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PtichkaEL [24]
3 years ago
6

PLEASE HELP ME THIS IS DUE BY 1 P.M AND I REALLY NEED HELP

Mathematics
1 answer:
irga5000 [103]3 years ago
5 0
It is not factored completely because it was only factored by 3ab but it could have been factored by 6a²b

6a²b(a+6+8a²)
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The shorter sides of an acute triangle are x cm and 2x cm. The longest side of the triangle is 15 cm. What is the smallest possi
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The longest side in the triangle is opposite to the largest angle of this triangle. If triangle is acute, then all angles are acute. Acute angle has cosine that is positive.

Use cosine theorem to determine the cosine of the largest angle:

15^2=x^2+(2x)^2-2\cdot x\cdot 2x\cdot \cos \alpha, where \alpha is the largest angle.

Then

225=x^2+4x^2-4x^2\cos \alpha,\\ \\\cos \alpha=\dfrac{225-5x^2}{-4x^2}=\dfrac{5x^2-225}{4x^2}.

Since \cos \alpha>0, then

\dfrac{5x^2-225}{4x^2}>0\Rightarrow 5x^2-225>0.

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Note that 3\sqrt{5}\approx 6.71, then the smallest possible whole-number value of x is 7.

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