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📊 Linear Equations
Solve the system of linear equations:
2x + 3y = 12
4x - y = 10
Show your work and explain each step.
📸 Visual Math Challenge
🔍 Graph Theory
Prove that if a graph G has n vertices and more than (n-1)(n-2)/2 edges, then G is connected. Use mathematical induction.
📈 Differential Equations
Solve the differential equation: dy/dx + 2y = e^(-x) with initial condition y(0) = 1. Show all steps.
🚀 Vector Calculus
A particle moves along a curve defined by r(t) = (t², t³, t⁴). Find the velocity vector and acceleration vector at t = 2.
💡 Tricky Math Problem
A store offers a 20% discount on all items. If the original price of an item is $100, and there's an additional 10% tax after the discount, what is the final price? Show your work and explain why this is different from a 30% discount.
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