Chapter 7 of the Jiuzhang suanshu presents a problem of two linear equations involving acres of land and their respective prices
2 answers:
You might be interested in
Options
A. Caroline rents exactly 7 games each month.
B. Caroline rents exactly 6 games each month.
C. Caroline rents 6 or more games each month.
D. Caroline rents from 1 to 5 games each month.
Answer:
D. Caroline rents from 1 to 5 games each month.
Step-by-step explanation:
Given
Plan A:
Plan B:
Required
Which options justifies A over B
The solution to this question is option (d).
In option d, n = 1,2,3,4,5
When any of the values of n is substituted in plan A and B, respectively; the cost of plan A is cheaper than plan B.
This is not so, for other options (A - C)
To show:
Substitute 1 for n in A and B
Plan A:
Plan B:
Substitute 5 for n in A and B
Plan A:
Plan B:
<em>See that A < B</em>
Answer:
Anything in the form x = pi+k*pi, for any integer k
These are not removable discontinuities.
============================================================
Explanation:
Recall that tan(x) = sin(x)/cos(x).
The discontinuities occur whenever cos(x) is equal to zero.
Solving cos(x) = 0 will yield the locations when we have discontinuities.
This all applies to tan(x), but we want to work with tan(x/2) instead.
Simply replace x with x/2 and solve for x like so
cos(x/2) = 0
x/2 = arccos(0)
x/2 = (pi/2) + 2pi*k or x/2 = (-pi/2) + 2pi*k
x = pi + 4pi*k or x = -pi + 4pi*k
Where k is any integer.
If we make a table of some example k values, then we'll find that we could get the following outputs:
- x = -3pi
- x = -pi
- x = pi
- x = 3pi
- x = 5pi
and so on. These are the odd multiples of pi.
So we can effectively condense those x equations into the single equation x = pi+k*pi
That equation is the same as x = (k+1)pi
The graph is below. It shows we have jump discontinuities. These are <u>not</u> removable discontinuities (since we're not removing a single point).
