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.

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.