In this graph, 𝑥 and 𝑦 are directly proportional. This means that when 𝑥 doubles, 𝑦 also doubles, and when 𝑥 triples, so does 𝑦. In fact, for all coordinates on this line, you could multiply or ...

Differential equations are fundamental tools in physics: they are used to describe phenomena ranging from fluid dynamics to general relativity. But when these equations become stiff (i.e. they involve ...

Penn researchers have developed a smarter AI method for solving notoriously difficult inverse equations, which help scientists uncover hidden causes behind observable effects. By introducing ...

The field of inverse problems in fractional differential equations centres on recovering unknown parameters or inputs in systems described by fractional‐order operators. Fractional calculus introduces ...

Make sure you are confident in calculating with negative numbers, which is a skill often needed to solve equations. To solve the equation, do the inverse operation. The inverse of multiplying by 12 is ...