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eduard
3 years ago
6

Elina’s friend Luke said that he could make more rectangles with 24 tiles then Elaine’s 10 tiles do you agree with Luke’s explai

n
Mathematics
2 answers:
icang [17]3 years ago
5 0
No, because it needs to equal 25, not 24.
LuckyWell [14K]3 years ago
4 0

Answer:

Yes, Luke's statement is correct and he could make more rectangles with 24 tiles than than Elaine's 10 tiles.

Step-by-step explanation:

Clearly, a tile is in the shape of a square.

Let 'a' be the side of a tile.

If we place two tiles side by side, we will get a rectangle whose length is '2a' and width is 'a'.

To make a single rectangle, the minimum number of tiles needed = 2.

So, Luke can make a maximum number of \frac{24}{2} = 12 rectangles.

But, Elaine can make \frac{10}{2} = 5 rectangles.

Hence, Luke's statement is correct and he could make more rectangles with 24 tiles than Elaine's 10 tiles.

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Step-by-step explanation:

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Sticking to either cosine or sine might help simplify the calculation. By the Pythagorean Theorem, \sin^{2}{x} = 1 - \cos^{2}{x}. Therefore, for the square of tangents,

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\displaystyle \frac{1 - \cos^{2}{x}}{\cos^{2}{x}} \cdot \frac{1}{\cos^{2}{x}} + \frac{2}{\cos^{2}{x}} - \frac{1 - \cos^{2}{x}}{\cos^{2}{x}} = 2.

To simplify the calculations, replace all \cos^{2}{x} with another variable. For example, let u = \cos^{2}{x}. Keep in mind that 0 \le \cos^{2}{x} \le 1 \implies 0 \le u \le 1.

\displaystyle \frac{1 - u}{u^{2}} + \frac{2}{u} - \frac{1 - u}{u} = 2.

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0 \le k.

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x = 0 or x = \pi.

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