Please list the exact intervals and try not to skip steps. I have been having a lot of trouble understanding this.
PART 1: They started testing their ideas on a small scale, using a closed interval of [0,1]. They first decided to test if 10 trees, named t, t,, t, --, t..- can be planted satisfying all the conditions below simultaneously
a The trees t,and t,are in different halves of the interval [0,1]
d) The above pattern continues when considering five, six, seven, eight or nine trees, and finally, the trees t, t, -.- , t,, are in different tenths of the interval [0, 1].
solutions. Write a paragraph explaining your thought process.
PART 2: Satisfied with their amazing math skills to solve the problem for 10 trees, students began exploring how many more trees they could fit on that interval using the same pattern. They realized that the work was getting harder, and decided to work in small groups. Group #1 tested the idea of planting 14 trees, in honor of the youngest member in their group Group #2 worked to fit 18 trees, to celebrate the birthday of their oldest member. Group#3, contemplated the possibility of planting n-trees, t, t, t, .-.t, where n > 18, to create a blueprint for other campuses to use, satisfying the conditions listed above.
Of course, for each new number, the groups needed to update their conditions.
a) List the updated conditions for Groups #1 and for Group #2. Can they implement their plan? Justify your answer using any technique. b List the updated conditions for Group #3. Then, make a conjecture about the general solution for n > 18: What would be the highest number of trees (below, at, or greater than 18 that students can recommend be planted in their blueprints on the closed interval [0,1]?
PART 3: Once the tree lining problem was solved, the next step was to create the layout of a playground as large as possible. In a meeting with the site contractor, the students learned that the school was planning to dedicate an area whose perimeter should be a specific length. Help the team answer the following questions:
build a rectangular playground. What dimensions would give the maximum playground area? Show all work in detail.
BE PREPARED TO DISCUSS: What is the maximum number of trees that can be planted
are available to plant trees. Give coordinates of all the locations of these trees on a Cartesian plane. Justify your answer. You should be able to provide some coordinates during the interview
