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3 years ago

Which transformation maps the strip pattern onto itself?

Mathematics

1 answer:

rodikova [14]3 years ago

5 0

The mapping of the strip pattern onto itself is a Glide reflection.

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.

Glide reflection is a combination of reflection over a line and then translation along that line.

As we can see, the mapping of the strip pattern onto itself is a Glide reflection.

Find out more at: brainly.com/question/25442628

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First, observe that, for n=0 and n=1 the statement is true:

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For n=1: $\sum^{n}_{i=0} (2i)^4=16 \leq 256=(4n)^4$

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Now, we will use the formula for the sum of the first 4th powers:

$\sum^{n}_{i=0} i^4=\frac{n^5}{5} +\frac{n^4}{2} +\frac{n^3}{3}-\frac{n}{30}=\frac{6n^5+15n^4+10n^3-n}{30}$

Therefore:

$\sum^{n}_{i=0} i^4 \leq 16n^4 \iff \frac{6n^5+15n^4+10n^3-n}{30} \leq 16n^4 \\\\ \iff 6n^5+10n^3-n \leq 465n^4 \iff 465n^4-6n^5-10n^3+n\geq 0$

and, because $n \geq 0$ ,

$465n^4-6n^5-10n^3+n\geq 0 \iff n(465n^3-6n^4-10n^2+1)\geq 0 \\\iff 465n^3-6n^4-10n^2+1\geq 0 \iff 465n^3-6n^4-10n^2\geq -1\\\iff n^2(465n-6n^2-10)\geq -1$