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There is no DIRECT solution to your ptoblem. However, iteration and interpolation will give you a couple of "real" answers. There are several complex answers as well:

k= 0.703501

k= 0.907723

yeah thanks guys, that's why I asked. Like it's so tempting to do this, but feels wrong :< . Anyway thanks again.

0.5*pi*2.8 = 4.3982297150257105

It's $3666.67 because 44000/12 = 11000/3 = 3666.66666...

Peasy.

A rational expression can be expressed as a fraction, while a radical expression cannot. For example, sqrt(2) cannot be expressed as a fraction, therefore it's radical. π cannot be expressed as a fraction, therefore it's radical. However, 3.3333... IS rational because it's equall to 10/3.

For easy reference, any square root of a non-square is radical.

A polynomial is a statement like this:

(x^2+x+1)

It's an addition statement in parentheses (that is, a quantity), with x values ordered by what power they're raised to. More examples include:

(3x^2+8x+18)

(-2x^2-3x+4)

Or even:

(x^16-18x^13+12x^8-52000x^2+12)

I hope this helps.

No, unfortunately, there's not much you can do......it is tempting to want to get rid of the logs  and solve  a * b  = c.......however.....we can quicly see that this will not work.......consider this....  [I'm using 10 as the base]

log(100) * log(1000)  =  log (1,000,000)      which is true

But

100 * 1000  ≠  1,000,000

So.....in general, for

log(a)*log(b) = log(c)

a * b ≠  c

No.   Because....

If you have a*b=c   and you take logs of both sides you get

log(a*b)= log c       .                             Now  log(a*b) = log a  + log b,  and not log (a)*log(b)

3x+3y= -6        the object here is to get y by itself.......first, divide through by 3

x + y  = -2        subtract x from both sides

y =   -x  - 2     

This is slope/intercept form.....the slope = -1    and the y intercept is at -2

3.141592653589793238462643383279

Using the Law of Cosines.......we can determine the distance, d, between his starting point and his ending point........so we have

d^2  = 4^2 + 8^2 - 2(4*8)cos(140)

d^2  =  about 129.03 mi

d = √129.03  = about 11.359 miles

And we can use the Law of Sines  to find the included angle, A, between the first leg of the journey and his last leg of the journey.........so we have

sin140/ 11.359  = sinA/8

8*sin140/11.359  = sinA

So

A = arcsin [ 8*sin140/11.359]  = about  26.92°

Subtract 25 from this  = 1.92°

Add this angle to the bearing of 270 =   271.92

So the yacht is about 11.359 miles from its starting position

And the bearing of the yacht to its starting position  is 271.92°

0.5555555555555555555

Of what ???

36x^2-65x+25=0

This factors as

(9x - 5) (4x -5)  = 0

Set both factors to 0    and we get that

9x - 5  = 0                                        and                  4x - 5  =  0

                                           add 5 to both sides

9x = 5                                                                     4x  = 5

divide both sides by 9                                          divide both sides by 4

x = 5/9                                    or                             x =  5/4

You should learn how to use the calculator here: (1/2)^5=1/32.

Guest # 2

.625 x 1000/1000=

625/1000 = divide both sides by 125

5/8=0.625

e=[1 + 1/n]^n.........as n goes to infinity.

The sequence  is given by :    3(2)^n-1

I don't know the exact way to do it, but if I have decimal 0.625 for example, I then put the decimal numbers over an exponential of 10, like 10000, so I would have the fraction 625/10000, which is equivilant to 0.625. From there, I find common factors and divide down to the simplified answer:

625 / 5 =     125 /25 =   5  / 5 =  1 

10000 / 5 = 2000 /25 = 80 / 5 = 16

So my final answer would be 1/16.

1) The sum of the first series is: [1,000 x 1,001] / 2=500,500.

2) The sum of the second series can be summed up using summation such as this one:

∑(n)(1.01)^(999-n), from n=0 to n=999, which =209,481,556.38. This summation maybe done on this calculator here, but I don't know how to use it. I summed it up on my computer. There is, however, a rather complicated financial formula that will do the same thing, but is a little more involved that the above summation.

3) The difference between them is rather large=209,481,556.38 - 500,500=208,981,056.38

Here's a good resource that explains it........http://www.purplemath.com/modules/percents2.htm#Decimal_to_Fraction