geno3141

y  =  (x + A) / ( Bx + C)

(4,0)     --->     0  =  (4 + A) / (B·4 + C)

                       0  =  (4 + A) / (4B + C)

                       0  =  4 + A

                       A  =  -4

(0,-4)     --->     -4  =  (0 + A) / (B·0 + C)

                         -4  =  A / C

                         -4  =  -4 / C

                          C  =  1

(-2,-2)     --->     -2  =  (-2 + A) / ( B·-2 + C)

                          -2  =  (-2 + -4) / (-2B + 1)

                          -2  =  -6 / (-2B + 1)

                    4B - 2  =  -6

                         4B  =  -4

                           B  =  -1

y  =  (x + -4) / (-1X + 1)

You can calculate the final answer to the problem ...

AX · XB  =  XY · XY

--->     15 · XB  =  8 · 8

--->            XB  =  64/15

AB  =  AX - XB

--->     AB  =  15 - 64/15

--->     AB  =  161/15

h(2)  =  f( g(2) )

g(2)  =  sqrt( f(2) ) - 3

f(2)  =  2(2) + 5  -  4 + 5  =  9

      --->     g(2)  =  sqrt( 9 ) - 3  =  3 - 3  =  0

      --->     h(2)  =  f( 0 )  =  2(0) + 5  =  0 + 5  =  5

Rewrite to find the vertex:

y  =  x² + 11x - 5 + 5x

y  =  x² + 16x - 5

y  =  (x² + 16x + .....) - 5

Complete the square:  (divide the coefficient of the x-term by 2 and square the answer):

y  =  (x² + 16x + 64) - 5 - 64

y  =  (x + 8)² - 69

The mininum will occur when x = -8; it is -69.

2x - 5  <=  x + 18

Subtract x from both sides:

  x - 5  <=  18

Add 5 to both sides:

       x  <=  23

Interval form:  (-infinity, 23]

Vertex:  (2,3)

Axis of symmetry:  the vertical line that passes through the vertex:  x = 2

I think that there are seventeen:

(68,68)

(51,102), (102,51)

(38,323), (323,38)

(36,612), (612,36)

(35,1190), (1190,35)

(33,-1122), (-1122,33)

(32,-544), (-544,32)

(30,-255), (-255,30)

(17,-34), (-34,17)

One way to do solve this problem:

--   find f(-6) and f(-5); if one of these answers is positive and the other is negative, the zero will be between

                 these two values

--   if not, find f(-5) and f(-4); if one of these answers is positive and the other is negative, the zero will be

                 between these two values

--   if not, find f(-4) and f(-3); ...

--   if not, find f(-3) and f(-2); ...

Each minute is descends  12% of 75 meters; find this amount  (hint:  0.12 x 75  =  ....)

To find how far in two minutes, multiply the above answer by 2.

Set up the proportion:  15 / 50  =  x / 3500  and solve for x.