Sixty identical drippers, each with a hole of diameter 1.00 mm, are used to water a yard. If the water in the main pipe of diameter 2.54 cm is flowing at speed 3.00 cm/s, (a) how much water is used in one hour and (b) how fast the water is coming out the drippers

a

b

Explanation:

From the question we are told that

   The number of identical drippers is  n =  60

   The diameter of each hole in each dripper is    

   The diameter of the main pipe is  

    The speed at which the water is flowing is  

Generally the amount of water used in  one hour = 3600 seconds is mathematically represented as

Here A is the area of the main pipe with value

=>      

=>        

So  

=>  

=>  

Generally the area of the drippers is mathematically represented as

=>    

=>    

Generally from continuity equation we have that  

=>      

=>  

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .