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Ivenika [448]
3 years ago
13

Prove that there does not exist integers m and n such that 2m+4n=7

Mathematics
1 answer:
slamgirl [31]3 years ago
8 0
2m+4n=7\iff m+2n=\dfrac72

There is no choice of integers (m,n) such that the left hand side is a rational number.
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What radius of a circle is required to inscribe a regular hexagon with an area of 210.44 cm2 and an apothem of 7.794 cm
alekssr [168]
We know that

[area of a regular hexagon]=6*[area of one <span>equilateral triangle]
</span>210.44=6*[area of one equilateral triangle]
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[area of one equilateral triangle]=b*h/2
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the length side of a regular hexagon is 9 cm
<span>applying the Pythagorean theorem
</span>r²=h²+(b/2)²------>r²=7.794²+(4.5)²------> r²=81--------> r=9 cm

<span>this last step was not necessary because the radius is equal to the hexagon side------> (remember the equilateral triangles)
</span>
the answer is
the radius is 9 cm
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