CPhill

As long as  k> 0, the range  on [, inf)   will  be  the  same ⇒  [ 1, inf )

She has 25%  left   =.25 * 300  = 75 pages left

75 pages * 2 min /page  =     150 min  left

y^3 - x^3 = (y-x)(y^2 + xy + x^2)

So

(y - x) ( y^2  + xy + x^2)   =  (y^2  + xy + x^2)

(y - x)   =  1

y = x + 1

And

yz + 1  = y^2 + z

(x + 1)z + 1  = (x+1)^2  + z

xz + z + 1  = x^2 + 2x + 1  + z

x^2 + 2x - xz  =  0

x ( x + 2 - z)  =  0

x = 0   or     x + 2   = z

So

{x , y , z}   =   { x, x + 1, x + 2 }

The number of ordered triples  =   {1730, 1731, 1732} .....( 1996, 1997, 1998}  = 1996 - 1730 +  1  =  267

No prob  !!!!

Note  that  the  small  cone formed  by the water  is similar to the  larger cone

The scale  factor  for the small cone to the large cone =   2 / 6  =  1/3

The  fraction of the  volume of the cone when  filled to 2 in = scale factor^3 =  (1/3)^3  =  1/27

BTW.....good to see you, GM  !!!!

LOL!!!!!!!

Good job  !!!!

Note  that  we  have  the points   (8,12)    and (53,22)

One leg  = ( 53 - 8)  =   45

The other  =  (22 - 12)  =  10

Proof

By the Pythagorean Theorem......PQ =  sqrt  [ 45^2 + 10^2 ]

And using the distance formula PQ   =sqrt [ (53 - 8)^2  + ( 22 - 12)^]  =  sqrt [ 45^2  + 10^2]

And  the  distance  PQ  is  =   sqrt   [ 2125]  ≈  46.1  units

You're welcome   !!!

Blueprint diameter  =  18 cm

3cm  =  4 ft

So

18 cm = 24 ft  = actual diameter

So  12 ft is  the actual radius

So....area =   pi (12)^2   ≈  452.39 ft^2