Alighthouse is located on a small island 2 km away from the nearest point p on a straight shoreline and its light makes four revolutions per minute. how fast is the beam of light moving along the shoreline when it is 1 km from p? (round your answer to one decimal place.)

62.8 km per min

Step-by-step explanation:

Let the diagram of this situation is shown below,

In which is the angle made by light to the straight line joining the lighthouse and P,

∵ Light makes 4 revolutions per minute.

Also, 1 revolution = radians

So, the change in angle with respect to t ( time ),

Let x be the distance of beam from P,

Differentiating with respect to x,

If x = 1 km,

Hence, the beam of light moving along the shoreline with the speed of 62.8 km per min

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.