for a particular set of atmospheric conditions, the function $y = \\frac{340}{x}$ models the frequency, $y$…

for a particular set of atmospheric conditions, the function $y = \\frac{340}{x}$ models the frequency, $y$, in waves per second, of sound waves with a wavelength of $x$ meters. a note played on a guitar has a frequency of 440 waves per second. to the nearest centimeter, what is the wavelength of the note? centimeters

for a particular set of atmospheric conditions, the function $y = \\frac{340}{x}$ models the frequency, $y$, in waves per second, of sound waves with a wavelength of $x$ meters. a note played on a guitar has a frequency of 440 waves per second. to the nearest centimeter, what is the wavelength of the note? centimeters

Answer

Explanation:

Step1: Sustituir el valor de y

Dado $y = \frac{340}{x}$ y $y = 440$, sustituimos $y$ en la ecuación: $440=\frac{340}{x}$.

Step2: Resolver para x

Multiplicamos ambos lados por $x$: $440x = 340$. Luego, dividimos ambos lados por 440: $x=\frac{340}{440}=\frac{17}{22}$ metros.

Step3: Convertir a centímetros

Sabemos que 1 metro = 100 centímetros. Entonces $x=\frac{17}{22}\times100=\frac{1700}{22}\approx 77.27$ centímetros. Redondeando al centímetro más cercano, $x\approx 77$ centímetros.

Answer:

77