Applied Mathematics
Problems related to numerical analysis, optimization, mathematical modeling, etc.
Problems in this category
We are asked to calculate the apparent power in KVA of a 3-phase, 415V, 50 Hz, star system. The line...
Electrical EngineeringThree-Phase PowerApparent PowerPower FactorVoltageCurrent
2025/3/12
The problem provides two vectors, $u$ and $v$, defined as $u = -i + 3j + k$ and $v = 4i + 7j$. This ...
VectorsDot ProductLinear Algebra3D Vectors
2025/3/12
A company wants to have $20,000 at the beginning of each 6-month period for the next $4\frac{1}{2}$ ...
Financial MathematicsPresent ValueAnnuity DueCompound Interest
2025/3/11
A company wants to have $20,000 at the beginning of each 6-month period for the next $4\frac{1}{2}$ ...
FinanceAnnuityPresent ValueCompound Interest
2025/3/11
The problem gives a cost function $C(x) = 850 \ln(x + 10) + 1700$, where $x$ is the number of units ...
Cost FunctionLogarithmsOptimizationCalculus
2025/3/11
The problem gives the total cost function for a product as $C(x) = 850\ln(x+10) + 1700$, where $x$ i...
Cost FunctionLogarithmsCalculusOptimizationModeling
2025/3/11
A metal cable of length 10 m and mass 200 kg is hanging vertically from a bridge. We need to calcula...
WorkPotential EnergyPhysicsCalculusIntegrationCenter of Mass
2025/3/11
Solve the first-order linear differential equation $y' - \cot(x)y = \tan(x)$.
Differential EquationsFirst-Order Linear Differential EquationIntegrating FactorCalculusTrigonometry
2025/3/11
We are asked to solve the second-order linear non-homogeneous differential equation: $y'' + y' = 4x ...
Differential EquationsSecond-Order Linear Differential EquationsHomogeneous EquationNon-homogeneous EquationCharacteristic EquationParticular SolutionGeneral Solution
2025/3/11
We are given a first-order differential equation $(x^2 + 4)y' + xy^2 + x = 0$ with the initial condi...
Differential EquationsFirst-Order Differential EquationsInitial Value ProblemIntegrationSeparable Equations
2025/3/11