CPhill

I'm not sure what is wanted on these two questions, GM

1/x + 1/y = 1/6

[ x + y ] / xy =  1 / 6

xy / [ x + y ]  = 6

xy =  6 [ x + y]

xy = 6x + 6y

xy - 6y  = 6x

y ( x - 6) = 6x

y =  6x / (x - 6)

When  x = 7    y = 42

When x = 8 , y = 24

When x = 9, y = 18

Whex = 10, y = 15

When x = 12, y = 12

So....these are the solutions...........note..... x and y are abrbitrary......so these answers can be "reversed" for x and y

Really need to see a diagram here, Bleh........we don't know the orientation of the given points

Not sure about this...but....

Put one coin in any unit square

Then the second coin can be placed in any of the other 15 unit squares

But.....only 6 of them are either in the same row / column

So.....9 aren't

So......the probability that the two coins do not lie in the sane row/column = 9 /15  =   3 / 5

Easy....

In the form   ax2 + bx + c = 0

The discriminant  is

b^2 - 4ac

So....for 

x^2 + 2x + 3 = 0                a = 1       b = 2     and c = 3

So.....the discriminant is

(2)^2 - 4(1)(3) =

4 - 12 =

-8

Based on this.....Can you figure out the other two GM ????

Well....it  first traveled 1000 km west

And from this point it traveled another 500 km west

So....the total displacement =  1000 + 500  =  1500 km

1500  km

98.     18/59   ≈  30.5%

99.      34/41 ≈   82.9%

100.    48 /100  =  48%

See my answer under the original post.....

Here....I'm assuming that the base of the box is contained within the sides of the box rather than the sides sitting on top of the base.....

The surface of the bottom is 2 (14 *  18)  = 504 cm^2

The inside of the box has the surface area of  2 (14 * 7 + 18 * 7 ) = 448cm^2

The outside of the box has the surface are of   2 (14*9 + 18*9) = 576 cm^2

So....the total surface area is

[ 504 + 448 + 576 ] cm^2 =  1528 cm^2