answers

School for me starts tomorrow Melody

oh no, this cant be happening!!!!

god **** it! School means more annoying *****, i liked it a whole lot better when it was summer...

$$\small{\text{Factorize $(81b^4 - 18b^2 + 1)$. }}\\\\$$

$$\small{\text{$
\begin{array}{rcl}
81b^4 - 18b^2 + 1 \\
&=& [9b^2-1]^2 \\
&=& [(3b-1)(3b+1) ]^2\\
&=& (3b-1)^2(3b+1)^2 \\
&=& (3b-1)(3b-1) (3b+1)(3b+1) \\
d. &=& (3b+1)(3b+1) (3b-1)(3b-1) \\
\end{array}
$}}$$

Well off the top of my head I will say that only a function can be differentiated. So it is very important for calculus. AND calculus is an immensely important branch of mathematics.

• The square root of 10, or 10 radical 2, or the square root of 10 is written as ²√10 or √10 = ±3.162278

COOL! Why is it important to know this?

What does it mean mathematically?

@@ End of Day Wrap  Tues 11/8/15     Sydney, Australia Time   11:46pm    ♪ ♫

Hi everyone,

Some students must be back aty school, the forum seems a little busier.  We has some great answers today from Geno3141, Alan, jdh3010, Heureka, Parke, ShimmyCocopang and TitaniumRome.  Thanks  

Thanks Denzel, I enjoyed your clips.  I didn't know school detentions could be so much fun. LOL

The last one was pretty cool too   

There isn't one 

The degree of a polynomial is the highest power.        theis time its 1

The leading term is the one with the highest power.          3x

The leading coefficient is the coefficient (number in front) of the pronumeral with the highest power.   3

I haven't heard the expression number term before.  I suppose I might call it the independant term but it is 12

This is a simplistic view.  There is a mathsisfun web page that deals with this more fully :)

Here is a number of sites that cover this topic.  Why don't you take a look.  :)

Thanks jdh3010 too  

Thanks Alan, I learn something every day :))

$$x^{\frac23} \cdot y^{\frac13}\\\\
=(x^2)^{\frac13}\cdot y^{\frac13}\\\\
=(x^2\cdot y)^{\frac13}\\\\
=\sqrt[3]{x^2\cdot y}$$

Nice work Heureka :))

Well, that is an approximation anyway :/

A Mach number is a measure of speed.  It is the speed of the plane divided by the speed of sound.  For example, a plane flying at Mach 2 is travelling at twice the speed of sound.

.

What is mach?

Thanks Alan :)

Say you want to enter 3 and a half - 6 and a quarter

you do it like this

(3+1/2)-(6+1/4)     don't forget the brackets   :))

$$\left({\mathtt{3}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{2}}}}\right){\mathtt{\,-\,}}\left({\mathtt{6}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{4}}}}\right) = {\mathtt{\,-\,}}{\frac{{\mathtt{11}}}{{\mathtt{4}}}} = -{\mathtt{2.75}}$$

As of 11 August 2015 it still isn't working!

.

Thanks Alan, 

I had started the pic before you posted I just kept getting side tracted :)

Thanks Melody, the picture makes it much clearer.

.

Hi Parke,

Welcome to the forum :)

The first wire is h long, the second is 2h long    the last one is f h long

h, 2h, 3h, .......  f h

This is an arithmetic progression.  The first term is h, the common diff is h  the last term is f h

The sum of all these terms is given by the forumula

$$s_n=\frac{n}{2}(a+L)$$          n=f,     a=h,    L=f h

$$\\S_f=\frac{f}{2}(h+f*h)\\\\
S_f=\frac{f*h}{2}*(1+f)\\\\$$

tan A = 2/3 and tan b= -3/5 . what exact value of cot (A-B)

$$\small{\text{$
\boxed{~\cot{(A-B)}
=\dfrac{ 1+\tan{(A)} \cdot \tan{(B)} }{ \tan{(A)} - \tan{(B)} }
~}
$}}$$

$$\small{\text{$
\begin{array}{lcl}
\cot{(A-B)} &=&\dfrac
{ 1+\dfrac23 \cdot \left(\dfrac{-3}{5}\right) }
{ \dfrac23 - \left(\dfrac{-3}{5}\right)}\\\\
\cot{(A-B)} &=&\dfrac
{ 1-\dfrac23 \cdot \left(\dfrac{3}{5}\right) }
{ \dfrac23 + \dfrac35 }\\\\
\cot{(A-B)} &=&\dfrac
{ 1-\dfrac25 }
{ \dfrac23 + \dfrac35 }\\\\
\cot{(A-B)} &=&\dfrac
{ \dfrac35 }
{ \dfrac23 + \dfrac35 }\\\\
\cot{(A-B)} &=&\dfrac
{ \dfrac35 }
{ \dfrac{19}{15} }\\\\
\cot{(A-B)} &=& \left(\dfrac35 \right) \cdot \left(\dfrac{15}{19}\right)\\\\
\mathbf{\cot{(A-B)}} & \mathbf{=} & \mathbf{\dfrac{9}{19}} \\\\
\end{array}
$}}\\\\$$