Answer:
The next number selected should be between 2 and 3 .
Step-by-step explanation:
x. x f(x) g(x)
0 10 17
1 11 19
2 14 21
3 19 23
4 26 25
3.5 22.25 24
<u>2.5 16.25 22</u>
1.5 12.25 20
0.5 10.25 18
We see the pattern that it is increasing with only a unit. The last given data is mid of the last two values that is 3 and 4.
So the next value would be the mid of the next last two values that is 2 and 3 and will be 2.5
Now it is moving in the reverse direction in the same pattern with a difference of a unit.
The range is the set of all y-coordinates.
R = {2, 6, 8}
Answer: The number is 26.
Step-by-step explanation:
We know that:
The nth term of a sequence is 3n²-1
The nth term of a different sequence is 30–n²
We want to find a number that belongs to both sequences (it is not necessarily for the same value of n) then we can use n in one term (first one), and m in the other (second one), such that n and m must be integer numbers.
we get:
3n²- 1 = 30–m²
Notice that as n increases, the terms of the first sequence also increase.
And as n increases, the terms of the second sequence decrease.
One way to solve this, is to give different values to m (m = 1, m = 2, etc) and see if we can find an integer value for n.
if m = 1, then:
3n²- 1 = 30–1²
3n²- 1 = 29
3n² = 30
n² = 30/3 = 10
n² = 10
There is no integer n such that n² = 10
now let's try with m = 2, then:
3n²- 1 = 30–2² = 30 - 4
3n²- 1 = 26
3n² = 26 + 1 = 27
n² = 27/3 = 9
n² = 9
n = √9 = 3
So here we have m = 2, and n = 3, both integers as we wanted, so we just found the term that belongs to both sequences.
the number is:
3*(3)² - 1 = 26
30 - 2² = 26
The number that belongs to both sequences is 26.
Answer:
1
Step-by-step explanation:
The radius is half the size of the diameter.
2 / 2 = 1
