Melody

$$a^3-b^3=(a-b)(a^2+ab+b^2)$$

$$\\\frac{((4x)^3-3^3)}{4x-3}\\\\
=\frac{((4x)-3)((4x)^2+3*(4x)+3^2}{4x-3}\\\\
=\frac{(4x-3)(16x^2+12x+9)}{4x-3}\\\\
=16x^2+12x+9\qquad $Where x cannot = 3/4$$$

Yes that is fine Fiora  

@@ End of Day Wrap  Sun 5/7/15   Sydney, Australia Time   11:45pm  ♪ ♫

Hi everyone,

Today our wonderful answerers were Alan, MathsGod1 Eloise1st, CiciPurple, CPhill, Radix, Badinage and Fiora.  Thank you  

Sat 11/7/15

If you would like to comment on other site issues please do so on the Lantern Thread.  Thank you.    

Interest Posts:

FTJ means 'For the juniors' 

Question 2

What is this shape?          Triangular prism       Correct

If you cut it anywhere, parallel to the front triangle side.  What will be the shape of the cross section?

A triangle      Correct

What is the area of the front triangle? (Show working)

6.4*8.2 = 52.48 . As we are finding the area of a triangle we do the formula L*W/2.   52.48/2 = 26.24cm^2

Yes that is correct

If this was made of mm^3 blocks (some would need to be cut up) How many cubes would be needed to cover the front face?     ???     Well there are 10 mm in a cm so you have to change the dimensions to mm and then work out the area of the front face.   I will leve you to do this.  :)

How many rows of block triangles would you need to make the whole shape?    15.7

if the blocks were 1cm^3 then you would be correct but they are 1mm^3  so you better answer again :)

What is the volume of this shape? (Show working)

Formula = (L*H)/2*W

(8.2*6.4)/2=26.24cm^2

26.24*15.7= 411.968cm^2             No:  Volume is not measured in cm^2

How many mm^3 are there in a cm^3?      You have to show your working.  I don't get the 'mm/cm^3' bit...

If there are 10 mm in a cm ?   Hoe many mm^3 are there in a cm^3?    Try thinking on it :)

Try to re-answer the ones you got wrong please MG  :)

I'll post more questions for you soon :))

Thanks for having a good shot at these questions MG  

Question 1     4 out of 5 for you :)

Look at this shape.  This is made up of cubic blocks  Each side is 1cm. 

What is the area of the front face? (include units) 

36cm^2           Correct

How many cubes are in the front row?

30                  

No there are 36 cubes, the front of the cubes makes up the area that you wrote correctly above

How many rows of blocks are there counting back from the front row?

3 rows                Correct

What is the volume of the prism?

108cm             No it is 108cm^3

Write a sentence as to why.

The formula is (L*H)*W     

Mmm yes I guess so but I wanted you to say that there are 36 blocks in the first row and there are 3 rows so that makes 36+36+36 = 108 cm cubes

or if you prefer, it makes  36*3=108 cm cubed

Hello Fiora,

None of us mind you posting questions like this, it is good that the forum is used in a variety of ways and your challeges are good ones.  

But I think it is polite for you to state that you know the answer and that you are posting it as a challenge to other people if they are interested.

I was very tired last night and spent a long time on your question because I thought you were waiting for an answer.  If I had known that I was doing it only for my own education I would have chosen to use my time differently.

It doesn't matter though, next time I will know.  

$$\\tan(\frac{5\pi}{6})\\\\
=-tan(2\pi\;-\;\frac{5\pi}{6})\\\\
=-tan(\frac{\pi}{6})\\\\
=-tan 30^0\\\\
=\frac{-1}{\sqrt3}\\\\
=\frac{-\sqrt3}{3}\\\\$$