Answer:
⅕
Step-by-step explanation:
Given that points X, Y, and Z are collinear, and X is said to partition segment XZ in the ratio XY to XZ = 1:5, it means that segment XY = ⅕ of XZ. That is XY/XZ = ⅕
See attachment below to understand how point Y divides segment XZ.
Therefore, the k value Brianna would use when solving the problem should be the fraction, ⅕.
k value = XY/XZ = 1/5
Answer: The first diagram you selected is the correct visual representation.
Check out the diagram I posted below. The red vertical line is x = 0, aka the y axis. The blue parabola is 3x = y^2. The green horizontal line is y = 6. The region bounded by these curves is the gray shaded region.
Spinning that gray region around the y axis results in the first diagram in your answer choices. The disk in pink is a cross section to help find the volume (through the use of integral calculus).
