Aband is marching in a rectangular formation with dimensions n-2 and n + 8. in the second stage of their performance, they re-arrange to form a different rectangle with dimensions n and 2n - 3, excluding all the drummers. if there are at least 4 drummers, then find the sum of all possible values of n?

The sum of all possible values of n is 9.

Step-by-step explanation:

We are going to solve this problem by subtracting areas.

For the first stage, the rectangular area of the formation is :

In the second stage, the rectangular area of the formation is :

We know that in this second formation they excluded all the drummers and also we know that there are at least 4 drummers.

Therefore, the difference between the areas of the first and the second formation is :

and this area must be at least 4 (because of the drummers excluded)

(I)

We need to solve this and find the possibles ''n'' that satisfy the inequality.

First we look for the values that satisfy

(II)

Using the quadratic equation :

For this values of ''n'' the inequality (I) is satisfied.

Now we study the vertex.

Given a quadratic function

The coordinate ''x'' of the vertex is

For (II)

This is the coordinate ''x'' of the vertex.

For the coordinate ''y'' we calculate

That is positive. The coordinates of the vertex are

In the quadratic function

So it is a negative quadratic function.

We conclude that for the interval

[4,5] the quadratic function is positive, therefore between [4,5] the inequality (I) is satisfied.

The two possible values for n are 4 and 5.

Finally, is the sum of all possible values of n

(Notice that n must be an integer number)

the answer is vanilla

step-by-step explanation:

answer: all the values are within because it has a pattern that repeats from -6 to 4.

good luck!