Answer:
(5,30)
Step-by-step explanation:
That is the constant change in the y's as the x's increase by 1?
12 - 6 = 6
18 - 12 = 6
24 - 18 = 6
The common difference is 6 so the next coordinate will be 6 more on the y and 1 more on the x.
(5,30)
There really is no single "obvious" choice here...
Possibly the sequence is periodic, with seven copies of -1 followed by six copies of 0, or perhaps seven -1s and seven 0s. Or maybe seven -1s, followed by six 0s, then five 1s, and so on, but after a certain point it would seem we have to have negative copies of a number, which is meaningless.
Or maybe it's not periodic, and every seventh value in the sequence is incremented by 1? Who knows?
I'll go ahead and assume the latter case, that the sequence is not periodic, since that's technically somewhat easier to manage. We can assign the following rule to the

-th term in the sequence:


for

.
So the generating function for this sequence might be

As to what is meant by "closed form", I'm not sure. Would this answer be acceptable? Or do you need to find a possibly more tractable form for the coefficient not in terms of the floor function?
Vertex is -b/2a. The variable b=2 and a=2. That finds the x coordinate of the vertex. Then to find the y coordinate you just plug the number you got for x (-1/2) into the equation. Like so:
y = 2x+2
y = 2(-1/2)+2
y = -1+2
y = 1
So your vertex is ( -1/2, 1 )
To graph your vertex you take your x coordinate (-1/2) and find it on the x axis of the graph (horizontal line). Then do the same for y (1) (on the vertical axis.
Now that you have your vertex graphed you can find out if it is minimum or maximum by looking at the direction in which the slope is going. If it goes in the positive direction (up) then it is a minimum since that is the lowest point that the line touches. If it is maximum it is opposite. The line faces down and the highest point the line touches is that point.
Answer:
Step-by-step explanation:
= tan 29°
x =
≈ 34.28