CPhill

If K(H) = 0 , this implies that.....

-((x^2+1)^2) + 4  = 0   multiply both sides by -1

(x^2+1)^2 - 4  = 0    simplify

(x^2 + 1)^2  = 4    and by the square root property, we have

x^2 + 1  = ± 2     subtract 1 from both sides

x^2  =  ± 2 - 1   ....so either.....

x^2  = -3    .......which leads to two  "non-real " solutions   ....  or .....

x^2  = 1    so that, using the square root property again,   x = ± 1

And these are the two "real" solutions.....check that they make the specified condition true .........

3sin2x=2cos^2x+1   

There are  8 parts......Mick gets 5/8 and Sharon gets the remainder.....

So (5/8)(12)  = 60/8  = £ 7.5

And Sharon gets  [12 - 7.5] = £ 4.5

Hey, ND.....good to see you back....don't be a stranger !!!!!

Since, apparently, anyone is eligible to row the boat....one photographer and one cannibal get into the boat and row across.....the photog steps out and the cannibal rows back....

A second cannibal gets into the boat with the other cannibal and they row across......one cannibal steps out...and one cannibal rows back...at this point there are two photographers and one cannibal at the starting point, one cannibal in the boat and one photog and one cannibal at the final destination

The second photog gets in the boat and he and the cannibal row across, the photog steps out and the cannibal rows back......now, one photog and one cannibal are at the starting point, one cannibal is in the boat and two photogs and one cannibal are at the final destination....

The lone cannibal at the starting point gets into the boat with the other cannibal and they row across and one of the cannibals steps out.......at this point.....there is one photog at the starting point......one cannibal in the boat and two photogs and two cannibals each at the destination

The cannibal rows back and picks up the lone photog at the strating point........they both come across (either rowing) and both step out at the final destination.......everyone safe!!!

Call "N" the anount that she inherited

Then....in the first situation, she ended up with an amount equal to....

(3/5)N (1.1)

In the second situation......she ended up with an amount equal to....

[(2/5)N + 500] (.80)    ..... and since these are equal, we have.....

(3/5)N(1.1) = [(2/5)N + 500] (.80)  simplify

.66N = .32N + 400     subtract .32N from both sides

.34N = 400   divide both sides by .34

She inherited about $ 1176.47   ......each account contains $776.47

I used a slightly different approach from heureka's.......we still get the same answers....!!!

1, 5, 13, 25.....

It appears that the series is defined by ......

1 = 1 +  0   =  1 +  4(0)

5 = 1 +  4   =  1 + 4(1)     

13 = 1 + 12  = 1 +  4(3)

25 = 1 + 24  =  1 + 4(6)

41= 1 + 40   = 1 + 4(10)

So, the nth total is defined as........

1 + 4[sum of the first n whole numbers] =

1 + 4[(n)(n - 1)/2]  =

1 + 2[(n)(n-1] =

So....the 20th figure will have  ...

1 + 2[(20)(19)]   =  1 + 2[380] = 1 + 760 = 761 turquoise squares.....

I think so, Z Man !!!!!

Fill the 5 cup container full....pour 3 cups into the 3 cup container....throw these 3 cups out.........there will be 2 cups now in the 5 cup container....pour these 2 cups into the 3 cup container.....

Fill the 5 cup container full, again......pour 1 cup into the 3 cup container which is now full.......the 5 cup container will now contain exactly 4 cups.....!!!!

1.2*10^-3+2.7*10^-4 = 0.00147

I don't know what you mean by "correctly rounded".......it depends upon what you want to round to.......nearest integer???.....nearest thousandth???.......nearest ten thousandth.....???