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madam [21]
2 years ago
12

6+f49-8=2)

\\ " align="absmiddle" class="latex-formula">
​
Mathematics
1 answer:
madam [21]2 years ago
7 0

Answer:

The speed of a wave depends on the characteristics of the medium. For example, in the case of a guitar, the strings vibrate to produce the sound. The speed of the waves on the strings, and the wavelength, determine the frequency of the sound produced. The strings on a guitar have different thickness but may be made of similar material. They have different linear densities, where the linear density is defined as the mass per length,

μ

=

mass of string

length of string

=

m

l

.

In this chapter, we consider only string with a constant linear density. If the linear density is constant, then the mass

(

Δ

m

)

of a small length of string

(

Δ

x

)

is

Δ

m

=

μ

Δ

x

.

For example, if the string has a length of 2.00 m and a mass of 0.06 kg, then the linear density is

μ

=

0.06

kg

2.00

m

=

0.03

kg

m

.

If a 1.00-mm section is cut from the string, the mass of the 1.00-mm length is

Δ

m

=

μ

Δ

x

=

(

0.03

kg

m

)

0.001

m

=

3.00

×

10

−

5

kg

.

The guitar also has a method to change the tension of the strings. The tension of the strings is adjusted by turning spindles, called the tuning pegs, around which the strings are wrapped. For the guitar, the linear density of the string and the tension in the string determine the speed of the waves in the string and the frequency of the sound produced is proportional to the wave speed.

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Which of the following statements are true?
Eduardwww [97]

Answer:

B, C

Step-by-step explanation:

Consider all options:

A. The graph of the function f(x)=\dfrac{1}{2}\sqrt[3]{x} is vertically shrunk by a factor \frac{1}{2} the graph of the function f(x)=\sqrt[3]{x}, so the domain and the range of both functions are the same. This option is false.

B.  The graph of the function f(x)=\dfrac{1}{2}\sqrt[3]{x} is vertically shrunk by a factor \frac{1}{2} the graph of the function f(x)=\sqrt[3]{x}, so the domain and the range of both functions are the same. This option is true.

C. The graph of the function f(x)=\dfrac{1}{2}\sqrt[3]{(x-2)} is translated 2 units to the right and vertically shrunk by a factor \frac{1}{2} the graph of the function f(x)=\sqrt[3]{x}, so their graphs are similar except the first graph is shifted right and shrunk vertically by a factor of \frac{1}{2}.. This option is true.

D. The function f(x)=\dfrac{1}{2}\sqrt{x} has the domain and the range all non-negative real values. The function  f(x)=\sqrt[3]{x} has the domain and the range all real values. So this option is false.

3 0
3 years ago
Complete the equation of the line whose y intercept is (0,6) and slope is 3
m_a_m_a [10]
Y = mx + b
m = slope
b= y intercept

so the equation is y= 3x + 6
6 0
3 years ago
The average temperature change in degrees Fahrenheit per hour if the temperature fell 22degree Fahrenheit in 10 hours
Nonamiya [84]

Answer:

2.2 degrees per hour

Step-by-step explanation:

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4 0
3 years ago
Read 2 more answers
Given the sequence 1/2 ; 4 ; 1/4 ; 7 ; 1/8 ; 10;.. calculate the sum of 50 terms
miv72 [106K]

<u>Hint </u><u>:</u><u>-</u>

  • Break the given sequence into two parts .
  • Notice the terms at gap of one term beginning from the first term .They are like \dfrac{1}{2},\dfrac{1}{4},\dfrac{1}{8} . Next term is obtained by multiplying half to the previous term .
  • Notice the terms beginning from 2nd term , 4,7,10,13 . Next term is obtained by adding 3 to the previous term .

<u>Solution</u><u> </u><u>:</u><u>-</u><u> </u>

We need to find out the sum of 50 terms of the given sequence . After splitting the given sequence ,

\implies S_1 = \dfrac{1}{2},\dfrac{1}{4},\dfrac{1}{8} .

We can see that this is in <u>Geometric</u><u> </u><u>Progression </u> where 1/2 is the common ratio . Calculating the sum of 25 terms , we have ,

\implies S_1 = a\dfrac{1-r^n}{1-r} \\\\\implies S_1 = \dfrac{1}{2}\left[ \dfrac{1-\bigg(\dfrac{1}{2}\bigg)^{25}}{1-\dfrac{1}{2}}\right]

Notice the term \dfrac{1}{2^{25}} will be too small , so we can neglect it and take its approximation as 0 .

\implies S_1\approx \cancel{ \dfrac{1}{2} } \left[ \dfrac{1-0}{\cancel{\dfrac{1}{2} }}\right]

\\\implies \boxed{ S_1 \approx 1 }

\rule{200}2

Now the second sequence is in Arithmetic Progression , with common difference = 3 .

\implies S_2=\dfrac{n}{2}[2a + (n-1)d]

Substitute ,

\implies S_2=\dfrac{25}{2}[2(4) + (25-1)3] =\boxed{ 908}

Hence sum = 908 + 1 = 909

7 0
3 years ago
If <img src="https://tex.z-dn.net/?f=%5Crm%20%5C%3A%20x%20%3D%20log_%7Ba%7D%28bc%29" id="TexFormula1" title="\rm \: x = log_{a}(
timama [110]

Use the change-of-basis identity,

\log_x(y) = \dfrac{\ln(y)}{\ln(x)}

to write

xyz = \log_a(bc) \log_b(ac) \log_c(ab) = \dfrac{\ln(bc) \ln(ac) \ln(ab)}{\ln(a) \ln(b) \ln(c)}

Use the product-to-sum identity,

\log_x(yz) = \log_x(y) + \log_x(z)

to write

xyz = \dfrac{(\ln(b) + \ln(c)) (\ln(a) + \ln(c)) (\ln(a) + \ln(b))}{\ln(a) \ln(b) \ln(c)}

Redistribute the factors on the left side as

xyz = \dfrac{\ln(b) + \ln(c)}{\ln(b)} \times \dfrac{\ln(a) + \ln(c)}{\ln(c)} \times \dfrac{\ln(a) + \ln(b)}{\ln(a)}

and simplify to

xyz = \left(1 + \dfrac{\ln(c)}{\ln(b)}\right) \left(1 + \dfrac{\ln(a)}{\ln(c)}\right) \left(1 + \dfrac{\ln(b)}{\ln(a)}\right)

Now expand the right side:

xyz = 1 + \dfrac{\ln(c)}{\ln(b)} + \dfrac{\ln(a)}{\ln(c)} + \dfrac{\ln(b)}{\ln(a)} \\\\ ~~~~~~~~~~~~+ \dfrac{\ln(c)\ln(a)}{\ln(b)\ln(c)} + \dfrac{\ln(c)\ln(b)}{\ln(b)\ln(a)} + \dfrac{\ln(a)\ln(b)}{\ln(c)\ln(a)} \\\\ ~~~~~~~~~~~~ + \dfrac{\ln(c)\ln(a)\ln(b)}{\ln(b)\ln(c)\ln(a)}

Simplify and rewrite using the logarithm properties mentioned earlier.

xyz = 1 + \dfrac{\ln(c)}{\ln(b)} + \dfrac{\ln(a)}{\ln(c)} + \dfrac{\ln(b)}{\ln(a)} + \dfrac{\ln(a)}{\ln(b)} + \dfrac{\ln(c)}{\ln(a)} + \dfrac{\ln(b)}{\ln(c)} + 1

xyz = 2 + \dfrac{\ln(c)+\ln(a)}{\ln(b)} + \dfrac{\ln(a)+\ln(b)}{\ln(c)} + \dfrac{\ln(b)+\ln(c)}{\ln(a)}

xyz = 2 + \dfrac{\ln(ac)}{\ln(b)} + \dfrac{\ln(ab)}{\ln(c)} + \dfrac{\ln(bc)}{\ln(a)}

xyz = 2 + \log_b(ac) + \log_c(ab) + \log_a(bc)

\implies \boxed{xyz = x + y + z + 2}

(C)

6 0
2 years ago
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