Respuesta :
A particle moves in the cartesian plane from any lattice point $(a,b),$ the particle may only move to $(a 1,b), (a,b 1),$ or $(a 1,b 1).$, f(0,0) are different paths can the particle take from $(0,0)$ to $(5,5)$.
we can use a technique called recursion. Recursion involves defining a function in terms of itself, so that the function can be used to solve a problem by breaking it down into smaller subproblems. In this case, we can define a function f(a,b) that represents the number of different paths the particle can take from the point (a,b) to the point (5,5). We can then use this function to find the number of paths from (0,0) to (5,5) by starting at (0,0) and using the recursion relation to move the particle one step at a time until it reaches (5,5). We can start by writing the base case for the function, which is the case where the particle is already at the destination point (5,5). In this case, there is only one path the particle can take, so we can set f(5,5) = 1. Next, we can define the recursion relation for the function. This tells us how to calculate f(a,b) in terms of f(a+1,b), f(a,b+1), and f(a+1,b+1). Since the particle can only move to the points (a+1,b), (a,b+1), or (a+1,b+1) from the point (a,b), we can set:
f(a,b) = f(a+1,b) + f(a,b+1) + f(a+1,b+1)
We can then use this recursion relation to calculate f(a,b) for all the points on the path of cartesian plane from (0,0) to (5,5). For example, to calculate f(0,0), we can use the recursion relation to find f(1,0), f(0,1), and f(1,1). Then, we can use these values to find f(0,0).
We can continue this process until we reach the destination point (5,5). The number of paths from (0,0) to (5,5) will be equal to f(0,0).
To know more cartesian plane about please refer: https://brainly.com/question/13266753
#SPJ4
