Answer the questions below.
1. The equation of a plane in space is x + 3y + 2z = 6.
a.) Accurately sketch the plane on the set of axes, showing all your calculations below.
b.) The three planes of the axes and the plane you have sketched create a triangular pyramid.
Find the volume of this pyramid, showing the formula you are using and all calculations below.
2. Study the diagram below:
a.) If D is a right angle and lines PN, FG, and BD are parallel to each other, prove
b.) Use the diagram to solve this practical problem:
A person who is 1.5 m tall casts a shadow of 8 m. The distance along the ground from the person (N) to the flagpole (G) is 32 m, and the distance from the flagpole (G) to the building (D) is 200 m. Find the height of the flagpole (FG) and the height of the building (BD), showing all calculations.
3. Given rectangles ABCD and PQRS, and given that rectangle ABCD is fully rotated about line BC, answer the following questions.
a.) Describe the figure generated by the rectangle rotating about line BC.
b.) About which line could you rotate rectangle PQRS to generate a figure that is similar to the first solid?
c.) What are the ratios of the surface areas and volumes of the solids generated from ABCD and PQRS?
d.) Are ABCD and PQRS golden rectangles? Why or why not?
4. The diameter of circle C is 18 cm. Chord AD is the same length as a radius. Use this information, the diagram, and your experiences in geometry this semester to answer these questions. (Use Π = 3.14.)
a.) What are the measures of angles BDA and DBA?
b.) What is the sine of angle DBA?
c.) Find the length of arc AB to the nearest hundredth.
d.) How does the length of arc AD compare to the length of arc AB?
e.) If EF = 1/2 BD, then what is the degree measure of arc EF?