SOLUTION: A plate made from a rectangular sheet of metal x metres by y metres has one corner "rounded" to a quadrant of a circle with radius r. Show that r= 2* sqrt xy-A/4-pi, where A is th

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: A plate made from a rectangular sheet of metal x metres by y metres has one corner "rounded" to a quadrant of a circle with radius r. Show that r= 2* sqrt xy-A/4-pi, where A is th      Log On


   

Question 1178511: A plate made from a rectangular sheet of metal x metres by y metres has one corner "rounded" to a quadrant of a circle with radius r.
Show that r= 2* sqrt xy-A/4-pi, where A is the area of the "finished" plate, given that r>0.
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
.
Total+area+=+r%28x-r%29+%2B+x%28y-r%29+%2B+%28pi%2F4%29+r%5E2
A= xr - r^2 +xy -xr +(pi/4) r^2

A = xy -r^2 +(pi/4)r^2
A = xy -r^2 (1-(pi/4))
A= xy -r^2 ( (4-pi)/4))

r%5E2+%28+%284-pi%29%2F4%29%29+=xy-A
r%5E2+=+%28xy-A%29%2F%28%28%284-pi%29%2F4%29%29
r%5E2+=+4%2A%28xy-A%29+%2F+%284-pi%29
r=+2%2A+sqrt%28%28xy-A%29%2F%284-pi%29%29