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Risolto
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 : ...
9 giorni fa
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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...
9 giorni fa
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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...
9 giorni fa
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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...
9 giorni fa
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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...
9 giorni fa
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Simulate full-stop emergency braking scenario.
Emergency braking events demand rapid deceleration to bring the vehicle safely to rest. Given initial vehicle speed and constant...
9 giorni fa
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Compute optimal regenerative and friction brake torque blending.
Electric and hybrid vehicles combine regenerative braking with traditional friction braking to maximize energy recovery while en...
9 giorni fa
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Estimate brake disc temperature rise during braking.
During braking, kinetic energy is converted into thermal energy, causing brake discs to heat up. Excessive temperature rise can ...
9 giorni fa
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Compute optimal front–rear brake force distribution.
Modern braking systems dynamically distribute braking forces between front and rear axles to maintain stability, reduce stopping...
9 giorni fa
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Compute wheel slip ratio during braking.
During braking, a difference develops between the vehicle’s forward speed and the rotational speed of its wheels. This differenc...
9 giorni fa
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Estimate dynamic load transfer to front axle during braking.
During braking, load shifts from the rear axle to the front axle. Given mass, deceleration, center of gravity height, and wheelb...
9 giorni fa
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Estimate brake line pressure required for a given force.
Hydraulic braking systems amplify pedal input to generate braking force. Given braking force and piston area, compute the hydrau...
9 giorni fa
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Compute the required brake torque at wheel to stop the car
Brake torque defines how effectively braking force translates into wheel deceleration. Given braking force and wheel radius, det...
9 giorni fa
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Compute braking force using vehicle mass and acceleration.
Compute braking force required to stop a vehicle of mass 'm' and with acceleration 'a' Remember: F = m × a.
9 giorni fa
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Compute vehicle stopping distance using initial speed and constant deceleration.
Given vehicle speed v (m/s) and constant deceleration a (m/s²), compute stopping distance Remember: d = v² / (2a)
9 giorni fa
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Estimating Monthly Electricity Cost for a Household Appliance
You recently bought an electric kettle for your kitchen, and you want to estimate how much it costs to run every month. The kett...
9 giorni fa
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Voltage Divider Calculation
A voltage divider is a simple circuit used to obtain a reduced voltage from a higher voltage source using two resistors in serie...
9 giorni fa
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LED Current Calculation
In an electrical circuit, the current (III) flowing through an LED is determined using Ohm’s Law: Where: I is the current ...
9 giorni fa
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Inductor Energy Storage Calculation
The energy (EEE) stored in an inductor is given by the formula: Where: E is the energy in joules (J) L is the inductance in...
9 giorni fa
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Calculate Charge Using Capacitance and Voltage
The charge (Q) stored in a capacitor is given by the formula:Q=C×V where: C is the capacitance (in farads) V is the voltage (...
9 giorni fa
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Energy Stored in a Capacitor
The energy (E) stored in a capacitor is given by the formula: where: C is the capacitance (in farads) V is the voltage (in ...
9 giorni fa
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Calculate Current in a Series Circuit Using KVL
Kirchhoff's Voltage Law (KVL) states that the sum of voltages around a closed loop is zero. Given a voltage source (V) and three...
9 giorni fa
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Calculating the Total Resistance in a Series Circuit
Description: In a series circuit, the total resistance is the sum of the individual resistances. This problem asks you to write ...
9 giorni fa
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Simple Electrical Power Calculation
Calculate the electrical power using the formula: P=V×I where: V is the voltage (in volts) I is the current (in amperes)
9 giorni fa
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Ohm’s Law - Calculate Resistance
Ohm’s Law states that resistance R can be calculated as:R=V/I where: V is the voltage (in volts) I is the current (in ampere...
9 giorni fa
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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...
9 giorni fa
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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...
9 giorni fa
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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...
9 giorni fa
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No Fives Permitted
Create a function that gives users an custom error message if the matrix A contains a five. The error message should say "No Fiv...
9 giorni fa
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A Fiveless Factorial
Given a positive integer x, compute its factorial y, but exclude any muliplication by five if applicable.
9 giorni fa
