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Anna71 [15]
4 years ago
8

A regular 18-sided polygon is rotated with the center of rotation at its center. What is the smallest degree of rotation needed

to map the polygon back on to itself?
Mathematics
2 answers:
faltersainse [42]4 years ago
8 0
360/18=20 therefore the smallest degree of rotation would be 20
dem82 [27]4 years ago
4 0
It will be easier to explain how to solve this question in a square. If you rotate 4-sided square from the centre, you need to rotate it 90 degrees. The formula for this would be: 360 ° /the side count. In a square, it would be 360° /4= 90°.

In 18-sided polygon, the calculation would be: 360°/ 18 side= 20°
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For this, the first thing to do is to assume that the function of temperature with respect to r is written in one of the following ways:

Way 1:

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Way 2:

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To find the instant variation we must find the derivative of the temperature with respect to the distance r.

We have then:

For function 1:

\frac {dT} {dr} = 40 \frac {d ((r ^ 2 + 2r))} {dr}\\

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Rewriting

\frac {dT} {dr} = 80r + 80

For function 2:

\frac {dT} {dr} = 40 \frac {d ((r ^ 2-2r))} {dr}

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Rewriting

\frac {dT} {dr} = 80r-80

Answer:

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\frac {dT} {dr} = 80r + 80

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\frac {dT} {dr} = 80r-80

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