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Step-by-step explanation:
According to this description we need a number that can be divided by 2,3 and 4 since the amount of rocks can be described by a natural number. However if a number is divided by 4 it is divided by 2 as well since 2*2=4.
If α is a natural number then 2*α is a natural number as well as the product of two natural numbers.
Which means that we need a number devided by 3 and 4.
The smallest number that fulfills this demand is 3*4=12.
Also any product of 12 with any natural number can be devided by 3, 4 and 2.
If the exercise asks for the numbers that are divided only by 2,3 and 4 these are:
We were given the points, A(5,-3) and the midpoint of AB, M(-4,2).
Let point B have coordinates (c , d).
Then the midpoint of A(5, -3) and B(c,d)
Now let us compare to the given midpoint M(-4, 2).
We can then write the following equations for the corresponding coordinates.
Comparing x coordinates, we have;
Multiplying both sides of the equation by 2 gives,
5+c = 2(-4)
Simplifying the right hand side gives,
5 + c = -8
Grouping like terms, we have,
c = -8 - 5
This simplifies to,
c = -13
Comparing y coordinates we have,
Multiplying through by 2 gives,
-3 + d = 2(2)
This means that,
-3 + d = 4
Making the subject we have,
d = 4+3
This implies that,
d = 7
Hence the coordinates of B are (-13,7).
Let point B have coordinates (c , d).
Then the midpoint of A(5, -3) and B(c,d)
Now let us compare to the given midpoint M(-4, 2).
We can then write the following equations for the corresponding coordinates.
Comparing x coordinates, we have;
Multiplying both sides of the equation by 2 gives,
5+c = 2(-4)
Simplifying the right hand side gives,
5 + c = -8
Grouping like terms, we have,
c = -8 - 5
This simplifies to,
c = -13
Comparing y coordinates we have,
Multiplying through by 2 gives,
-3 + d = 2(2)
This means that,
-3 + d = 4
Making the subject we have,
d = 4+3
This implies that,
d = 7
Hence the coordinates of B are (-13,7).