CPhill

Here's my attempt at the second

1) It is geometric    the first few terms are  2, 3, 9/2, 27/4......   the generating "formula"  for any term is : 2*(3/2)^{(n - 1)}

2)  We can prove this by  dividing the (n+ 1)th term by the nth term....we have :

[2(3/2) ^{((n - 1) + 1)} ] / [ 2 (3/2)^n-1 ] =    (3/2)ⁿ / (3/2)^n-1  =  3/2   =  r = the common difference between terms

Here's the first one :

1) 10, 50, 250, 1250, 6250, 31250, 156250, 781250, 3906250, 19531250

2) u₅₀  = 10*5^{(50 - 1)}  = 10*5⁴⁹ = 177635683940025046467781066894531250

3)  Sum of the first 49 terms =  u₀ * [ 1 - rⁿ ] / [ 1 - r ]   = 10 * [ 1 - 5⁴⁹] / [ 1 - 5]  =

44408920985006261616945266723632810

(17/28)/ (4/27)  =     invert the second fraction and multiply

17/28  x 27/4 =

459 / 112

your height / length of your shadow  = object's height / length of object's shadow.....so.....

object's height = [length of object's shadow] x [ your height ]  /  [length of your shadow]

 22570/185  - 80   = $42 less

sqrt ( x + 36) + 6  = x   subtract 6 from both sides

sqrt (x + 36) = x - 6      square both sides

x + 36 = x^2 - 12x + 36     subtract 36 from both sides

x =  x^2 - 12x       rearrange as

x^2 + 13x = 0      factor

x ( x + 13) = 0     set both factors to 0 and x = 0 [reject this]  or x = 13 [accept this]

Post the problem....we'll give it a shot  !!!!

It's a symbol denoting the "empty set"....it might denote that thare is no solution to a particular problem, or, in set theory, it might denote a set having no members......

(-1)^1/3 = -1

x = 8 - (-2.25)   =  10.25

y = 6 - 4.2 - (-4.9)  = 6.7

Thus, x - y =  10.25 - 6.7 =  3.55