All Answers 358090 Answers

-74.8888888888888889

Cheers Alan. I just noticed you can't do a 3 x 1 for the constants matrix. Unless i'm missing something (which is very possible!) 2 is the lowest i see in the options.

Not too much of a problem multiplying the inverse with the constants and adding everything up to get the answers just by hand. But it would be nice to just have that constant matrix with the 3 rows 1 column option and multiply it straight with the SC.

What do you think is the best route for calculating these systems of equations say if you have more than 3 equations? There are so many options, sometimes as a relative novice you're in a bit of a quandary as to what to use.

I was reading about Cramer's rule but the Algebra book i'm looking at says that get's more involved and is a bit more work. I think it looks quite a good way to calculate though.

For me i think after you know the steps to take to set up the equations in matrix form, using a calculator like the SC would be best as it saves you a major headache!!!

[PERCENTAGE]/100
50% =1/2
34%=17/50

thank you Aziz!

Thankyou Rosala

That is a really lovely welcome back.

The Queen I most pleased. 👸

Good Melody!happy to see you back!

So now i would like to hand over your precious forum to u!i've taken its care a lot ...as it was in my hands ...remember!

At last i am going to get to read the day wraps!when u were not there , my day ddint even wrap itself!lol!

See i have made arrangements to welcome our beautiful Queen!

The kingdom of Camelot welcomes the queen!

I assume we have

∫x^(-3/4) dx

So we have

4[16^(1/4) - 1^(1/4)] =

4[2 - 1] =

4 [1]  = 4

....؟؟

(3/4)-(2/5*7/12)

3/4 -[(2/5)*(7/12)]       perform the multiplication in the brackets, first

3/4 - (14/60)         reduce 14/60 = 7/30

3/4 - (7/30)

[30(3) - 4(7)] / 120

62/120 =

31/ 60

22-32-5x3-6=30

(22-3(2-5)x(3))(-6) = 30

(22 -3(3)x(3))(-6) = 30

(22 -9x(3))(-6) = 30

(22-27)(-6) = 30

(-5)(-6) = 30

Whew!!!...that one was pretty tough !!!!

Tues 19/8/14

Lets end the day with a laugh - Thanks Rosala

@@ End of Day Wrap :     Mon 18/8/14          Sydney, Australia     Time 11:15pm      ♬  

Hello all,

Well I am back!  I have travelled 2000km (by car) in the last 5 days and attended a wedding.  How about that!

I have been really lucky to have DragonSlayer (the Defender), and Bumblebee (The Queens eyes and ears) caring for camelot while I have been away. Thank you, you have done an excellent job.  Thanks also to Chris and Alan, Aziz and Rosala, Ninja, Kitty and Zegroes.  Plus anyone else who has helped.  I really do not know who has been answering all the questions while I have been preoccupied.  I've been on the forum for many hours this afternoon but I did not get very far I am sorry.  

Also, now that Mr. Massow has changed the layout it is more difficult for me to collect all the answerer names. 

Anyway, I will do the best I can.

If anyone writes or sees an excellent answer or post could you please let me know so that I can ask Ninja to include it in one of his threads.  

Ninja, are you about.  I don't remember stumbling over any of your posts recently? There are a couple of threads here I would like you to archive.

Here are a couple of threads that I put aside.  I am sure there are many others.  I have not seen a lot of the posts, again I am sorry.

What to do to combat pop-ups 

This isn't a perfectly linear relatioship....using a line of "best fit" calculator to model the data in a linear fashion as closely as possible, we have

y = 3.117143x  - 1.676190

y =  3.117143(6)  - 1.676190 ≈ 17.03 on Day 6

y =  3.117143(7)  - 1.676190 ≈ 20.14 on Day 7

There may be other functions that will fit the data more closely - (perhaps a  polynomial?? ).....but I'm not sure......

6x2 - 5x - 4 factors nicely into (2x + 1)(3x - 4)

$$6x^2-5x-4$$

To factor this you have to look for 2 numbers.

They have to multiply to give 6*-4=-24

Since this is negative, one of the numbers will be negative and the other one is positive.

They have to add to -5  this means the larger digit will be the negative one.

6*4=24 but there is no way these will add or subtract to give -5

2*12=24 but thes can't make -5 either.

8*3=24 and 8-3 is 5 they might be helpful.  How about 3-8=-5 excellent and 3*-8=-24 So the numbers are 3 and -8

We are going to split -5 up into -8x+3x  like this

$$\\6x^2-5x-4=0\\
6x^2-8x+3x-4=0\\$$

NOW we will factorise in pairs.  Like this:

$$\\2x(3x-4)+1(3x-4)=0\qquad so\\
(2x+1)(3x-4)=0\\$$

That is how I would do it.

HOWEVER

If the factors cannot be found easily it is easier to use the quadratic formula.

$$\\6x^2-5x-4=0\\
a=\;6\quad b=\;-5\quad and \quad c=\;-4 \\$$

$$\\x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\
x=\frac{5\pm \sqrt{(-5)^2-4*6*-4}}{2*6}\\\\
x=\frac{5\pm \sqrt{25+96}}{12}\\\\
x=\frac{5\pm \sqrt{121}}{12}\\\\
x=\frac{5\pm 11}{12}\\\\
x=\frac{5+ 11}{12}\qquad or \qquad x=\frac{5- 11}{12}\\\\
x=\frac{16}{12}\qquad or \qquad x=\frac{-6}{12}\\\\
x=1\frac{1}{3}\qquad or \qquad x=\frac{-1}{2}\\\\$$

Quadratic equation links:  It would be goof for you to look at these links.  

Nothing much with me , just preparing for tomorrow's test!What about you!

Z scores.

Half the area is 0.17 the whole area is 0.17*2=0.34  

The area represents the probabliity that the score will fall in this region.  That is why the area under the whole curve has to be 1.  If something has to happen it has a probability of 1.

An area of 0.34 means that 34% of all the scores are expected to lie in this region.

That is 34% of all the data will have z scores of between -0.44 and 0.44

I hope that makes sense.  

One, it cost $1.06.  The dogs will love it!  

LaTex  Dragon's question also answers Stu's question.

 Question 2) Why do I have to use $$, \begindocument, and \enddocument in @@LaTex? Please help me. Thanks.

 You do not need to use any of this dragon.  Not in this forum anyway.

 Alan and I do use $$ sometimes.

 When writing in Latex you can be in maths mode or in non-maths mode.

 In this forum the default mode is maths mode.  If you do not want this you can cancel it at the very beginning of your program by entering $$  However, you do not need to do this.  You can just work in maths mode which is what most people do.

 This symbol \ is called a backslash

\\ means start a new line.  This is not done automatically you have to 'tell the code to do it' with this command.

 One \ indicates a function is coming.  Sometimes functions have 1 or more 'arguaments' these must be put in parentheses { }

 like \frac{1}{2} or \sqrt{49} or \quad

 If you want to display a $ sign you need to put \$ because $ is a reserved key and so this will symolise that it is ONLY the symbol itself that you want.

 Now Dragon.  Yes if you want to do something that has been demonstrated.  Just copy the code and change little things.  You will slowly gain understanding about what everything means.

 I hope that all this information helps.  

How to draw an answer box in LaTex. Or any box for that matter.

\fbox{\begin{minipage}{0.6cm}\hfill\vspace{0.6cm}\end{minipage}}        $$\fbox{\begin{minipage}{0.6cm}\hfill\vspace{0.6cm}\end{minipage}}$$

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

5x= 21-2x what does x mean

In primary schoool it might have been written like this.

$$5\times
\fbox{\begin{minipage}{0.6cm}\hfill\vspace{0.6cm}\end{minipage}}
=21-2\times
\fbox{\begin{minipage}{0.6cm}\hfill\vspace{0.6cm}\end{minipage}}$$

EXACTLY the same number has to go in both boxes to make the statement true.

The box has been replaced with the the letter x.  The idea is to solve the number sentence to work out what x is.  You will learn all sorts of techniques to be able ot do this easily.

Let's make this a bit easier to understand and to solve.

We will pretend that the the boxes are two identical bags of lollies and you want to know how many lolies is in each bag.

5bags = 21lollies - 2bags 

We can add 2 bags to both sides then we will have 

7bags = 21 lollies

7*3=21

So there must be 3 lollies in each bag.  3 goes in the the box.  

So if 

5x=21-2x then 7x=21 and x=3

I hope that helps.  

Homework 3.2

Sally has 3 dogs, one day she was walking home from work and bought a dog toy for her 3 dogs. The toy was $1.06. How many cats does Sally have?

This is an approximation of pi.

Pi is an irrational number so it cannot ever be written exactly in digits.   

Thank CPhill!i'll just do it!Points for u as well!

deleted!

The phase shift is -3 

The amplitude is 1 and the wavelength is 2pi units