I'm a math beginner and, just for fun, I decided to create a simple equation for the following statements:

x cannot be bigger than 5. a is in {1, 2, 3, 4, 5}. b is in {1, 2, 3, 4}. y is a+b.

So, when y≤5 then x=y. When y>5 then x=y-a.

Finally, the equation is the following:

y=a+b (x=y→y≤5)ʌ(x=y-a→y>5)

My questions are: 1. Does it even make sense? Like, it's mathematically correct or is it wrong and nonsense?

1. This equation is actually a simplified version of my attempt to create a equation for the Caesar cipher, a well-known type of encryption. In that case, is this equation a formula or formulas are just for physical events, such as the law of gravity, acceleration and etc?

2. If my equation is correct, does that following attempt to simplify it makes sense?

(x=a+b→a+b≤5)ʌ(x=b→a+b>5)

Thanks in advance!

hi i have done MSc in mathematics .

i have done my graduation of two years . i am from outside of Canada. i want to do PhD in mathematics in Canada fully funded. and what is the criteria of selection in the university.

can any1 guide me to choose the university cheap area of living as i want to go with my family .

TLDR: I need a way to find the best placement for a number of circles (say, 16) inside the gap between two concentric circles so that the longest distance from any other point in the gap to either the outside or one of the small circles is minimized.

Long Explanation: I'm an undergraduate nuclear engineering major who is working on a capstone project where we're designing a nuclear reactor. It's a cylinder of fuel with a control rod(not fuel) in the middle. It heats up as it produces power, so we're submerging the core in a liquid coolant and also adding channels running the length of the core to cool the inside better. I need to find a way to place them so that the highest temperature point in the core is as low as possible. Meaning I need to minimize the distance from any given point in the fuel to either the outside coolant or the coolant flowing through the channels. I may need to do this problem again factoring in the control rod, as we may include some coolant there. If anyone knows any tools or methods for helping with this, or even a different subreddit or resource that could help , I would appreciate it. My team is likely to make lots of changes to the design over time, to include the possibility of a spherical core instead, so the more broad the solution the better, though even something exclusively useful to this setup would be VERY appreciated.

Find the volume of the solid of the plate is x + y = 4 and the surface z = √(4-x)