Step-by-step explanation:
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Answer:
Step-by-step explanation:
Our inequality is |125-u| ≤ 30. Let's separate this into two. Assuming that (125-u) is positive, we have 125-u ≤ 30, and if we assume that it's negative, we'd have -(125-u)≤30, or u-125≤30.
Therefore, we now have two inequalities to solve for:
125-u ≤ 30
u-125≤30
For the first one, we can subtract 125 and add u to both sides, resulting in
0 ≤ u-95, or 95≤u. Therefore, that is our first inequality.
The second one can be figured out by adding 125 to both sides, so u ≤ 155.
Remember that we took these two inequalities from an absolute value -- as a result, they BOTH must be true in order for the original inequality to be true. Therefore,
u ≥ 95
and
u ≤ 155
combine to be
95 ≤ u ≤ 155, or the 4th option
The equation of the demand function is D(x) = 1400√(25-x²) + 11400
<h3>How to determine the demand function?</h3>
From the question, we have the following parameters that can be used in our computation:
Marginal demand function, D'(x) = -1400x÷√25-x²
Also, we have
D = 17000, when the value of x = 3
To start with, we need to integrate the marginal demand function, D'(x)
So, we have the following representation
D(x) = 1400√(25-x²) + C
Recall that
D = 17000 at x = 3
So, we have
17000 = 1400√(25-3²) + C
Evaluate
17000 = 5600 + C
Solve for C
C = 17000 - 5600
So, we have
C = 11400
Substitute C = 11400 in D(x) = 1400√(25-x²) + C
D(x) = 1400√(25-x²) + 11400
Hence, the function is D(x) = 1400√(25-x²) + 11400
Read more about demand function at
brainly.com/question/24384825
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