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In designing experiments it is important to be sure that the data measured will be sufficient to reach a desired conclusion. In each of the following situations, will the information provided always, sometimes or never be sufficient to determine the required information about the reactants? Provide a clear analysis in each case.
Three equilateral triangles ABC, AYX and XZB are drawn with the point X a moveable point on AB. The points P, Q and R are the centres of the three triangles. What can you say about triangle PQR?
P is the midpoint of an edge of a cube and Q divides another edge in the ratio 1 to 4. Find the ratio of the volumes of the two pieces of the cube cut by a plane through PQ and a vertex.