A graph is a straight line through the point (0, 5). Can the graph represent a proportional relationship? Explain.
1 answer:
Answer:
The graph cannot represent a proportional relationship
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form or
In a proportional relationship the constant of proportionality k is equal to the slope m of the line and <u><em>the line passes through the origin</em></u> (0,0)
That means----> The x-intercept and the y-intercept of the line must to be the origin (0,0)
If the given line passes through the point (0,5), then the line not passes through the origin
therefore
The graph cannot represent a proportional relationship
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Hello there. To solve this question, we'll have to remember some properties about convergence of sequences.
Given the following sequence:
If it is a finite sequence, then it converges to its last term, that is the lim sup (or greatest term of the sequence).
If it is infinite, then the sequence only converges if this limit exists and is equal to zero, that is:
With this, we'll be able to determine whether the following sequence is convergent or not:
Since it is a finite sequence, we already know it converges.
The lim sup of this sequence is its largest term, in this case, 408, and we write:
If it was an infinite sequence, on the other hand, we would have to determine the general term a_n and see if the limit is equal to zero.
Notice that there is a pattern between the values: the difference between two consecutive numbers is equal to 100.
In other words, it is an arithmetic progression with ratio equal to 100.
This means that we can use the following formula:
Where a_1 = 8 and r = 100, therefore:
And taking the limit as it goes to infinity, we have that:
That is, the limit is not zero (not even a real number), so the sequence would not converge.