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.
Answer:
b)−2° C
Step-by-step explanation:
hello! To solve this problem you should remember how are the operations with negative numbers, for this the only thing we must do is make a subtraction between the initial temperature (8° C) and the negative change of temperature (10° C)
Ti= initial temperature =8° C
ΔT= temperature change =10° C
new temperature=Ti-ΔT
new temperature=8° C-10° C=-2° C
in conclusion the answer is -2° C
Answer:
The value of 2 in 2000 is 10 times greater than the value of 2 in 200
Step-by-step explanation:
from the value of 2 in 200 to reach 2000, it takes 10 times as much because we're moving only one place (which is the thousand's digit).
Answer:
answer is D
Step-by-step explanation:
2^4=16
16+(16-12)=20
over
(6+9)/(7-4)
15/3=5
so the new equation is 20/5=4
The ads aren’t working, it’s weird. you have to wait a really long time
