3 years ago

A. Write each of the following decimals using digits.

Mathematics

1 answer:

g100num [7]3 years ago

7 0

Answer:

21.0.26

22. 0.9

23.0.30

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Let point D lie on the ray BC to the right from points B and C and let CD=x. Then BD=a+x, AB=a.

Consider triangle ACD. In this triangle, m∠ACD=180°-m∠ACB=180°-60°=120°.

By the cosine theorem,

$AD^2=AC^2+CD^2-2\cdot AC\cdot CD\cdot \cos \angle ACD,\\\\AD^2=a^2+x^2-2\cdot a\cdot x\cdot \cos 120^{\circ},\\\\AD^2=a^2+x^2+ax,\\\\AD=\sqrt{a^2+x^2+ax}.$

Since $a^2+x^2+ax=a^2+x^2+ax+ax-ax=(a+x)^2-ax,$ then

$AD^2=(a+x)^2-ax$

and

$AD^2=a^2+x^2+ax>a^2=AB^2\Rightarrow AD>AB.$

Therefore, you get double inequality

$AB$ or $BD>AD>AB.$

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