Given:
Polynomial is .
Term is added in the given polynomial.
To find:
The end behavior of new polynomial.
Solution:
Let, .
New polynomial is
Highest power of x is 6 which is even and leading coefficient is negative. So,
Both ends of the graph will approach negative infinity.
Therefore, the correct option is A.
Given :
All the natural numbers below 1000 that are multiples of 3 or 5 .
To Find :
The sum of all the multiples of 3 or 5 below 1000.
Solution :
Max multiple of 3 is 999 .
Max multiple of 5 id 995 .
So , number of multiple of 3 is :
Similarly for 5 .
Now , sum of all multiple of 3 is given by :
Also , sum of all multiple of 5 is :
Therefore , total sum :
Now , there are some common number which we add two times like :
15 , 30 , 60 ......
So , we should subtract the sum of all multiple of 15 from T .
Now , sum of all multiple of 15 is 33165 .
So ,
Therefore , the sum of all the multiples of 3 or 5 below 1000 is 233168 .
Using the recurrence relation, we can find a couple more values in the sequence:
First differences are 0, 2, 4, 6, ...
Second differences are constant at 2, so the function is quadratic.
The sequence can be described by the quadratic ...
... an = n² -n +2
_____
We know the value for n=0 is 2, so we can find <em>a</em> and <em>b</em> using the given values for a1 and a2.
... an = an² +bn +2
... a1 = 2 = a·1² +b·1 +2 . . . . for n=1
... a + b = 0
... a2 = 4 = a·2² -a·2 +2 . . . . for n = 2; using b=-a from the previous equation
... 2 = 2a
... a = 1 . . . . so b = -1
Answer:
Step-by-step explanation: