\(0.85 * 2500 = 2125\)

That wasn't my comment...it was a comment FROM someone TO me.....   I thought it was cool!

Using synthetic division and dividing x^3+kx^2-2x+k+4    by  x+k    results in a remainder of

3k+4     if this remainder is set to = 0    you will find   k = -4/3  will answer this question.

EP: Sorry, but you are "dead wrong!!". You try and get  just a few hundred accurate digits, using the expression as it is written down, and you will have tough time doing it. You have to come up with some tricks and some clever shortcuts to be able to do what I did, because the "exponent" is such a huge number that most arbitrary precision calculators cannot handle it.

THAT was FUNNY.....I sent it out to a few folks too !  

I have never answered a  question like this one either EP.

Don't be afraid to post things that you are unsure of.

 I am sure you have seen me make posts and state quite clearly that I am not sure if it is right.  

The asker always has the ability to accept or dismiss your answer. That is not our responsibility :))

Hmmmm.... I do NOT know if any of these calculations are correct, but here is my try

v = vo + at      (1)

t=10.5 sec

+a = 9.81 m/s^2

-a = air resistance = 1.5 m/s^2  x  v m/s  /  7.5 m/s = .2 v      (2)

Substituting into equation (1):

v = 0 + (9.81 - .2v)(10.5)  = 103 - 2.1v

v+2.1v = 103

3.1v = 103     or v  = 33.225 m/s   at 10.5 seconds

Now let's find the height

x = xo + vot + 1/2 at^2           xo and vo are zero for this application, so we are left with

x = 1/2 a t^2     

x = 1/2 (9.81 - .2(33.225))(10.5)^2  = 174.47 m   (??)

Terminal velocity is where air resistance EQUALS gravity

1.5m/s^2 x v m/s / 7.5m/s  = 9.81 m/s^2

.2 v = 9.81

v(terminal) = 9.81 /  .2  = 49.05  m/s

I am VERY unsure of ANY of this ...I hope someone will confirm it or laugh out loud at my answers!  (I'm almost afraid to post it!)

You are very welcome amnesia :)

You can do a lot of mathematics, including calculus, with limited understanding but the more underlying concepts that you can grasp the easier it all is.  Plus it is MUCH easier to remember, and utilize, and build on concepts that you fully understand. 

You are right, it will be fuzzy for a while. :)

This isn't mental gymnastics -- the computer is doing all the work.

It is like mental msturbation, though!

EP: Just for the sake of "mental gymnastics"!!.

So heres my try on the puzzle. (A bit late ik)

Well I dont have a really good answer.

I first tried to get an answer without decimals( didnt really worked out) the farthest i went with that was 99

without having decimal numbers:

4! * 4 + 3 = 99

But jea i then tried to get 100 by using exponential numbers and then using the gauss bracket to get 100.

Im not sure if this kinda cheating but i got 2 results: (and im not sure if this is the right way to use the brackets)

Gauss bracket [ 3^ 4.sqrt(4) ] = [3^4.2] = [100.9...] = 100

Gauss bracket [ 4! * 4.sqrt(3) ] = [24 * 4.1732... ] = [100.15692...] = 100

Holy Cow!!!!   That is incredible....don't know what you are going to DO with it, but it is pretty cool.

I think I might understood it. Well its still a bit cloudy, but when understanding something new its always cloudy at first and gets better the more I invest into the topic. I might have to look a few more times at your explanations before I fully get the context.Thanks to both you Melody and Alan for all those greate and comprehensive Explanations :) Great stuff to learn from

After the first year,you would have $650 x (100% base + 9% interest)=650x1.09=$708.5

After the second year,you would have $708.5 x 1.09=$772.27

And at last,you will have a total of $772.27x1.09=$841.77

Spend your $190 interest wisely.

If 'percentage added' means compunded annually

FV=PV(1+i)^n    FV= Future Value  PV=Present Value   i =decimal interest (.09)   n = number of periods (3)

FV=650(1.09)^3=841.77

If it is just simple interest    650(.09)(3)+ 650 = 825.50

For a factory having 1000 devices, after inspection 20 devices were defectives, find the probability distribution and the cumulative probability distributions if 5 devices were selected ?

P(defective)= 20/1000 = 0.02

This is a strangly worded question - maybe that is because I don't fully understand it.

Anyway there is a binomial calculator to get what you want maybe.

From its integral definition

\(\displaystyle \Gamma(x)=\int^{\infty}_{0}t^{x-1}e^{-t}\: dt\),

it can be shown that the gamma function has the property

\(\displaystyle \Gamma(x+1)=x\Gamma(x)\).

It can also be shown that \(\displaystyle \Gamma(1)=1\).

It follows that if x = n, where n = 0, 1, 2, ... , and where 0! = 1, that

\(\displaystyle \Gamma(n+1)=n!\)

This relationship holds only when n = 0, 1, 2, ... .

If n is negative or non-integer it becomes meaningless.

\(\displaystyle \Gamma(1.5) = \Gamma(0.5+1)=0.5\Gamma(0.5)\) for example, has a value, it is equal to \(\displaystyle \sqrt{\pi}/2 \approx 0.88623\) ,

but it's wrong to try to relate this to any particular factorial.

Use the table button in the ribbon.

Maybe this will work well ....

I assume you mean 348 plus 25% of 348   =   348 (1 + .25)  = 435

Yes I think that is correct.  Sorry EP you were right.

The price is not based on the length of the jouney or on the time taken. It is based on the speed of the train.

So you are both correct and my answer is wrong  :)

The rail-motor is 1/6 slower than the first train, for which the person is charged $1.20. To see that rail-motor is 1/6 slower, try and solve the following equations based on the clues given: T=3/4.D/A, and:

2T=1/4.D/B, where T is the time taken for the first leg of the journey, D is the distance of the whole journey, A is the speed of the first train and B the speed of the secod. The result is:6B = A. Therefore, the price of the second leg is:$1.20/6 =.20 cents.

The opposite of what?

lots