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1 month ago
7

Noah drew a scaled copy of Polygon P and labeled it Polygon Q. If the area of Polygon P is 5 square units, what scale factor did

Noah apply to Polygon P to create Polygon Q?

Mathematics
2 answers:
babunello [11.8K]1 month ago
8 0

Answer:

The scale factor equates to 3.

Detailed explanation:

Please refer to the provided image for clarity regarding this issue.

We know that

If two shapes are similar, then the ratio of their areas corresponds to the square of the scale factor.

Let

z -----> scale factor

x -----> area of polygon Q

y ----> area of polygon P

Thus, we have

z^{2}=\frac{x}{y}

so, we proceed with

y=5\ units^2

Determining the area of polygon Q

The polygon Q can be divided into five distinct squares.

Refer to the additional figure N 2.

The area of polygon Q, which represents the total area of the five squares, is

x=5(3^2)=45\ units^2

Calculating the scale factor

z^{2}=\frac{x}{y}

Thus, we derive

x=45\ units^2

y=5\ units^2

By substituting the values, we find

z^{2}=\frac{45}{5}

z^{2}=9

Taking the square root of both sides results in

z=3

Thus,

The scale factor resolves to 3.

Svet_ta [12.7K]1 month ago
5 0

Answer:

The answer is 3.

Detailed explanation:

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A pipe that is 120 cm long resonates to produce sound of wavelengths 480 cm, 160 cm, and 96 cm but does not resonate at any wave
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Response:

A 120 cm long pipe produces resonance at wavelengths of 480 cm, 160 cm, and 96 cm, but fails to resonate with any wavelengths longer than those. Consequently, this pipe is classified as:

A. closed at both ends

B. open at one end and closed on the other

C. open at both ends.

D. we cannot determine since we lack information about the sound frequency.

The correct answer is:

B. open at one end and closed at the other.

Explanation in steps:

The given data states that the pipe has a length of

= 120 cm

with wavelengthsL = 480 cm

                             

= 160 cm and \lambda_1 = 96 cm

We need to ascertain if the pipe is open, closed, or of an open-closed nature.

\lambda_2Note:\lambda_3

For a pipe open at both ends, the fundamental wavelength is 2L.

For a pipe closed at one end and open at the other, the fundamental wavelength is 4L.

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Now let’s verify with the subsequent wavelengths.

In the case of a pipe with one open end and one closed end:[

Odd multiples of one-quarter wavelength must fit within the length L4L=4(120)=480\ cm.

⇒  

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⇒

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⇒                                    ⇒  ⇒

                             ⇒  

 Thus, it confirms that the pipe is open at one end and closed at the other.

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