A circular tabletop is to be cut from a rectangular piece
of wood that measures 1.20 m by 1.80 m.
What is the radius of the largest tabletop that could be cut?
Justify your answer. Include a sketch

The largest table top that could be cut in the given rectangle piece is 0.6 meters, If the given rectangular piece is 1.20 m by 1.80 m.

Step-by-step explanation:

The given is,

               Rectangular piece of wood that measures 1.20 m by 1.80 m.

Step:1

               For the circular table top, from the rectangular piece. We consider the dimensions of the rectangular.

                The circle from the rectangular,

                Ref the attachment,

                Minimum dimension of rectangle = Diameter of circle

                From the given dimensions,

                                                           1.20 m = Diameter of circle

                                                                    d = 1.20 m

Step:2

                 Conversion of diameter to radius,

                         Radius of circle table top, r = 0.6 meters

Result:

           The largest table top that could be cut in the given rectangle piece is 0.6 meters, If the given rectangular piece is 1.20 m by 1.80 m.        

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

so the change in y-value for function f is (6 )) = 9.

the table tells us

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).