Write a of function [use y= f(x) unless other letters ofthe alphabet are given]

Question

Write a of function [use y= f(x) unless other letters ofthe alphabet are given] that accurately represents each of thesesituations: 1) the area of a rectangle with perimeter100 as a function ofthe length of oneside. 2) the volume of an open box with square base x2 asa function of x if its surface area is 100. Write a of function [use y= f(x) unless other letters ofthe alphabet are given] that accurately represents each of thesesituations: 1) the area of a rectangle with perimeter100 as a function ofthe length of oneside. 2) the volume of an open box with square base x2 asa function of x if its surface area is 100.

Explanation / Answer

1) the area of a rectangle with perimeter100 as a function ofthe length of one side.
answer: if x the length of one side, the other side is 50-x (sothat perimeter is 100).
area= f(x) = x(50-x)
2) the volume of an open box with square base x2 asa function of x if its surface area is 100.
answer: if the height is h, then total surface area = x^2+4xh =100.
h= (100-x^2)/(4x)
volume = f(x) = x^2*h = x^2(100-x^2)/(4x)= x(100-x^2)/4

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