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Solved
Check Bertrand-Chebyshev's theorem about prime numbers
Historical context Bertrand's postulate, also later known as Chebyshev's theorem, is a very important theorem in number theory ...
2 months ago
Solved
Check p = 6n +/- 1, the generic formula for odd prime numbers greater than 3
Problem statement For all odd prime number p greater than 3, there exists a positive integer n, such that p = 6n +/- 1 : ...
2 months ago
Solved
Check p = 4n +/- 1, the generic formula for odd prime numbers
Problem statement For all odd prime number p, there exists a positive integer n, such that p = 4n +/- 1 : Check this f...
2 months ago
Solved
Chek the Delta = p' - p = 6k gap theorem about arithmetic progressions in the prime number set
Context In the prime numbers set there are some arithmetic progressions (sequences of three or more consecutive prime number...
2 months ago
Solved
List the near-square primes, p = n² + 1 (Landau's 4th problem)
Historical context At the 1912 International Congress of Mathematicians, Edmund Landau listed four basic problems about prime...
2 months ago
Solved
List primes which are the sum of two consecutive lower primes plus minus one
Problem statement Some prime numbers can be written as the sum of two consecutive lower primes plus / minus one : Like t...
2 months ago
Solved
Laws of motion 4
Given the initial velocity 'u', final velocity 'v' and acceleration 'a', find the distance travelled.
2 months ago
Solved
Estimating Battery Lifetime Based on Load Profile and Depth of Discharge (DoD)
In a Battery Management System (BMS), the lifetime of a battery depends on various factors, including the Depth of Discharge (Do...
2 months ago
Solved
Estimating the Range of an Electric Vehicle (EV)
In Electric Vehicles (EVs), the driving range is the estimated distance a vehicle can travel on a fully charged battery. The ran...
2 months ago
Solved
Estimating Battery Backup Time for an Inverter
In a Battery Management System (BMS), estimating the backup time of a battery-powered inverter helps determine how long it can s...
2 months ago
Solved
Battery Charge Rate Calculation
In a Battery Management System (BMS), the charge rate () of a battery can be calculated using the formula: where: is th...
2 months ago
Solved
Battery State of Health (SoH) Calculation
In a Battery Management System (BMS), the State of Health (SoH) of a battery is an indicator of its overall condition. It is cal...
2 months ago
Solved
Battery Charge Efficiency Calculation
In a Battery Management System (BMS), the efficiency of battery charging can be estimated using the formula: where: is the...
2 months ago
Solved
Battery Voltage Drop Estimation
In a Battery Management System (BMS), the voltage drop (V_drop) due to the load can be calculated using the formula:V_drop=I×R ...
2 months ago
Solved
Battery Discharge Time Estimation
In a Battery Management System (BMS), the estimated discharge time (T) of a battery can be calculated as: where: is the ...
2 months ago
Solved
State of Charge (SoC) Estimation for a Battery
The State of Charge (SoC) of a battery represents its remaining charge as a percentage. It can be calculated using the formula: ...
2 months ago
Solved
Battery Life Estimation for a Device
A battery-powered device consumes a constant current while operating. The estimated battery life (T) can be calculated using the...
2 months ago
Solved
Comparison of floating-point numbers (doubles)
<https://au.mathworks.com/help/matlab/matlab_prog/floating-point-numbers.html Floating-point numbers> cannot generally be repres...
2 months ago
Solved
The Five Infection (Boss Level)
Given a 3x3 matrix A, replace: every value that is equal to five every value that is directly adjacent to a five with zero in...
2 months ago
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Fives Begone
Given any sentence as an input value 'sentence', turn all fives into the letter X and return the improved sentence. Also, turn a...
2 months ago
Solved
Broken Clock
Create a function that outputs t, an inputted matrix time x, in hours and minutes (hr:min) unless the time contains a five. In t...
2 months ago
