Arectangle is constructed with its base on the x-axis and two of its vertices on the parabola y equals = 100 100 minus −x squared 2. what are the dimensions of the rectangle with the maximum area? what is that area?

Step-by-step explanation:

Given that a rectangle is constructed with its base on the x axis and two of its vertices on the parabola

This parabola has vertex at (0,100) and symmetrical about y axis.

Any general point above x axis can be written as (a,b) (-a,b) since symmetrical about yaxis.  

Hence coordinates of any rectangle are

Length of rectangle = 2a and width =

Area of rectangle = lw =

To find max area, use derivative test.

Hence maxima when first derivative =0

i.e. when a =2

Thus we find dimensions of the rectangle are l =4 and w = 96

Maximum area =

irrational, then, just means all the numbers that aren't rational. every integer is a rational number, since each integer n can be written in the form n/1. however, numbers like 1/2, 45454737/2424242, and -3/7 are also rational, since they are fractions whose numerator and denominator are integers.

step-by-step explanation: