Melody

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 :)

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 :))

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

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  :))

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?

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)    :))

EDIT:  Sorry, I didn't see the point.

18 x 2.9% + 0.30=

=18 * 2.9 / 100   +0.30

=0.522 +0.30

=$0.822

= 82 cents to the nearest cent

Reposted here:

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

Please answer  on  the new thread.    :/