Final answer:
To use advanced mathematical functions such as sqrt, ceil, floor, and others, import the math module in Python or access the functions on a calculator, and ensure that values are dimensionless when required for certain functions.
Step-by-step explanation:
To use mathematical functions like sqrt(x), ceil(x), floor(x), factorial(x), cos(x), sin(x), exp(x), and log(x), you need to import the math module in Python by using the statement from math import *. This allows you to access these functions directly. If you are making calculations on a calculator, you can usually find these functions built into the device, but knowing how to access and apply them correctly is crucial for solving various mathematical problems.
In more complex equations, such as equilibrium problems, it may be necessary to perform operations like square roots or logarithms to find a solution. It's important to be familiar with how to execute these functions, either manually or using a calculator, especially when the values need to be dimensionless for the functions to be properly executed.