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📊 Linear Equations
Solve the system of equations:
2x + 3y = 12
4x - y = 10
Show your work and explain each step
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 in your proof.
Use mathematical induction in your proof.
📈 Differential Equations
Solve the differential equation:
dy/dx + 2y = e^(-x)
Initial condition: y(0) = 1
dy/dx + 2y = e^(-x)
Initial condition: y(0) = 1
🚀 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
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 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
Show your work and explain why this is different from a 30% discount
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