Melody

NOTE:

W+W+3W=95

5W=95

W =  19

Will gets 19,  Debbie gets 19 and  Dave gets  57

Debbie E      Dave  A     Will W

Will has some sweets.

Dave has 3 times as many as Will whilst          A=3W           (1)

Debbie has 3 less than Dave.                            E = A/3   so    A=3E     (2)

So Will and Debbie have the same number of sweets.  3 times less than Dave.    W=E

W+W+3W=95

Will : Dave : Debbie

 W  :     3W :    W                Divide by W

  1   :      3   :     1               

This page was put together on 18/3/16

At this time posts cannot be edited :/

CAMELOT

Royal officials

Hi Gibsonj

The unsigned number part is n!

I don't know about the negative part. ://

log(36÷25)^3+3log(2÷9)-log(2)=2log(16÷125)

\(log(36÷25)^3+3log(2÷9)-log(2)=2log(16÷125)\\ LHS=3log(\frac{6}{5})^2+3(log2-log9)-log2\\ LHS=6log(\frac{6}{5})+3log2-3log9-log2\\ LHS=6log(6)-6log5+3log2-3log9-log2\\ LHS=6log(6)-6log5+3log2-3log3^2-log2\\ LHS=6log(6)-6log5+3log2-6log3-log2\\ LHS=6log(6)-6log5+2log2-6log3\\ LHS=2[3log(6)-3log5+log2-3log3]\\ LHS=2[log(6^3)-log5^3+log2-log3^3]\\ LHS=2[log\frac{2*6^3}{5^3*3^3}]\\ LHS=2[log\frac{2*2^3*3^3}{5^3*3^3}]\\ LHS=2[log\frac{16}{125}]\\ LHS=2log(16\div 125)\\ LHS=RHS \qquad QED\)

Thank you guest.  Do you understand this answer alright Katie-Leigh ?

It looks like there is a lot of explanation there - thanks Guest.

Hi Matt, you have asked me to comment on this so I will.

This is a international forum.  I am from Sydney, New South Wales, Australia. 

All our schools teach Calculus.  Students do not have to take it of course but any student who intends to have a science type degree is encouraged very strongly to do Advanced or extension mathematics.  These are 2 year courses and I'd say approximately 1 of those years is entirely calculus.  :)

5.

For Descartes rule you must look at the sign changes of rthew coefficient

\(f(x)=-2x^3+3x^2-5x-2\\ \mbox{-2 then +3 first sign change}\\ \mbox{+3 then -5 second sign change.}\\ \mbox{-5 then -2 Sign did not change}\\ \)

So there is a maximum of 2 roots on the positive x axis. but they could be complex roots so there are either 2 roots or 0 roots on positive x axis.

Now look at f(-x)

\(f(-x)=2x^3+3x^2+5x-2\\ \mbox{+2 then +3 Sign did not change}\\ \mbox{+3 then +5 Sign did not change.}\\ \mbox{+5 then -2 first and only sign change}\\ \)

So there is 1 root on the negative x axis.

So this graph will have  0 or 2 positive roots and 1 negative root.

I've never seen Descarte's rule before.  I like it to find the number of positive roots BUT once you have the number of positive roots it is easy to know how many negative roots there could be.

For the example above the degree is 3.  This means that the graph will change directions up to three times and it MUST finish in the 4th and 2nd quadrants because the leading coefficient is negative.  -2 to be precise.

Since it changes direction up to 3 times, if it has up to 2 positive roots it MUST have 1 negative root.  I don't need descarte's rule to tell me that.  :)

Here is the graph

Hi Eloise :)

I think it is probably easiest to use a unitary method for these. 

1. It takes 3 pumps 15 hours to fill a swimming pool. How many pumps would it take to fill the pool in 9 hours?

3   pumps       take       15 hours

so 1 pump must take 3 times longer than that.      15*3=45hours

1pump         takes      45 hours

Now 45 divided by 5 = 9 hous which is the number you want.

If you are going to do it 5 times faster then it will take 5 times more pumps   1*5=5 pumps

So

it will take 5 pumps to fill the pool in 9 hours

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

2. It takes 200 tiles to tile a room when each tile covers 36cm2. If I use tiles which covers 25cm2, how many tiles would I       use?

200 tiles    when each is    36cm^2         

If the tiles are only 1cm^2 then the tiles are 36 times smaller and you will need 36 times 200 tiles   36*200 = 7200 tiles (if they are really little just 1cm^2 each)

But the ones we want are 25cm^2 each, that is 25 times bigger than the really little ones.  They are a 25 times bigger so we will need to divide the number of tiles by 25

7200 divided by 25 = 288 tiles.

So if the tiles cover 25cm^2 each, you will need 288 tiles.

You had best buy some extra ones because there will be some cut peices that you will not want to use ;)

This one is MUCH harder than you have made it Solviet.

Nauseated might come up with a neat formula for you but if you want to work it out logically that might be a real challenge ://

I'll think on it ://