How many multiples of 4 are natural numbers less than or equal to 10?
1 answer:
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Answer:
Part A)
In interval notation:
Or, as an inequality:
Part B)
Part C)
V(x) is increasing for 1 < x < 3.5 and decreasing for 3.5 < x < 5.
Step-by-step explanation:
The building boxes have lengths represented by (<em>x</em> + 1), widths by (5 - <em>x</em>), and heights by (<em>x</em> - 1).
Part A)
Since they are side lengths, they must be positive. In other words:
Solving for each inequality yields:
We can eliminate the first inequality. Thus, our compound inequality is:
So, the reasonable domain for V(x) will be all values greater than one and less than five.
In interval notation:
Or as an inequality:
Part B)
We only need to look at the part of the graph within our domain.
For 1 < <em>x</em> < 5, we can see that its maximum is 17.
This occurs around <em>x</em> = 3.5.
Part C)
Again, we only need to look at the part of the graph within our domain.
As we can see, starting from <em>x</em> = 1 to <em>x</em> = 3.5 (approximately), our function is increasing (i.e. sloping upwards).
From <em>x</em> = 3.5 (approximately) and ending at <em>x</em> = 5, our function is decreasing.
Therefore, V(x) is increasing for 1 < x < 3.5 and decreasing for 3.5 < x < 5.