ElectricPavlov

divide x-2   into   x-1  :

       ___1_1/x-2_________

x-2  |  x-1

          x-2       

              1

It looks like it IS simplified....I suppose you could divide it out to get    1  1/(x-2)   

What would you like to do with that EXPRESSION ?

The smalles value of  t    will be given by   -b/2a     where b = -9    and a = 1 for this bowl shaped parabola

   NOTE:   this is the smalles value of t    NOT the smallest value of the function ....you find THAT by putting in the 't' value and calculating.

https://web2.0calc.com/questions/help-please_67220#r2

x = sgrt3+y     sub into second equation

sqrt3 +y + y = 2

2y = 2 - sqrt 3

y = 1 - 1/2 sqrt3 

x + 1- 1/2sqrt3  = 2

x = 1 + 1/2 sqrt3

You can multiply them for the answer.......

The broken pole forms a RIGHT triangle with the ground

the slanted portion we will cal 'h'    (as in 'hypotenuse' )

the vertical portion is   5 - h

and the other leg of the triangle (the ground ) = 3

(5-h)^2 + 3^2 = h^2

h^2 -10h+25+9 = h^2

-10h = -34

h = 3.4                      the pole broke 3.4 meters from the top .... AC is thus: 5-3.4 = 1.6 meters

Hmmmm..... I am not sure this is possible....

  sqr (x^2-9)  will always be positive     which would mean  |x-3| must be NEGATIVE for the terms to ADD to 0......absolute values cannot be negative.....  Did you enter your question correctly?

The minumum TIME will be   - b/ 2a =  - -5/4 =   5/4       Yes you got that part right

Now sub  t =  5/4  into the equation to find the minimum HEIGHT

Height_min= 25  7/8  ft     Ye, you got that part correct too !  (or ...at least we got the same answer! )

Put 7 in for 'x'   and   1 in for 'y in the equations to find which equation is true.....