Answer:
Step-by-step explanation:
Which one of These is a rational number
1 answer:
Answer:
OPTION D: 0
Step-by-step explanation:
Rational numbers are subset of real numbers. These are the numbers that can be represented by a ratio of two integers i.e., of the form , where 'q' is non-zero. The numbers after the decimal forms a pattern. Since, 'q' can be equal to 1, we conclude all integers are rational numbers.
Irrational numbers are the numbers which cannot be represented as ratios. They can only be represented as an approximate value. The numbers after the decimal do not form a pattern.
Here, A is 11.761038... Clearly, the decimal is non-terminating and does not follow a pattern.
In Option B we have √20. √20 = √2 . √10. We know that √2 is an irrational number. So, √20 is also irrational.
In Option C, we have the famous . The value of
is 3.14.... It is an irrational number. The approximate representation of
is
.
In Option D, we have 0. It is an integer. So, it is rational as well.
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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
______
