MATHEMATICS HIGH SCHOOL

When two musical notes are a “sixth” apart, the frequency of the lower note is 3/5 the frequency of the higher note. Using f as the frequency of the higher note, write an expression for the frequency of the lower note. HELP!1. f - 2/5

2. 3/5 f

3. 2/5 f

4. 3/5 + f

Answers

Answer 1
Answer:

The correct expression for the frequency of the lower note when two musical notes are a sixth apart is: 3/5 f

Given that two musical notes are a “sixth” apart, the frequency of the lower note is 3/5 the frequency of the higher note.

We need to determine the expression for the frequency of the lower note.

When two musical notes are a "sixth" apart, it means that there are five whole steps or intervals between the two notes.

In music theory, each whole step corresponds to multiplying the frequency by a constant factor.

If we denote the frequency of the higher note as f, then the frequency of the lower note, which is 3/5 times the frequency of the higher note, can be calculated by multiplying f by 3/5.

Therefore, the correct expression for the frequency of the lower note is 3/5 f.

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Answer 2
Answer:

Answer:

2. 3/5 f

Step-by-step explanation:

the lower note is the product of it's fractional part and the frequency of the higher note.

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Answers

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Answers

(4)/(2+\sqrt3+\sqrt7)\cdot(2-(\sqrt3+\sqrt7))/(2-(\sqrt3+\sqrt7))=(8-4\sqrt3-4\sqrt7)/(2^2-(\sqrt3+\sqrt7)^2)=(8-4\sqrt3-4\sqrt7)/(4-3-2√(3\cdot7)-7)\n\n=(8-4\sqrt3-4\sqrt7)/(-6-2√(21))=(-2(2\sqrt3+2\sqrt7-4))/(-2(3+√(21)))=(2\sqrt3+2\sqrt7-4)/(3+√(21))\cdot(3-√(21))/(3-√(21))\n\n=(6\sqrt3-2√(63)+6\sqrt7-2√(147)-12+4√(21))/(3^2-(√(21))^2)=(6\sqrt3-2√(9\cdot7)+6\sqrt7-2√(49\cdot3)-12+4√(21))/(9-21)

=(6\sqrt3-6\sqrt7+6\sqrt7-14\sqrt3-12+4√(21))/(-12)=(-8\sqrt3+4√(21)-12)/(-12)=(-4(2\sqrt3-√(21)+3))/(-12)\n\n=(2\sqrt3-√(21)+3)/(3)

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(4)/(2\sqrt3+\sqrt5)\cdot(2\sqrt3-\sqrt5)/(2\sqrt3-\sqrt5)=(8\sqrt3-4\sqrt5)/((2\sqrt3)^2-(\sqrt5)^2)=(8\sqrt3-4\sqrt5)/(4\cdot3-5)=(8\sqrt3-4\sqrt5)/(12-5)\n\n=(8\sqrt3-4\sqrt5)/(7)
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