Look at the pentagonal numbers. Use finite differences to determine which function represents the pattern.
2 answers:
Answer:
f(x) = 1.5x - 0.5x
Step-by-step explanation:
The function of the pattern represented by the pentagonal numbers is the sum of three triangular numbers.
The triangular number general formula
x (x + 1) / 2
For example,
The sequence
1, 3, 6, 10
*
* * *
* * * * * *
* , * *, * * *, * * * *
_____________________________
The pentagonal numbers
The sequence:
1, 5, 12, 22, 35
As shown in the picture can be divided into three triangles
Triangle 2
x (x + 1) / 2
Triangle 1 and 3 (they are triangles one unit smaller than 2)
n (n + 1) / 2
n= x-1
Replacing n
(x-1) ((x-1) + 1) / 2
(x-1) (x) / 2
(x-1) x / 2
______________
Function represents the pattern
Triangle 2 + (Triangle 1 + Triangle 3)
Triangle 1 = Triangle 3
So then,
Triangle 2 + 2* Triangle 1
x (x +1) /2 + 2* (x -1) x/2
Rearranging
0.5 x (x +1) + x(x -1)
0.5x^2 + 0.5x + x^2 -x
(0.5 x^2 + x^2) + (0.5x -x )
1.5 x^2 - 0.5 x
______
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Answer:
Step-by-step explanation:
In order to convert 0.0004578, which is in decimal, to scientific notation, all we need to do in this case is to move our decimal point to the right till we arrive at the first number that is not a zero, and then eliminate all the zero.
In this case, we will have to move the decimal point 4 spaces to our right, which would mean our exponent would be negative. The number of decimal spaces we moved to our right would be the value of our exponent, which is -4 in this case.
Thus, we have: