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storchak [24]
3 years ago
14

1. The C major key, starting with the middle C, consists of seven notes (white keys on the piano) with the following frequencies

.
Note; C D E F G A B
Frequency;(Hz) 261.6 / 293.7 / 329.6 / 349.2 / 392.0 / 440.0 / 493.9
Determine the ratio of the note A to middle C.
a. 1.6818
b. 1.4983
c. 1.5348
d. 1.3654
2.The C major key, starting with the middle C , consists of seven notes (white keys on the piano) with the following frequencies.
Note: C D E F G A B
Frequency(Hz): 261.6 / 293.7 / 329.6 / 349.2 / 392.0 / 440.0 / 493.9
Determine the ratio of the note D to middle C.
a. 1.1227
b. 1.4566
c. 1.234
d. 1.3454
3. When an octave is divided into twelve equal steps, a chromatic scale results. The ratios between sucessive notes is constant.
c- 261.6 c#-277.2 d- 293.6 d#- ? e-329.6 f- 249.2 f#-370.0 g-392.0 g#- ? a-440 a#-466.1 b- 493.8 c-523.2
Determine the missing frequency for D# using the ratio 1.0595. Round to the nearest tenth.
a. 311.0
b. 415.3
c. 311.1
d. 625.2
4. A chord consists of notes that sound good together. The C major chord, starting at middle C, has the following frequencies:
C - 262 Hz
E - 330 Hz
G - 392 Hz
Determine the ratio of the frequency of G to C. Express the answer in a simple integer ratio. (Due to rounding the ratio will be approximate.)
a. 5 to 4
b. 3 to 2
c. 6 to 5
d. 9 to 8
5. A chord consists of notes that sound good together. The C major chord, starting at middle C, has the following frequencies:
C - 262 Hz
E - 330 Hz
G - 392 Hz
Determine the ratio of the frequency of E to C. Express the answer in a simple integer ratio. (Due to rounding the ratio will be approximate.)
a. 5 to 4
b. 3 to 2
c. 6 to 5
d. 9 to 8
6.Which component in a musical note is referred to as the pitch of a sound?
a. wavelength
b. frequency
c. time
d. distance
PLEASE HELP!!
Mathematics
2 answers:
Lorico [155]3 years ago
8 0
1.) <span>the ratio of the note A to middle C = 440.0 / 261.6 = 1.6820 ≈ 1.6818

2.) </span><span>the ratio of the note D to middle C = 293.7 / 261.6 = 1.1227

3.) </span><span>D# = 293.6 x 1.0595 = 311.1

4.) </span><span>the ratio of the frequency of G to C is 1 : 262/392 = 1 : 0.6683 ≈ 3 : 2

5.) </span><span>the ratio of the frequency of E to C = 1 : 262/330 = 1 : 0.7939 ≈ 5 : 4

6.) The </span><span>component in a musical note is referred to as the pitch of a sound is the frequency.</span>
Mariulka [41]3 years ago
7 0

Answer:

I am not going to steal your thunder by putting up the same answers, but all of them are correct.  Thanks for the help. :)

Step-by-step explanation:

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Lemur [1.5K]

First translate the question into an equation.

"What percent" means x/100, "of 40" means times 40, "is 14" equals 14.

So we have (x)(40) = 14 or 40x = 14.

Dividing both sides by 40, we find that x = 0.35.

Now, we want to write our answer as a percent.

So we move the decimal 2 places to the right and we have 35%.

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2 years ago
4) The path of a satellite orbiting the earth causes it to pass directly over two
Naily [24]

Answers:

  • Satellite is approximately <u>2446.43 km</u> from station A.
  • Satellite is approximately <u>2441.61 km</u> above the ground.

=========================================================

Explanation:

I'm assuming tracking stations A and B are at the same elevation and are on flat ground. In reality, this is likely not the case; however, for the sake of simplicity, we'll assume this is the case.

The diagram is shown below. Points A and B describe the two stations, while point C is the satellite's location. Point D is on the ground directly below the satellite. We have these lengths

  • AB = 60 km
  • AD = x
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Focusing on triangle ACD, we can apply the tangent rule to isolate h.

tan(angle) = opposite/adjacent

tan(A) = CD/AD

tan(86.4) = h/x

x*tan(86.4) = h

h = x*tan(86.4)

We'll use this later in the substitution below.

--------------------

Now move onto triangle BCD. For the reference angle B = 85, we can use the tangent rule to say

tan(angle) = opposite/adjacent

tan(B) = CD/DB

tan(B) = CD/(DA+AB)

tan(85) = h/(x+60)

tan(85)*(x+60) = h

tan(85)*(x+60) = x*tan(86.4) .............  apply substitution; isolate x

x*tan(85)+60*tan(85) = x*tan(86.4)

60*tan(85) = x*tan(86.4)-x*tan(85)

60*tan(85) = x*(tan(86.4)-tan(85))

x*(tan(86.4)-tan(85)) = 60*tan(85)

x = 60*tan(85)/(tan(86.4)-tan(85))

x = 153.612786190499

--------------------

We'll use this approximate x value to find h

h = x*tan(86.4)

h = 153.612786190499*tan(86.4)

h = 2441.60531869599

h = 2441.61 km  is how high the satellite is above the ground.

Return to triangle ACD. We'll use the cosine rule to determine the length of the hypotenuse AC

cos(angle) = adjacent/hypotenuse

cos(A) = AD/AC

cos(86.4) = x/AC

cos(86.4) = 153.612786190499/AC

AC*cos(86.4) = 153.612786190499

AC = 153.612786190499/cos(86.4)

AC = 2446.43279498247

AC = 2446.43 km is the distance from the satellite to station A.

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3 years ago
Suppose the population of a town is 17,400 and is growing 2% each year.
sveticcg [70]

Answer: 20,532

Step-by-step explanation:

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8 0
2 years ago
Read 2 more answers
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IRISSAK [1]

The length of the line is the difference between the endpoints of the line

The length of each line to the nearest fourth inch is 0.25 inch

<h3>How to measure the length of each line</h3>

The length of the horizontal line is given as:

Length = 2 inches

This is calculated as:

Length = 3 inches - 1 inch

Length = 2 inches

8 lines are to be drawn between the 1 inch and 3 inches point.

So, the length (l) of each line is:

l = \frac{2\ inches}{8}

Simplify the fraction

l = \frac{1\ inches}{4}

Divide

l = 0.25\ inch

Hence, the length of each line to the nearest fourth inch is 0.25 inch

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1 year ago
How many sets of three consecutive integers are there in which the sum of the three integers equals their product?
skad [1K]

Answer:

3

Step-by-step explanation:

since the 3 integers are consecutive, we are dealing with x, x+1, x+2.

and their sum is the same as their product :

x + (x + 1) + (x + 2) = x(x + 1)(x + 2)

3x + 3 = x(x² + 3x + 2) = x³ + 3x² + 2x

x³ + 3x² - x - 3 = 0

this is a polynomial of third degree.

and as such it has 3 solutions.

of course, it could be that some of them are the same or are even in the realm of complex numbers (i = sqrt(-1)), but usually these 3 solutions are different real numbers.

I tried x=1 just to see, and, hey, it is a solution for this equation.

x = 1 means that the other 2 consecutive integers are 2 and 3.

and indeed, 1+2+3 = 1×2×3 = 6.

now it is easier to find the other 2 solutions, as a zero solution can be expressed as a factor of the whole expression.

for x = 1 the factor term is (x - 1), as this term is then turning 0, when x = 1.

I can divide the main expression by this factor and then analyze the quotient about the other 2 solutions.

x³ + 3x² - x - 3 : x - 1 = x² + 4x + 3

- x³ - x²

----------------

0 4x² - x

- 4x² - 4x

-----------------------

0 + 3x - 3

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0 0

so, the original expression can be written as

(x² + 4x + 3)(x - 1).

now we need to find the 2 zero solutions for x²+4x+3

the general solution to a quadratic equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

a = 1

b = 4

c = 3

so,

x = (-4 ± sqrt(4² - 4×1×3))/(2×1) =

= (-4 ± sqrt(16 - 12))/2 = (-4 ± sqrt(4))/2 =

= (-4 ± 2)/2 = -2 ± 1

x1 = -2 + 1 = -1

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so, we have the additional solutions :

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and there we have it fully proven :

there are 3 different sets of 3 consecutive integers with the same sum as product.

4 0
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