Learn Math with live MCPCalc tools
Explore proofs, worked examples, and clear explanations, then try the math yourself with graphing, CAS, proof builder, spreadsheets, and calculators.
Showing 4 pages in Engineering.
Filter By Subject
Proofs
Structured arguments in Proof Builder, with theorem statements, line-by-line reasoning, and nearby variations.
Worked Examples
Standard problems where the computation and the explanation stay tied to the live tool.
Explanations
Concept pages that build intuition first and then connect it to formal notation and exact calculations.
Worked Examples
Common examples from different branches of math, each written with clear step-by-step instructions.
Calculate the moment of inertia of an I-beam
The strong-axis second moment of area of an I-beam, found two ways: subtract the empty pockets from the outer rectangle, or add the flanges and web with the parallel axis theorem. Both give for a 150 by 250 mm section.
Open worked example →
Calculate a compound gear ratio
A compound gear train multiplies the ratios of its stages. Two stages give , so rpm in becomes rpm out and the ideal torque is multiplied by .
Open worked example →
Calculate flow rate from pressure and pipe diameter
Pressure and diameter alone do not fix a flow rate. What the pressure is doing decides the method: a known velocity gives , an orifice turns a pressure difference into flow, and a long pipe loses pressure to friction and has to be solved by iteration.
Open worked example →
Calculate pressure drop from flow rate
With the flow known, pressure drop in a pipe is a direct calculation: find the velocity, the Reynolds number, the friction factor, then apply Darcy-Weisbach and add fitting losses. For L/s through m of mm pipe with two elbows it comes to about kPa.
Open worked example →