Expert: Sherman D. - 11/4/2007

Question
a)Express the side length of a square as a function of the length d of the square's diagonal, then express the area as a function of the diagonal length
b)a point p in the first quadrant lies on the graph of the function f(x)=sqrtx. express the coordinates of p as functions of the slope of the line joining p to the origin.
I will be very thankful to you if you send me the answer as soon as possible ....thanks..

Answer
a.)
a^2 + b^2 = d^2
since a = b
a^2 + a^2 = d^2
2a^2 = d^2
a^2 = (d^2)/2
a = sqrt((d^2)/2)
a = sqrt(d^2)/sqrt(2)
a = (dsqrt(2))/2 or (d/2)sqrt(2)

so in function form, it would be

f(x) = (sqrt(2)x)/2

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b.)
as far as this one goes, check with answers.yahoo.com