19. from two ships due east of a lighthouse and in line with its foot, the angles of
elevation of the top of the lighthouse are x and y, with x > y. the distance between the
ships is m. the distance from the lighthouse to the nearer ship is?

Step-by-step explanation:

tan x= AB/ BC+M

tan y=AB/ BC

tan y * BC = tan x*(BC +M)

tan y* BC /tan x=( BC +M)

tan y * BC - M* tan x/ tan x= BC

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.