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Which option bests describes the relationship: h(x) =1/2x2?


Quadratic variation


Direct linear variation


Inverse variation


Explain how you got your answer to question #2 using 1-2 complete sentences



Which option bests describes the relationship: xy = 12?


Direct linear variation


Quadratic variation


Inverse variation


Explain how you got your answer to question #4 using 1-2 complete sentences.



The length, g, of a cello string varies inversely as the frequency, f, of its vibrations (cycles per second). Suppose it is known that an 18-inch-long cello string vibrates 300 cycles per second.


write an inverse variation equation for the situation above.


Then, show how to find the frequency of a 15-inch-long cello string.

Respuesta :

Answer:

quadratic variation

inverse variation

frequency = 360  

Step-by-step explanation:

[tex]h(x)=\frac{1}{2}x^2[/tex]

Here in h(x), we have x^2. x^2 always represents quadratic

x^2 at the top. so its is a quadratic variation

[tex]xy = 12[/tex]

Divide both sides by x

so [tex]y=\frac{12}{x}[/tex]

y is inversely proportional to x

so its inverse variation

length varies inversely as frequency, the equation is [tex]g=\frac{k}{f}[/tex]

18-inch-long cello string vibrates 300 cycles per second.

g=18 and f=300, solve for k

[tex]g=\frac{k}{f}[/tex]

[tex]18=\frac{k}{300}[/tex]

5400=k

[tex]g=\frac{5400}{f}[/tex]

length g= 15

[tex]15=\frac{5400}{f}[/tex]

multiply by f on both sides and divide both sides by 15

f=360

frequency = 360

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