Hearing aids: Nationwide shortage of batteries prompts rationing

When we hear a sound, our nervous system is detecting sound waves—pressure waves of mechanical energy traveling through a medium. The frequency of the wave is perceived as pitch, while the amplitude is perceived as loudness.

A battery is a galvanic cell that is used as a source of electrical power for specific applications. Modern batteries exist in a multitude of forms to accommodate various applications, from tiny button batteries such as those that power wristwatches to the very large batteries used to supply backup energy to municipal power grids. Some batteries are designed for single-use applications and cannot be recharged (primary cells), while others are based on conveniently reversible cell reactions that...

Rational expressions are algebraic fractions in which both the numerator and the denominator are polynomials. These expressions follow the arithmetic rules of numerical fractions but require extra care due to the presence of variables. A fundamental part of working with rational expressions is identifying values that make the expression undefined, typically those that result in division by zero or undefined radicals.Determining the DomainThe domain of a rational expression includes all real...

Integrals involving non-rational functions are often difficult to evaluate using standard techniques, especially when radicals appear in the integrand. Rationalizing substitution provides a systematic method for simplifying such integrals by converting them into rational forms that are easier to handle.Consider a rod whose linear mass density depends on a constant linear density, a characteristic length, and the distance from the left end of the rod. Determining the total mass requires...

A conductor needs to be a component of a path that creates a closed loop or full circuit to have a continuous current flowing through it. A current starts to flow if an electric field is created inside an isolated conductor that is not part of a full circuit. The conductor quickly develops a net positive charge at one end and a net negative charge at the other. These charges generate an electric field opposite the direction of the applied electric field, which reduces the current. Eventually,...

A rational function is defined as the quotient of two polynomials:  where Q(x)≠0, These functions often exhibit asymptotes, which are the lines that the graph approaches but never touches. These asymptotes are classified based on how the function behaves near specific values of the input.Vertical asymptotes occur where the denominator is zero, and the numerator is not, causing the function to be undefined. These are found by solving Q(x)=0. For example:  has a vertical...