A manufacturer with a product in the decline stage of the product life cycle would most likely decide to ________ if there is re
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Answer:
Number of units possible in S are 4.
Explanation:
Given <em>S</em> is a set of complex number of the form where <em>a</em> and <em>b</em> are integers.
is a unit if
exists such that
.
To find:
Number of units possible = ?
Solution:
Given that:
Taking modulus both sides:
Using the property that modulus of product of two complex numbers is equal to their individual modulus multiplied.
i.e.
So,
......... (1)
Let
Then modulus of z is
Given that a and b are <em>integers</em>, so the equation (1) can be true only when (Reciprocal of 1 is 1). Modulus can be equal only when one of the following is satisfied:
(a = 1, b = 0) , (a = -1, b = 0), (a = 0, b = 1) OR (a = 0, b = -1)
So, the possible complex numbers can be:
Hence, number of units possible in S are 4.
Answer:
1. That values that you must plot are:
- (1, 4.08))
- (20, 5.08)
- (40, 6.18)
2. Yes, the plot of those three points is straight enough.
Explanation:
<em><u>A. What are the values you will plot? </u></em>
The x-ccordinate of your plot is still the number of years the exmployees have worked for the company.
The y-coordinate of your plot is the the base-10 logarithm of the salary.
Therefore:
<u>1) A part-time shipping clerk</u>: 1 year, $12,000
⇒
<u>2) A manager</u>: 20 years, $120,000
⇒
<u>3) The CEO</u>: 40 years ago, $1,500,000
⇒
Summarizing, the points to plot are:
- (1, 4.08)
- (20, 5.08)
- (40, 6.18)
<u><em>B. Will the plot of these three points be straight enough?</em></u>
To find whether the plot is straight enoguh, you may either plot them, make a regression, or, since they are only three points, you can whether the change of rate of the points is constant.
- <u>Change of rate of the first two points, r</u>:
r = rise/run = Δy / Δx = (5.08 - 4.08) / (20 - 1) =1.00/19 ≈ 0.05
- <u>Change of rate of the second and the third points, r</u>:
r = rise/run = Δy / Δx = (6.18 - 5.08) / (20 - 1) = 0.05
Since both rate of changes are equal (or reasonably equal) the plot is straight enough.