For the point P(−19,18) and Q(−14,23), find the distance d(P,Q) and the coordinates of the midpoint M of the segment PQ.
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Answer:
see the attached
Step-by-step explanation:
To fill in the data table, you need information about the layers of the Earth. That information is provided in the second attachment.
Among other things, it shows the density of the rock layers varies over a range of almost 6 to 1 from the top layer to the inner core. Your representative liquids vary in density over a range of about 1.8 to 1, so clearly cannot match the relative densities.
In the attached spreadsheet, we have used the average of the top and bottom density values for each layer to represent the density of the layer. Then we did a <em>linear</em> mapping so that the minimum density maps to lamp oil, and the maximum density maps to honey. (You get slightly different results if you use a different mapping strategy.)
For your convenience in stacking your "density cylinder", we have shown the relative thickness of each of the layers as a percentage of the overall radius of the Earth. That is, if your cylinder is 100 mL deep, for example, then the top layer will be 0.5 mL deep, the next layer 11.3 mL deep, and so on.
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We have elected not to use alcohol for the top layer, because it is miscible with all of the liquids immediately below that in the table. That is, you could not maintain alcohol as a separate layer in your cylinder because it would dissolve into the layer below. It might take a little effort (or care) to keep the lamp oil separated from the vegetable oil, as we expect those might try to mix, as well.
If you compare the scaled density values with the values for the "representative" liquids we have chosen, you will see that some are closer than others. The idea is to try to get the best match, while also choosing liquids that don't mix well.
