F(x) = x² increases at a faster rate than g(x) = 2x.
f(x)
Reason:
x = 0, 1, 2, 3, 4, 5, 6, 7
f(x) = 0, 1, 4, 9, 16, 25, 36, 49
g(x) = 0, 2, 4, 6, 8, 10, 12, 14.
Comparing the values of f(x) and g(x), we can see that that of f(x) are far higher than that of g(x) for the same values of x.
So f(x) increases at a faster rate.
Using function concepts, it is found that it is increasing on the interval:
(–∞, –5] ∪ [3, ∞)
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The function is given by:

The graph is given at the end of this question.
- If the function is pointing upwards, it is increasing. Otherwise, it is decreasing.
- In the graph, it can be seen that it is pointing upwards for x of -5 and less, or 3 and higher, thus, the interval is:
(–∞, –5] ∪ [3, ∞)
A similar problem is given at brainly.com/question/13539822
A geometric series is written as
, where
is the first term of the series and
is the common ratio.
In other words, to compute the next term in the series you have to multiply the previous one by
.
Since we know that the first time is 6 (but we don't know the common ratio), the first terms are
.
Let's use the other information, since the last term is
, we know that
, otherwise the terms would be bigger and bigger.
The information about the sum tells us that

We have a formula to compute the sum of the powers of a certain variable, namely

So, the equation becomes

The only integer solution to this expression is
.
If you want to check the result, we have

and the last term is

This is the concept of scale factor. The linear scale factor is given by:
(height of sculpture)/(height of clothespin)
=20/(5/12)
=48
Given that a woman is 5ft 7 in, the sculpture of this woman would be:
height of sculpture=(scale factor)*(height of the woman)
height of the woman=5 ft 7 inches=5 7/12 ft=67/12 ft
hence the height of the sculpture will be:
67/12×48
=268 ft
Answer: 268 ft