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How do you factor 3-8u^3?

\(a^3-b^3=(a-b)(a^2+ab+b^2)\\ \\ a=3^{1/3}\qquad b=2u\\ \\ 3-8u^{1/3}\;=\;(3^{1/3}-2u)(3^{2/3}+3^{1/3}*2u+4u^2)\)

Tues 20/10/15

1)  Find the last digit of       3^ (a large number)     Thanks Heureka   

http://web2.0calc.com/questions/help_77727#r3

2) Tricky money one - For the juniors.           Melody

http://web2.0calc.com/questions/finding-the-constant#r2

3) How many lockers are open?  Great puzzle question.    Thanks CPhill

http://web2.0calc.com/questions/math-help_79172#r2

4) Inscribed circle - finding lengths.          Melody

http://web2.0calc.com/questions/geomerty-sum#r1

5)  Manipulating indices.     Melody and guest

http://web2.0calc.com/questions/neml-old-version#r2

6) James Bond, speed, distance and trigonometry.  

http://web2.0calc.com/questions/a-trigonometric-spy-story#r2

7) Find the min and max value of a function.

http://web2.0calc.com/questions/find-minimum-and-maximum-values#r1

Thanks Heureka,

I started doing it the same as you but I have not as yet commited this technique to my brain.

so I got a bit lost.  

Thanks so much for reminding me, maybe next time I will answer one like this myself  

 Could you look at this one please and either answer it or comment on it.  That would be great. :)

Thans you :)

web2.0calc.com/questions/f-x-e-x-x-1_2

@@ What is Happening?  [Wrap4]    Mon  19/10/15     Sydney, Australia Time 9:50pm   ♪ ♫

Hi,

Here are the interest posts:

1)  Number puzzle

     web2.0calc.com/questions/variables_4

2) Difficult limit             Not answered

    This is a repeat question.  I am really hoping some clever mathematican can answer it or at least comment on it.

                Thanks    

    web2.0calc.com/questions/f-x-e-x-x-1_2

3) Find all the roots of a polynomial equation           Thanks Guest and Rom

    web2.0calc.com/questions/solve-the-polynomial-equation-by-finding-all-roots

4) What is Pascal's triangle      (For everyone)       Thanks guest.

    web2.0calc.com/questions/pascals-triangle-pattern

5) Recurring decimals    (Fo rthe juniors)

    web2.0calc.com/questions/if-a-number-has-the-same-repeating-number-after-the-decimal-what-is-it-called-or-what-do-you-put-at-the-end#r2

If you want to comment an any issues please do so.    

Have a great day and I will see you next time  

Thanks Rom,

Decimals that have one digit or a series of digits repeating at the end are called repeating or recurring decimals.

Decimals with a definite end digit are called terminating decimals

In Australia we use a slightly different convention

\(0.333333... is\; written\; as \;\;0.\dot3\\ and\\ 0.07658658658.... is\;written\;as\;\;\;0.07\dot65\dot8\)

Other counties do it slightly differently again.   

I do not think it has been standardized yet.  :)

It is like the decimal point you most likely use.  Some countries use a comma instead :)

What is the units digit of 3^1992?

\(3^{1992} \pmod {10} = \ ?\\\)

\(\begin{array}{rcl} 3^{4} \equiv 81 \equiv 1 \pmod {10} \end{array}\)

\(\begin{array}{rcl} 3^{1992} &\equiv& 3^{4\cdot 498}\pmod {10} \\ &\equiv& (3^{4})^{498}\pmod {10} \qquad 3^{4} \equiv 1 \pmod {10}\\ &\equiv& (1)^{498}\pmod {10}\\ &\equiv& 1 \pmod {10}\\ \mathbf{3^{1992}} & \mathbf{\equiv} & \mathbf{ 1\pmod {10} } \end{array} \)

There is a calculator on the home page ! 

i want to calculate the possibilities of a pattern, its a 10 digit field, you can add all uppercase and lowercase letters and numbers from 0-9, how many possibilities do i need to calculate all possible patterns?

Welll

Capial letter = 26   little letters = 26    digits = 10       That it  62 possible characters for each of the 10 digit field.

So there will be    62^10 possibilities = approx    8.39*10^17

It will most likely take a while to guess the correct combination   LOL    :))

You can do this yourself.  Don't be so lazy!

Lynne walks dogs every day to earn money.The fees she charges per month are 1 dog,$40.2 dogs,$37.25 each 3 dogs,$34.50 each 4 dogs,$31.75 each.A pet store wants her to walk 8 dogs.If the pattern continues,how much will Lynne charge to walk each of the 8 dogs.

40-37.25=2.75

37.25-34.5=2.75

34.5-31.75=2.75

So it is getting $2.75 cheaper with each extra dog.

You see if you can finish it now :)

this question is asking one-year value @ par bond yield. Because value @ par, Yield = Coupon rate. 

Assume face value 100 (can be eliminated later)

Denote Yield to be Y, build up equation to calcuate Bond Yield. 

Left Hand Side you have DCF of Coupon and Principle using 3% and 4%

Righ Hand side you have DCF using Y, 

they are equal. You get a third order equation wil the only unknown variable Y.

you will arrive at answer Y=3.99%

As below:

.

A retired couple has 190,000 to invest to obtain annual income. They want some of it invested in safe certificates of deposit yielding 7%. The rest they want to invest in AA bonds yielding 10% per year. How much should they invest in each to realize exactly $17,200 per year ?

First I am going to assume that you are not diminshing the capital.   So the $17200 is made up entirely of the interest paid.

Let x dollars be invested at 7%   and    (190000-x) dollars be invested at 10%

10% of (190000-x) + 7% of x = 17200

0.1 (190000-x)  +0.07x = 17200

19000 - 0.1x + 0.07x = 17200

1800 = 0.03x

x=60000

I am sure that you can finish it :))

I'm only 14 I want to try this out can someone give me another one? Please

If you have 1 stick and get another stick you have 2 sticks thats 1 + 1 = 2

Here's one way:

\(\begin{bmatrix} 0 && 4 \\ -6 &&5 \end{bmatrix}\\\\ Determinant = (0*5)-(4*-6)=0+24=24\\ inverse = \frac{1}{24} \begin{bmatrix} 5 && -4 \\ 6 && 0 \end{bmatrix}\)

You should watch this vidoe and then do some more examples from the khanacademy site. :)

https://www.khanacademy.org/math/precalculus/precalc-matrices/inverting_matrices/v/inverse-of-a-2x2-matrix

Huh??

What matrix ?

find the inverse of the matrix [1 0 0 ] -1 1 0 1 1 1

Maybe you mean ?

\(\begin{bmatrix} 1&0& 0 \\ -1&1& 0\\ 1&1& 1\\ \end{bmatrix}\)

Let me think about this...........

If you enter this in Google

"how do you find the inverse of a 3x3 matrix"

You will find that a great many people are just dying to teach you this  :))

Adding positive numbers....just add as usual,,,,the answer, of course, will be positive

Adding negative numbers....forget the signs......add as you would two positives......go back and append a "negative" sign to the answer....Example   -21 +  (- 13 )   =  -21 - 13.....Add 21  + 13  = 34     .....append the negative sign to the result   = -34

Numbers with different signs.....this usually causes the most trouble.......here's the "trick'  :

Forget the signs.......take the "smaller" number and subtract it from the "larger"......in the answer, use the sign that was on the "larger" number

Ex :

-21  + 6

Forget the signs

Take the "larger" number, 21, and subtract the "smaller" number

21 - 6   = 15

Now.....use the sign that was originally on the "larger" number.....this is a negative......so....the aswer is :   - 15

One more note....subtracting a negative turns it into a positive

Ex :

-15  - (-9)   =   -15 + 9     and now.....we just use the last rule

15  - 9   = 6   ....and since the "larger" number  was negative......the answer is - 6

Hope that helps......

1. 29x2=58

2. 58+2.50= 60.50

3. 90-60.50= 29.50

The answer is $20.50

Go ahead and post your question(s)

h=L*tan(a)*d-(.5g*(d^2)*(cos(a)^-2)*(L^-2))

Lets try to make sense of this.

\(h=L*tan(a)*d-(.5g*(d^2)*(cos(a)^{-2})*(L^{-2}))\\ h=Ld*tan(a)\quad-[0.5gd^2cos(a)^{-2})*(L^{-2})]\\ h=Ld*tan(a)\quad-[0.5gd^2cos(\frac{1}{a^{2}})*(\frac{1}{L^{2}})]\\ h=Ld\;tan(a)\quad-\frac{gd^2cos(\frac{1}{a^{2}})}{2L^2}\\ \)

At this point I need to ask,  did you intend   cos(a^-2) like I have done

or 

did you intend     (cos(a))^-2

The meaning is not clear.  :(

Is the rest correct, I mean is it what you are asking?

Let P be the cost of a pizza slice and S be the cost of a soft drink.....and we have this system...

8P + 4S  = 29.40

7P + 6S =  30.30     multiply the first equation by 6 and the second by -4  and we have

 48P + 24S  =  176.40

-28P -  24S  = -121.20      add these equations 

20P   = 55.20     divide both sides by 20

P = $2.76

This is a repeat question from yesterday.

Perhaps one of our top mathematicians would like to sink their teeth into it.

I have already ear marked it for our Questions of interest post!

To the asker, hopefully you will get and answer today  (I  am not good with limits)    :))

$18 x 2.9% + 0.30=

Is it: $18 X 2.9% or,..............(1)

$18 + 2.9% + .30=................(2)

(1)-$18 X .029 + .30=$.822

(2)-$18 +  .522 + .30=$18.822

Chose the one you want.