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4 years ago

A mandolin string's first harmonic is 392 Hz. How long is the string if the wave speed on it is 329 m/s?

1 answer:

Taya2010 [7]4 years ago

6 0

Velocity is given by:
velocity=wavelength×frequency
We note that the wavelength of a wave is twice the length of the string (2w) in the first harmonic.
velocity=329 m/s
wavelength=2w
frequency=392
substituting the values in our equation we get:
329=2w(392)
329=784w
solving for w we get
w=329/784
w= 0.41964~0.42 m

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compare the value of the 5 in 19,654 is _____________ times ____________ than the value of the 5 in 4,502

emmainna [20.7K]

The value of the first 5 is 10 times smaller than the value of the second 5.

You can find this by eliminating each of the other numbers and using 0's in their place.

The first 5 becomes 00,050 or 50. The second 5 becomes 0,500 or 500. Since 50 is 1/10 of 500, we know that it is 10 times smaller.

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3 years ago

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Which of the following is the solution to the equation 25(z − 2) = 125? (6 points)

makvit [3.9K]

Answer:

z=7

Step-by-step explanation:

25(−2)=125

25−50=125

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3 years ago

a rectangle is 8cm longer then it is wide, and it’s area is 153cm^2. Find the dimensions of the rectangle.

Stolb23 [73]

Answer:

Width of 9cm and length of 17cm.

Step-by-step explanation:

To calculate an area of a rectangle, use the formula A=l*w. We know the length is 8cm longer than the width. So l = 8 + w. So the area is A= (8+w)*w.

We also know the area is 153. Substitute this value for A and solve.

$153 = (8+w)(w)\\153 = 8w+w^2\\w^2+8w-153 = 0$

To solve the quadratic, use the quadratic formula:

$\frac{-b+/-\sqrt{b^2-4ac} }{2a}$

Here a=1, b=8 and c=-153.

$w=\frac{-b+/-\sqrt{b^2-4ac} }{2a} \\w=\frac{-8+/-\sqrt{8^2-4(1)(-153)} }{2(1)} \\w=\frac{-8+/-\sqrt{64+612} }{2} \\w=\frac{-8+/-\sqrt{676} }{2} \\w=\frac{-8+/-26 }{2} \\w=\frac{-8+26 }{2}=\frac{18}{2}=9 \\and\\w=\frac{-8-26 }{2} =\frac{-34}{2}=-17$

Since w=9 or w=-17, substitute this value for w in l= 8+w to find l.

l = 8+9 = 17

l=8+-17 = -9

Since length cannot be positive, it must be l=17 and w=9.

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3 years ago

What must the measure of angle LMN be? m∠LMN = °

luda_lava [24]

Both 25x and 22x + 9 have the same answers. So you set those two equal to each other.
$25x = 22x + 9$
Subtract 22x from both sides.
$3x = 9$
and you're left with this.
Next, divide 3 from both sides.
$x = 3$
re-insert 3 into one of the equations.
$25(3) = 75$
add up both angles
$75 + 75 = 150$
all angles (for quadrilaterals)added up equals 360.
$150 + 2x = 360$
solve for x. Subtract 150 from both sides.
$2x = 210$
and divide 2 from both sides
$x = 105$
AngleLMN= 105

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3 years ago

Evaluate the expression(-3.8)+0+y for the given values of y.

11111nata11111 [884]

Answer:

y = -3.3 then -7.1

y = -7.1 then -10.9

y = -2.6 then -6.4

y = 1 then -2.8

y = 4.2 then 0.4

Step-by-step explanation:

(-3.8)+0+y can be simplified to -3.8 + y. Evaluate each value for y by substituting it into the expression and solving.

y = -3.3 then -3.8 + -3.3 = -7.1

y = -7.1 then -3.8 + -7.1 = -10.9

y = -2.6 then -3.8 + -2.6 = -6.4

y = 1 then -3.8 + 1 = -2.8

y = 4.2 then -3.8 + 4.2 = 0.4

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3 years ago