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melisa1 [442]
3 years ago
6

Most intruments produce notes across ranges called octaves which are made up of 8 notes how many octaves do 51 notes span?

Mathematics
1 answer:
mojhsa [17]3 years ago
8 0

Answer: 51 notes span 6 octaves.

Step-by-step explanation:

The word "octave" is a Latin word that means "eight".

In an instrument, Each octave is made up of 8 musical notes.

If we have 51 notes , the number of octaves can be made in it = \dfrac{51}{8}

=6.375\approx6\ \ \ \ \ \text{[Rounded to the nearest whole number]}

Hence, 51 notes span 6 octaves.

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I need help with number 4
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\bf \begin{cases}
\quad3x+2y=-9\\
-10x+5y=-5
\end{cases}

so hmm the idea behind the elimination, is to make the value atop or below, of either variable, the same but with a negative sign

so hmmm say... we'll eliminate "y"

so... let's see, we have 2y and 5y, both positive
what do we multiply 2y to get a negative -5y, that way, -5y +5y = 0 and poof it goes

well let's see, let's try "k"     \bf 2yk=-5y\implies k=-\cfrac{5y}{2y}\implies k=-\cfrac{5}{2}

so.. if we multiply 2y by -5/2, we'll end up with -5y

well, let's multiply that first equation then by -5/2

\bf \begin{array}{rllll}
3x+2y=-9&\qquad\times -\frac{5}{2}\implies &-\frac{15}{2}x-5y=\frac{45}{2}\\\\
-10x+5y=-5&\implies &-10x+5y=-5\\
&&---------\\
&&\frac{-35}{2}x+0\quad=\frac{35}{2}
\end{array}\\\\
-----------------------------\\\\
\cfrac{-35}{2}x=\cfrac{-35}{2}\implies \cfrac{-35x}{2}=\cfrac{-35}{2}\implies x=\cfrac{2}{-35}\cdot \cfrac{-35}{2}
\\\\\\
\boxed{x=1}

so.. now we know x = 1.... so let's plug that in  say hmmm 2nd equation

\bf -10(1)+5y=-5\implies -10+5y=-5\implies 5y=5\implies\boxed{ y=1}
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