Answer:
Option 2?
Step-by-step explanation:
Answer:
Constructive Proof
Step-by-step explanation:
Let x be a positive integer
x must be equal to sum of all positive integers exceeding it
i.e.
x = x + (x - 1) + ( x - 2) + ......... + 2 + 1
Equivalently,
x = ∑i (where i = 1 to x)
The property finite sum;
∑i (i = 1 to x) = x(x + 1)/2
So,
x = x(x + 1)/2 ------- Multiply both sides by 2
2 * x = 2 * x(x + 1)/2
2x = x(x + 1)
2x = x² + x ------- subtract 2x from both sides
2x - 2x = x² + x - 2x
0 = x² + x - 2x ----- Rearrange
x² + x - 2x = 0
x² - x = 0 ------ Factorise
x(x - 1) = 0
So,
x = 0 or x - 1 = 0
x = 0 or x = 1 + 0
x = 0 or x = 1
But x ≠ 0
So, x = 1
The statement is only true for x = 1
This makes sense because 1 is the only positive integer not exceeding 1
1 = 1
It is a Constructive Proof
A proof is constructive when we find an element for which the statement is true.
Number of cookie boxes bought by James = 5
Number of cakes bought by James = 2
Cost of each cakes = $4
Total bill paid by James = $28.50
Let us assume the cost of the each boxes of cookies = x
Then
5x + (2 * 4) = 28.50
5x + 8 = 28.50
5x = 28.50 - 8
5x = 20.50
x = 20.50/5
= 4.10
So we can see from the above deduction that the cost of each boxes of cookies bought by James is $4.10
Answer:
All of the functions required to transform inputs into outputs (goods and ... provide all of the materials and supplies required to create finished products and deliver ... System for determining the right quantity of various items to have on hand
Step-by-step explanation:
