A fence is to be built to enclose a rectangular area of 280 square feet. The fence along three sides is to be made of material that costs 6 dollars per foot, and the material for the fourth side costs 14 dollars per foot. Find the length L and width W (with W≤L) of the enclosure that is most economical to construct.

L = 21.60 ft

W = 12.96 ft

Step-by-step explanation:

Let 'W' be the length of the more expensive side and 'L' be the length of the perpendicular sides. The expressions for the total area (A) and total cost (C) of the rectangular fence are:

Writing cost as a function of W:

The cost will be minimal at the value of W for which the derivate of the cost function is zero:

Therefore, the value of L is:

step-by-step explanation:

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.