If I apply the xy = 10000, then the function becomes
p(x) = 10000x + 2000000
The problem is that this is a linear function of x and has no minimum.
If I break it down into shipment costs and storage costs respectively, it would be like this:
shipment cost = 10000x
storage costs = 200xy =...
I first tried to set up an expression for the total amount of money that the company would spend in a year. That would be:
p(x, y) = 10000x + 200xy
where:
p(x, y) = the amount of money (dollars) that the company would spend in a year.
x = the number of shipments ordered per year.
y = the...
I see. Well, just one more question
Let's say that I do use the CTC
x(s) = [0, 1, s, 0]
Now, we know that the proper time experienced when traveling along a timelike curve between two events can be calculated by evaluating the following integral from s1 to s2:
$$\int \sqrt{-g_{ab}\dot x^a...
I suppose what is confusing me then is this. Here is a quote from you from another thread:
That is from the following thread:
https://www.physicsforums.com/threads/how-do-you-find-or-notice-a-boost-or-a-loop-on-a-spacetime.977237/
Now I just took notice of this as I was typing this reply...
But I thought you said that timelike coordinates had to have their derivatives with respect to s be greater than 0. That is why I set t to being s. Besides, how would that even work with t being held constant? The t coordinate is the time measured in the "lab frame". If t is held constant then...
Cool. I recently decided to use this line element that you have found (I added the missing c terms back in)
$$
ds^2 = \frac{2}{\omega^2} \left[ - c^2dt^2 - 2c\sqrt{2} \sinh^2 r \ d t d \varphi - \left( \sinh^4 r - \sinh^2 r \right) d \varphi^2 + dz^2 + dr^2 \right]
$$
I was able to verify...
I hope this one is readable
The new line element that I got is:
ds2 = (1/2ω2)[-c2dt2 - 2cercos(θ)sin(θ)drdt - 2cercos(θ)rcos(θ)dθdt - (1/2)e2rcos(θ)sin2(θ)dr2 - re2rcos(θ)sin(θ)cos(θ)drdθ - (1/2)e2rcos(θ)r2cos2(θ)dθ2 + cos2(θ)dr2 - 2rsin(θ)cos(θ)drdθ + r2sin2(θ)dθ2 + dz2]
This was the...
The new line element that I got is:
ds2 = (1/2ω2)[-c2dt2 - 2cercos(θ)sin(θ)drdt - 2cercos(θ)rcos(θ)dθdt - (1/2)e2rcos(θ)sin2(θ)dr2 - re2rcos(θ)sin(θ)cos(θ)drdθ - (1/2)e2rcos(θ)r2cos2(θ)dθ2 + cos2(θ)dr2 - 2rsin(θ)cos(θ)drdθ + r2sin2(θ)dθ2 + dz2]
This was the transformation from the cartesian...
Ok, I made the necessary switching of the roles of y and z, and I got a new line element. However, I notice a certain problem:
When I set all the differentials except for that of the angular coordinate equal to 0, ds2 is negative most of the time, but depending on the value of theta, it is 0...
Lol, it is like you read my mind. I was just looking at those differentials and noticed how with the line element that I just used, t and z seem to always be timelike, but r and θ seem to always be spacelike.
In that case, would I need a different line element or something to see the case...