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Cylinder Inscribed in a Sphere and X-Intercepts of a Parabola

1. When a cylinder is inscribed in a sphere, the sphere's diameter is equal to the diagonal of the cylinder's height and diameter. Relate height of the cylinder to the radius of the sphere.

2. Which of x-values does the parabola defined by y = (x-3)2-4 cross the x-axis?

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Cylinder Inscribed in a Sphere and X-Intercepts of a Parabola are investigated. The solution is detailed and well presented.

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