ElectricPavlov

Amount of saline of constituents = amount of saline in final solution

.60 (70)   +   .30 (x)     =   .36 ( x+70)

42               + .3x         =  .36x  + 25.2

16.8                           =      .06x

x = 280 cc of 30% solution

As you approach from - inf to 1      the range goes from +inf   to a MINIMM of 0   (at x=0)  and then back to + inf

    on the other side of 1    it goes from - inf to a MAXIMUM of -4   at x = 2   and then to - inf

(+inf, 0 ]  U  (-inf, -4]        which I think is what you have.....maybe the order is incorrect for the software answer?   

originally    water to empty   =   w:e   =   1/5       water is   1/(1+5) = 1/6   

ADD 130      and water is   3/5     

3/5 x    -1/6 x  = 130       x is the amount of water when full

18 /30 x  - 5 /30 x   = 130

13/30 x = 130

x = 300 gallons             check:        50 : 250     =    1:5         180 : 120  =  3:2

With dimensional analysis:

Total hours needed   =   5 p x 6 hr/d x 16 d = 480 p - hr

480 p-hr /(8p 4h)/d   = 15 days

small circle area = pi r^2   is equal to Large circle area (pi L^2)   minus small circle area(pi r^2)

pi r^2  =  pi L^2 - pi r^2

2 pi r² = pi L²

2 r² = L²

2 = L² / r²

sqrt2 = L / r

Yeppers....

Right triangle    hypotenuse = l    (length of ladder)      base leg = l-20    height leg = l-10

Pythgorean theorem

(l-20)² + (l-10)² = l²       Expand, simplify to

l²-60l+500 = 0      Quadratic formula yields    l = 50 ft   or 10 (throw out)

The Height leg =  l-10 = 50 - 10 = 40 ft

   = 1  +  5  +  15  +  35     = 56

x+ 3y = -5      find slope, m when in the form   y = mx+b

3y = - x -5

y = -1/3 x  - 5/3        slope = -1/3    as is the parallel slope

y = -1/3 x + b

2  = -1/3 (-7) + b

2 = 7/3 + b

-1/3 = b

y = -1/3x  - 1/3          re-arrange to   'Ay + Bx = 3'   form

y + 1/3x  = -1/3

-3y -x = 1                  

-9y-3x=3         B-A   then equals  -3 - - 9   = +6

50 mach * 50 min /50 book   = 50 mach-min/ book

50 mach-min / book   / 20 mach       *  20 book    =   50 min