Answer:
8
Step-by-step explanation:
Each month your hair grows .5 inches
In the year 2009 there were 3500 birds on an island. If the bird population is declining 2.2% per year it means that in the year 2014 we will have 3500*
= 3131.57 birds.
The best prediction is that in the year 2014 the bird population will be 3132.
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:
D
Step-by-step explanation:
a "function" gives every x value exactly one y value.
A, B and C all have 2 or more y values for an x value.
use e.g. a pen and place it vertically (straight top-down, parallel to the y-axis) on the graphs.
how often does the pen intersect the function curve ?
that is what I am talking about.
if it is more than once, than the x value (the point on the x-axis), where you put your pen, has more than 1 y values.
and that is then not a function.
only D is a function. the pen intersects with the function curve only once, no matter where you put the vertical pen.
