1.
For Maurice to be correct (using the law of cosines), she would
need two sides and the
angle between them to find the third side and (if you need to find a missing
angle which in this case you don’t) all three sides need to be given to find an
angle. For Johanna to be correct (using the law of sines), an opposite side and
two angles must be known to find another side and (if you need to find a
missing angle which in this case you don’t) an opposite angle and two sides
must be given to find another angle.

2.
To find
the equation of the parabola, you can use the distance formula between the
focus and any point on the parabola. It is also important to involve the
distance from the directrix. Both of distances that are found are un-simplified.

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We have to make them equal to each other. Once these equations are set equal to
each other you can simplify.

3.
See file.

4.
See file. The location
of the main water connection is (- 7,5) and the center of the circle is (0,0).

5.
When
two solids have the same height, and a cross sectional cut through them reveals
the same area everywhere in the solid, then the two solids have the same volume
as stated in Cavalier’s Principle. You don’t need to know they are the same
shape depending on the information given.