All Answers 358233 Answers

oh goodness i cant eat anymore.......i gift that to you CPhill...enjoy!

Here is a video clip on monster prime numbers.

It is done by an Australian who is both a mathematician and a comedian.     Enjoy    

Yes,

Welcome to the forum Mikayla.      

Here's your breakfast, rosala....come and get it...!!!

5m-3-2m

5 mats -3 -2mats

= 5mats-2mats - 3 (not mats)

=3mats - 3    

=3m-3

When you are adding and subtracting algebraic terms it can help if you think of the letters (or groups of letters) as things 

You can only add terms (things) together is they are like terms ( the same things)

That is a broad field.  Do you want to give us an example of what you want to solve.

This might help

3 does not go into 112 so I can see straight off that it cannot be simplified.    

well....we have lunch at 2pm so this was my brunch!actually i woke up at 11am then lay on the sofa wrapped in my blanket watching TV......then i remembered "oh i need to have breakfast"......LOL

A towel dries you as it gets wet    

Sorry - this has already been answered.   

Hold on a bit here.

$$\\(-2)^2=-2*-2=4\\
but\\
-2^2=-2*2=-4$$

It is very important that you work out the difference.   

rosala....1:30 PM  sounds more like something I usually call  ...."lunch"

the coordinates of the points A and B are (-4,5) and (-5,-4) respectively.A' is reflection image of A with respect to y-axis.B is rotated anticlockwise about the origin O through 90^。     to B'

isA'B perpendicular to AB'?explain your answer.

$$\small{\text{
The vector dot product $\vec{A'B} *\vec{AB'}=0$, if $\vec{A'B}$ perpendicular $\vec{AB'}$ .
}}\\$
\small{\text{
We calculate: $\vec{A'B} = \vec{A'}-\vec{B}=\left(\begin{array}{c}4\\5\end{array}\right)-\left(\begin{array}{c}-5\\-4\end{array}\right)=\left(\begin{array}{c}4-(-5)\\5-(-4)\end{array}\right)}=\left(\begin{array}{c}9\\9\end{array}\right)$
}}$\\$
\small{\text{
and calculate: $\vec{AB'} = \vec{A}-\vec{B'}=\left(\begin{array}{c}-4\\5\end{array}\right)-\left(\begin{array}{c}4\\-5\end{array}\right)=\left(\begin{array}{c}-4-4)\\5-(-5)\end{array}\right)}=
\left(\begin{array}{c}-8\\10\end{array}\right)
$
}}$\\$
\small{\text{
$\vec{A'B} *\vec{AB'} =\left(\begin{array}{c}9\\9\end{array}\right)
*\left(\begin{array}{c}-8\\10\end{array}\right) =9*(-8)+9*10=-72+90=18
$
}}$\\$
\small{\text{
$18 \ne 0 $ so $ \vec{A'B} $ not perpendicular to $ \vec{AB'}$
}}$$

Geno and anon are of course correct.  

I am just going to look at WATER

1 litre of WATER weighs 1Kg.        

plus    

The rest is not just for water it is for any fluid

a cube that has sides 10cm will hold 1 litre of water.

$$10*10*10=1000cm^3\\



1 litre \equiv 1000cm^3 \equiv 1000ml

therefore

1cm^3\equiv 1ml$$

It is really handy to remember this.

Hi Mathew,

Pi is NOT infinite - Pi is an  irrational number      

irational numbers do have an infinte number of decimal places but the number it self is definitely not infinite (not infinity)!

Thanks for your answer.  I hope that you are learning as well  

Yes   $$\sqrt{\pi}\;\;is\;\;\;irrational\;\;too$$

$${\sqrt{{\mathtt{\pi}}}} = {\mathtt{1.772\: \!453\: \!850\: \!905\: \!515\: \!9}}$$

This is an approximation.

I probably should take my own advice.  LOL  

I keep having problems with Google Chrome    

$$11^2+-2=121-2=119$$

Thanks Alan 

4x^2-bx+(5-a)     ...I'm assuming that the "optimal value" occurs at the vertex

Taking the derivative of this, we have

8x - b ....  this gives the slope at any point...and since the slope at the vertex = 0 and the x value of the vertex = 10, we have

8(10) - b = 0  →   b = 80    and substituting this back into the original function, we can solve for "a"  thusly:

15 = 4(10)^2 - 80(10) + (5 - a)     simplify

15 = 400 - 800 + 5 - a     rearrange

a = 400 -  800 + 5 - 15  = - 410

So   a = -410 and b = 80 

And our function is

y = 4x^2 -80x + 415

How do I find the height of a triangle without the area??

$$\boxed{h_c=\dfrac{a*b}{c}}$$

How to add two angles   (-37.66deg -122.47deg)

This doesn't make sense to me......(anyone else ???)

(-1)ⁿ⁺¹(3)^n-1    ....where n is the nth term.....

So...you don't get paid for [5 x 1/2] hrs = 2.5 hrs out of every 40

So we have

(40 - 2.5) *(15) = 37.5 * 15 = $562.50   ...  just as Anonymous found...

√3 *√51  =

√3 *√(3 * 17) =

√3*√3*√17 =

3√17

4x^2 - bx + (5 - a)   we need to "complete the square," here.... first, factor out the 4...

4 [ x ^2 - (b/4) x + (5-a)/4]   ...take (1/2) the coefficient on the x term, (b/8), square it, and add and subtract it

4[ x ^2 - (b/4)x + (b^2/64)  + (5-a)/4 - (b^2/64)] =

4[(x - b/8)^2 + (16(5-a) - b^2)/64 ] =

4(x - b/8)^2 + [ (80 - 16a - b^2) / 16 ]