**Question: ** Temperature Distribution. Let \(T\left( x,y,z \right)=100+{{x}^{2}}+{{y}^{2}}\) represent the temperature at each point on the sphere \({{x}^{2}}+{{y}^{2}}+{{z}^{2}}=50\). Find the maximum temperature on the curve formed by the intersection of the sphere and the plane x-z = 0.

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