Math Is Fun Forum

hi Brendon,

If you put the variables at the top of a workbook then all formula cells should update when you change prices.  The only thing to watch for, and it happens in Access as well, is that a price increase will show up in all the old contracts as well which means your achives are wrong.

You can make an archive copy on a separate workbook page using paste special, paste values,  that will prevent subsequent changes to old data.  It should be possible to automate this but I think it means learning how to make macros.  You might prefer to steer clear of that and just do it 'manually' (ie. copy and paste special) when a contract is complete and when you are about to update your charges.

Before I retired I taught maths and ICT.  The Advanced level ICT course required students to do the sort of thing we've been talking about, as coursework, so mail again if you want to know how to do something.  I had quite a few worksheets on 'how to do xxx' , mostly for Access, which I could make available if you're interested. 

[http://www.bundy.demon.co.uk/rbuhelpfiles/aanRBUhelp%20Page.htm]

Bob

hi Onyx

To construct an algorithm to 'do' division you would have to start with the most significant bit.  To shorten the visible working I left out all the leading zero steps and started when the dividend had 5 bits like the divisor.

I noticed that the dividend (5 bits) was smaller so I entered a zero in the quotient and 'brought down' the next bit.  This time the dividend was clearly bigger (having 6 bits) so I subtracted.

The subtraction, as displayed,  is correct;  the step you highlighted  is 45 - 27 = 18 in base 10.

So where did you get the idea you only need to XOR the bits?    Have a look at

http://www.cs.uaf.edu/2000/fall/cs301/notes/node54.html

Added later:  Do subtraction by taking the 'twos complement' and adding.

Bob

hi learn_everything,

Having taught maths to children from age 11 to 18 for many years, I can understand why you, also, want to know "Why do I need this?"

I did try to show uses of a particular peice of mathematics, but sometimes it is hard to do this before the student has learnt enough to apply what has been learnt.

I also happen to think that the study of maths is good brain training; like doing sudoku or hard crosswords.

Also you can never be sure that an area of maths that seems to have no practical application, might one day become useful.  A good example of this is in the number theory surrounding prime numbers.  For years it just seemed to interest mathematicians and no one else.  And then the internet was invented and now this theory is an essential part of internet security.  You may not realise it, but every time you put in your on-line bank password, or send your credit card details, you are relying on prime number theory.

There are also some mathematicians who think that it is good to study maths just because 'its there'.  When my son completed his thesis in (S5, S5) amalgams and gained his PhD, I asked if I, as his supporting father and a taxpayer, could expect any practical use for all his work.  With a great deal of pride and a cheeky grin he said "Certainly not!" and I agree with him!

In the summer of 1999 I achieved one personal ambition when I arranged a holiday in Fuschel, Austria to witness the total solar eclipse.   The mathematics that enables astronomers to predict such events is complex and I think it involves square roots (plus a lot more).  My reason for making the pilgrimage was to see the prediction in action.  And thousands of others felt the same.  It's very satisfying to have a 'model' for something in the real world, work out that that means X will happen, and then see it happen.

And here's another thing:  Some of us think "Maths Is Fun"!

Bob

hi Onyx

I have set your division out like a long division.  The nice thing about doing this in binary is that there are only two possibilities at each stage;  either the dividend is smaller than the divisor, in which case write a zero in the quotient; or not, in which case write a one and subtract to get the remainder.  Do this for each step until you run out of dividend.

(glossary:  Your P is called the dividend; Q the divisor;  D the quotient; R the remainder.)

Here the quotient is 11011 and the remainder 1.

So you should be able to test the subtraction for negative; put zero or one in the answer bit; and roll for the next digit.

Is that what you were after?

Bob

hi b31den

Sorry not to have responded sooner.  I wasn't 100% about how I'd tackle this, so I waited to see someone else do it.

But no such luck, so I've had a think and this is my method.

Let S be the amount of impurities in the storage tank. (initially 5)

Then change in amount with time

So separate the variables and integrate from S = 5 to S = 0.5.  (are you OK to do this?)

I made it just over 85 mins.

To check my method, I have made a spreadsheet version with increments of 1 minute; calculating the amount of impurities removed and re-calculating how much is left for the next minute of processing.

This gave a close agreement with my integration method.

Hope that helps, 

Bob

hi bobbym,

Oh wow!  So much to consider and so many questions.  It would take a long time to address them all.

But here's where I stand on teaching maths:

When a 'reluctant_to_do_maths' child asks "What is the point?" ; "When will I ever use algebra again?", my answer is that the purpose of 'doing maths' is to make you think.  Exam grades are just a way of proving that you must have done some thinking; the real benefit is that the grey matter has been stretched.  If your brain is hurting from all that thinking, then it must be doing you good.

Analogy:  An athlete may do weight training even though his/her sport is, say, long jump.  Why?  To build up some muscle / stamina /coordination.  Doing algebra is one way of building up mental muscle.

Bob

Hi again,

I see what's wrong.  You cannot use

because that's a position vector for the original plane.  You need one for the new plane so choose from

Then it will work. :)

Bob

hi AISSAISHAK

Your posts show you as a guest not a member.

At the top of the page there is a register button.  Click this, agree to the rules, and fill in your details.

You will get emails if you 'subscribe' to a post thread.

Hope that helps, welcome to the forum,

Bob

hi Au101

OK. Here we go.

There are three forms for the equation of a plane (that I can think of, there may be more).

They are:
form 1

form 2; the dot product form

and
form 3

The first form is derived from the diagram in post 20.

This is the position vector for a point in the plane

and

are two vectors lying in the plane.

In the second form

is a vector that is perpendicular to all vectors lying in the plane.  r and n are being 'dotted' together and the result is a constant.

If you then replace 'r' by

and do the dot product

you get the cartesian version that is the third form.

From this you can see that form 2 and form 3 are the same plane.

Less obviously, so is form 1.

Proof:

In form 1  put lambda = 1 and mu = 1           and you get            x = 3,  y = 3,   z = 1
               put lambda = 1 and mu = -1          and you get            x = 1,  y = -1,  z = -1
               put lambda = 0 and mu = 1           and you get            x = 2,  y = 3,    z = 2

If you try each of these sets of values in x - y + z you get 1 every time.

So form 1 and form 3 have three non-collinear points in common.  That's enough to prove they represent the same plane because you only need three points to define a plane (provided they are not in the same straight line).

Now to the question.

You know the equation of the plane before the transformation.  The book method transforms points directly from this equation to get the equation after the transform.

I think the algebra for this is a bit horrid and you still have to convert it into form 2.

So my method was to pick three points in the plane and transform them.  Let's call them A, B and C.  That's just number work.  ***

Now get two vectors in the plane by doing AB = AO - OB etc.

Any two will do because, provided they are not parallel, any two vectors will 'span' the plane ie. will enable you to reach all points in the plane.

Now to get the vector that's at right angles to both these vectors.

Imagine by some trick of gravity you can stand on the plane with 'up' meaning 'at right angles to' the plane.  If I asked you to point a stick at right angles to the plane it would go straight up.  If you draw any line on the 'ground' = 'the plane'  , it would be at right angles to the stick.  And it wouldn't matter how long the stick was.  A stick twice as long, would still be at right angles to every line in the plane.

Call the vector at right angles

So do a dot product between one vector in the plane and 'n' and set it equal to zero.  Do again for the second vector.

You've got 2 equations with a, b and c as unknowns.  Choose any 'a' to make the calculations easy.  That will enable you to work out 'b' and 'c'.  That gives you a possible 'n' the vector perpendicular to the plane.  You might think it is cheating to choose 'a'.  But if you had chosen an 'a' that was twice as big, you'd have got 'b' and 'c' twice as big as before so all that would happen is you'd get '2n' for the perpendicular vector.  You can use any vector that is at right angles so the first would do!

Now to get 'p'.

The equation

is the equation for all points, 'r', in the plane.

Back at point *** we had three possible points so 'sub' in any one set of x, y and z values and you'll get 'p'

Check by 'subbing' in the other values from *** to see if you get the same p.

Problem done! 

Does that all make sense?

Bob

hi bry

First answer is correct! 

So 'plug in' weight = 25 N and acceleration = 10 (approx should be ok here) to get the mass in kilos

then density from top formula.

Bob

ps  you could make a picture in 'Paint', save as a GIF and do an image upload next time

hi

I see you are logged on at the moment.  I've just come in from gardening to have lunch.  I'll keep the computer running but you'll have to wait until later for the example as I want to take advantage of the light and fine weather to complete the garden jobs.

Bob

Your last post:

Did you mean that?  You cannot make a plane with the same vector for all three components.

Bob