Ben began at (3, 1) and walked to (4, 5); Katie decided to begin at (–3, 1), then tried to mirror Ben by walking to (–4, 5). Ben jumped to (5, 5) and side–stepped to (4, 3); Katie jumped to (–5, 5) then side–stepped to (–4, 3). Ben returned to (3, 1) and Katie returned to (–3, 1)

cosine

step-by-step explanation:

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for

thats not a system of equations, that is a solution

answer: the resulting cross section is a rectangle. solution: a plane parallel to the base of a triangular prism will intersect a cross section that is the same shape as its bases. so the cross section is a triangle.

step-by-step explanation: