A rectangular field is to be enclosed on four sides with a fence. Fencing costs $4 per foot for two opposite sides, and $3 per foot for the other two sides. Find the dimensions of the field of area 650ft2 that would be the cheapest to enclose.

Step-by-step explanation:

 Lets suppose the one side be x and the other side of the rectangle be y

 given area

   implies x = 650/y

  Cost = 2*4*x+2*3*y=8x+6y

            = 8*650/y + 6y

            = 5200/y  + 6y

upon differentiating we get

          =

          = 2600/3

          y= = 43.3

           x= 15

C(43.3)= >0 hence it is a minima value

optimizing the result we get

Cost = 8*15+6*43.3 =$ 379.8

b. an equilateral triangle inscribed in a circle

step-by-step explanation:

we are given the figure of two circles having a triangle inside.

now, we know that,

"when a figure is lying inside an another figure, then the outside figure is known as circumscribed figure and the figure lying inside is referred to as the inscribed figure".

as we see that, the circles are containing the triangle completely.

thus, the circles are the circumscribed figures and the triangle is the inscribed figure.

hence, we get, 'an equilateral triangle is inscribed in a circle'.