Applied Mathematics
Problems related to numerical analysis, optimization, mathematical modeling, etc.
Problems in this category
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
The problem is to solve the second-order linear non-homogeneous differential equation $2y'' - 2y' + ...
Differential EquationsSecond-Order Differential EquationsLinear Differential EquationsNon-homogeneous Differential EquationsCharacteristic EquationComplex Roots
2025/3/11
The total cost function for a product is given by $C(x) = 850 \ln(x+10) + 1700$, where $x$ is the nu...
Cost FunctionLogarithmExponential FunctionOptimization
2025/3/8
The problem provides a total cost function $C(x) = 850 \ln(x + 10) + 1700$, where $x$ is the number ...
Cost FunctionLogarithmExponential FunctionOptimizationBusiness Application
2025/3/8