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e is the Euler constant, defined as lim[1 + (1/n) ]ⁿ  as n --> infinity.

"f(x)"  is read as  "f of x"  and represents "the function whose name is 'f' and whose variable is 'x'".

The letter "f" doesn't have to be used...

y = 3x - 1  is the same as  f(x) = 3x -1  is the same as  a(x) = 3x - 1  is the same as  b(x) = 3x - 1  etc.

x!  =  x·(x - 1)!     with  0!  defined to equal  1.

So, if you know (x - 1)!  it isn't too difficult to find  x!.

However, if you are trying to find x! and you don't know  (x - 1)!  and don't have a calulator/computer,  you get to start at the beginning ...

2(x - 4) - 5x  =  65

First, use the distributive property:

2x - 8 - 5x  =  65

Simplify the left-hand side:

-3x - 8  =  65

Add 8 to both sides:

-3x  =  73

Divide both sides by -3:

x  =  - 73/3

The solution to the equation  3^x  =  5x - 1  can be found by graphing these two equations on the same graph:

y  =  3^x     and     y  =  5x -1     and finding the point of intersection.

There are two points of intersection, one at     x  =  .58     and the other is     x  =  2.

yeah... i meant arcsin or sin^-1, but i forgot. thanks anyway!

Works for me ..    .0191

ARCsin 1.1   will NOT WORK because sine only goes to +1 ---   -1

there is a different answer like who shot at him.

Sorry, I forgot 2 post the answer.  He was playing poker, the green field is the poker table, and the 53 bicycles are Bicycle brand playing cards. The chips are poker chips. there are only 52 cards in a deck, and he had an ace up his sleeve.  His opponents shot him because he was cheating.

I will assume a slightly different scenario, since it states that annual interest for the the first year is 2.5% compounded annually: So then we have:

2,000 x 1.025=2,050 balance at the beginning of the 2nd year. But, we have:

2,124.46 / 2,050=1.0363 - 1=.0363 x 100=3.63% interest for the remaining 2 years.

Sqrt(1.0363)=1.80% interest rate for the 2nd and 3rd year. So that:

2,000 x 1.025 x 1.018^2=2,124.46 pounds.

I'm NOT sure either BUT if you put Rachel in ANY car there are 11 people left who COULD be in the car with her and ONE of them is Tim for a 1/11 chance he will be in the same car.....but I do not know if this is correct.

First, will have to find how much money is she able to save for 40 years at $5,000 annual deposit.
The FV of her 40 deposits @ 6% comp. annually=$773,809.83.
Second, will have to find a 2 to 1 factor to apportion her withdrawal payments for the 30 years. And that factor comes to: 17.8174133152.
Then we just divide her total savings by this last factor and we get: $773,809.83 / 17.8174133152=$43,429.98, which would her withdrawals for the first 15 years.
Finally, $43,429.98 x 2 =$86,859.96, which will be her payments for the last 15 years.

P.S. ALL THESE FORMULAE ARE USED IN THE ABOVE CALCULATIONS:

1=PV=FV[1 + R]^-N=PV OF $1 IN THE FUTURE.

2=FV=PV[1 + R]^N=FV OF $1 TODAY.

3=FV=P{[1 + R]^N - 1/ R}=FV OF $1 PER PERIOD.

4=PV=P{[1 + R]^N - 1.[1 + R]^-N} R^-1=PV OF $1 PER PERIOD.

5=PMT=PV. R.{[1 + R]^N/ [1 + R]^N - 1}=PMT NEEDED TO PAY OFF A LOAN OF $1

Where R=Interest rate per period, N=number of periods, P=periodic payment, PV=Present value, FV=Future value.

What kind of 'compound interest' ???   Continous is what I will assume:

2000e^(.025) = 2050.63 at the beginning of year two

2050.63 e^(r*2) = 2124.46

e^(2r) = 2124.46/2050.63

ln (e^(2r) = ln (2124.46/2050.63)

2r=,03537

r= 1.768 % for years 2 and 3    CONTINOUS COMPOUNDING EXAMPLE

I agree with Guest1 ,....here is the calculation:

FV = PV e^(.034n) = 1500 e^(.034 x 30)= 4159.79

1^7  = 1x1x1x1x1x1x1 = 1

Volume of a sphere = 4/3 pi r^3    Now lets make r=2r  (doubling the radius of the baloon

     volume = 4/3 pi (2r)^3 = 4/3 pi 8 r^3

Now the second volume to the original volume ===   (4/3 pi 8 r^3)  / (4/3 pi r^3) = 8/1 = 8 times more volume!

 2^8⋅5^2pieces of mail each second X 2^8⋅3^4⋅5^2 seconds in 6 days

=2^16. 3^4. 5^4 pieces of mail delivered in 6 days.

what is the median of 34 and 70

34 + 70 =104

104 / 2 = 52 is the median or the average.

Your $1,500 should be worth=$4,159.79 after 30 years @ 3.4% comp. continuously.

4⋅2^−4+5

2^-4 means 1/(2^4), so that you have:

4 x [ 1/(2^4) ] + 5

1km=1,000 meters

1m=100cm

1km=1,000 x 100 =100,000cm

4km x 100,000cm =400,000cm.

((−3/4)^5)^2=(3/4)^10

If the radius of the balloon is doubled, then it means that the volume of the balloon will go up by a factor of: 2^3=8 times the volume of the smaller balloon. 

Sorry, I took it to mean: (rt)^1/2. But I see it is (rt)^12=r^12*t^12.

2^4⋅2^5−(2^2)^2

2^9 - 2^4=512 - 16 =496=2^4 x 31

im sorry bu there is no image i cant help you if there is no image sorry

(1/5k)^2=1 / {25k^2}