Find rates of change until you find a constant.
dy/dx=1,2,3,4,5,6
d2y/dx2=1,1,1,1,1
So the acceleration, d2y/d2x, is constant. This means that this is a quadratic sequence of the form a(n)=an^2+bn+c. So we can set up a system of equations to solve for the values of a,b, and c. Using the first three points, (1,1), (2,2), and (3,4) we have:
9a+3b+c=4, 4a+2b+c=2, and a+b+c=1 getting the differences...
5a+b=2 and 3a+b=1 and getting this difference...
2a=1, so a=1/2 making 5a+b=2 become:
2.5+b=2, so b=-1/2, making a+b+c=1 become:
1/2-1/2+c=1, so c=1 so the rule is:
a(n)=0.5x^2-0.5x+1 or if you prefer to not have decimals
a(n)=(x^2-x+2)/2
Answer:
0/6 <--------------------------
What is meant binary number?
Binary number system, in mathematics, positional numeral system employing 2 as the base and so requiring only two different symbols for its digits, 0 and 1, instead of the usual 10 different symbols needed in the decimal system.
What is decimal in number system?
- A number system which uses digits from 0 to 9 to represent a number with base 10 is the decimal system number.
- The number is expressed in base-10 where each value is denoted by 0 or first nine positive integers.
- Each value in this number system has the place value of power 10.
Similarities between binary and decimal systems -
- Arithmetic operations can be carried out on numbers in both the binary ands decimal systems
- Values of each bit and digit in binary and decimal numbers respectively depends on how close they are to the decimal point
- Integer and fraction components are represented in both decimal and binary systems.
Learn more about decimal systems
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