Alist contains n distinct integers. are all n integers consecutive? (1) the average (arithmetic mean) of the list with the lowest number removed is 1 more than the average (arithmetic mean) of the list with the highest number removed. (2) the positive difference between any two numbers in the list is always less than n.

  The list must contain consecutive integers. (They may not be arranged on the list in numerical order.)

Step-by-step explanation:

Assume that L and H are the lowest and highest integers on the list, respectively. Assume that the sum of the other numbers on the list is X. The condition (1) tells us ...

  (X + H)/(n -1) - (L + H)/(n -1) = 1

  H - L = n -1 . . . . . . . . multiply by n-1 and simplify

In order for the highest and lowest of the n distinct integers to have a difference of n-1, the integers must be consecutive. Any pair will have a difference no less than 1 and no greater than n-1, meeting condition (2).

Example:

  Consider the 5 integers 13, 14, 15, 16, 17. The difference between highest and lowest is 17-13 = 4 = 5-1.

The average with the lowest removed is 15.5; the average with the highest removed is 14.5, which differs from the previous average by 1.

addition

step-by-step explanation:

step-by-step explanation:

we can use this expression to calculate the energy gain as a particle moves with a field or the energy loss as it moves against it. (note that it is also used to define the electron-volt, a unit of energy equal to that gained by an electron as it falls through a pd of 1 v, i.e. w = 1 ev = 1.6 10-19 c 1 v = 1.6 10-19j).in fact this expression is really nothing more than the statement that potential is the potential energy per unit charge. in this case, v= w/qis simply stating that the change in potential energy(or work done) per unit charge is equal to the change in potential (or potential difference), v.student questions: uniform electric fields2electron beamcathode+5 kvanode0 v