Please help, will give brainliest and thanks :) Please attach any thing if needed.
1 answer:
Answer:
First of all, I expect you fulfill your word and give what you promise... ha ha just kidding, I already solved a question like this one, please see below explanation.
1. Tessellation is the covering of a surface with pattern(s) of flat shapes so that there are no overlaps or gaps. It is also called Tiling.
2. Triangles, Squares, and Hexagons are regular polygons.
3. Previous three shapes create a regular tessellation pattern because all their sides and all their angles are the same. the intersection point of the interior angles is called "Vertex". For a regular tessellation, the pattern is identical at each Vertex.
Unlike the triangle and quadrilateral case, the Pentagon's angle sum of 540° is not helpful when trying to fit a bunch of Pentagons around a vertex. Therefore, even though the Pentagon is a regular polygon, it cannot tessellate.
4. See attached screenshot of 3 tessellations created with Tessellation Artist Software online.
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Let's start by visualising this concept.
Number of grains on square:
1 2 4 8 16 ...
We can see that it starts to form a geometric sequence, with the common ratio being 2.
For the first question, we simply want the fifteenth term, so we just use the nth term geometric form:
Thus, there are 16, 384 grains on the fifteenth square.
The second question begs the same process, only this time, it's a summation. Using our sum to n terms of geometric sequence, we get:
Thus, there are 32, 767 total grains on the first 15 squares, and you should be able to work the rest from here.
Number of grains on square:
1 2 4 8 16 ...
We can see that it starts to form a geometric sequence, with the common ratio being 2.
For the first question, we simply want the fifteenth term, so we just use the nth term geometric form:
Thus, there are 16, 384 grains on the fifteenth square.
The second question begs the same process, only this time, it's a summation. Using our sum to n terms of geometric sequence, we get:
Thus, there are 32, 767 total grains on the first 15 squares, and you should be able to work the rest from here.