Quarter-Tank Problem

Author

Eric W. Weisstein
November 19, 2010

This notebook downloaded from http://mathworld.wolfram.com/notebooks/RecreationalMath/Quarter-TankProblem.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/Quarter-TankProblem.html.

©2010 Wolfram Research, Inc. except for portions noted otherwise

Equation

V7

$Version

Solve[(π/4)==ArcCos[1-x]-(1-x)(Sqrt[2x-(x^2)]),x]//Timing

V8

$Version

TimeConstrained[Solve[(π/4)==ArcCos[1-x]-(1-x)(Sqrt[2x-(x^2)]),x],60]//Timing

Solve[(π/4)==ArcCos[1-x]-(1-x)(Sqrt[2x-(x^2)]),x,Reals]

FullSimplify[%]

FindInstance[(π/4)==ArcCos[1-x]-(1-x)(Sqrt[2x-(x^2)]),x]

FullSimplify[%]

Angle

Solve[2θ==Sin[2θ]+π/2,θ,Reals]