Applied Mathematics
Problems related to numerical analysis, optimization, mathematical modeling, etc.
Problems in this category
We are given a gear train with four gears: A, B, C, and D. Gear A drives gear B, and gears B and C a...
Gear TrainsVelocity RatioRatio and ProportionMechanical Engineering
2025/4/29
A 20-tooth pinion drives a 40-tooth gear. The pinion has an angular velocity of 1000 rpm. We need to...
GearsMechanical EngineeringVelocity RatioAngular Velocity
2025/4/29
The problem is to solve the following differential equation: $2xy \frac{dy}{dx} + x^2 - y^2 = 0$.
Differential EquationsHomogeneous EquationsIntegrationSeparation of Variables
2025/4/29
We are asked to solve the following differential equation: $(x-y)\frac{dy}{dx} + x + y = 0$
Differential EquationsHomogeneous EquationsIntegrationVariable Substitution
2025/4/29
We are given the differential equation $3x + y + x\frac{dy}{dx} = 0$ and asked to solve it.
Differential EquationsFirst-Order Differential EquationsHomogeneous Differential EquationsIntegrationVariable Separation
2025/4/29
We are given the differential equation $y' = \frac{x^2 + 2y^2}{xy}$ and we are asked to solve it. Th...
Differential EquationsHomogeneous EquationsSeparation of VariablesIntegration
2025/4/29
The problem refers to a section of Flamingo Airways schedule. We are asked to find: (c) the average ...
RateSpeedTimeDistanceWord ProblemUnits Conversion
2025/4/28
The problem asks to determine the length of a line segment using a ruler. a. Find the length of the ...
MeasurementUnits ConversionError Analysis
2025/4/28
Bob said a man sat on a pole for $3.8 \times 10^7$ seconds. We need to determine the most appropriat...
Unit ConversionEstimationTime
2025/4/28
Paula calculated that a large oak tree can transpire $4.15 \times 10^5$ milliliters of water per day...
Unit ConversionScientific NotationRate
2025/4/28