Mathematics: If log 5=0.6990,log 7=0.8451 and log 8=0.9031.evaluate log(35×49 over 40÷56)

If log 5=0.6990,log 7=0.8451 and log 8=0.9031.evaluate - id50699070845180903114518801, QueenNerdy889

Ответ:

Blaise2653

05.10.2021

Mathematics

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Step-by-step explanation:

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Ответ:

Derp5013

17.08.2021

Mathematics

Solution-

Given, DF and DE are midsegments of ABC. so D is the mid point of AB and F is the mid point of AC.

Considering AB,

$\Rightarrow AB=2DB$

Then DE is parallel to AC, as mid-segments are parallel to the non included side of the triangle.

Also, according to corresponding angle theorem,

$m\angle FAD=m\angle EDB,\\\\m\angle FCE=m\angle DEB$

Then,

$\Delta ABC\approx \Delta DBE$

As,

$m\angle A=m\angle BDE\ \ (corresponding\ angle)\\\\m\angle C=m\angle DEB\ \ (corresponding\ angle)\\\\m\angle B=DBE\ \ \ \ \ \ \ (common\ to\ both)$

According to similarity of two triangles,

$\Rightarrow \frac{AB}{DB}=\frac{AC}{DE}=\frac{BC}{BE} \\\\\Rightarrow \frac{AB}{DB}=\frac{AC}{DE}\\\\\Rightarrow \frac{2DB}{DB}=\frac{AC}{DE}\ \ (\text{as D is the mid point of AB} )\\\\\Rightarrow 2=\frac{AC}{DE}\\\\\Rightarrow DE=\frac{AC}{2}$

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If log 5=0.6990,log 7=0.8451 and log 8=0.9031.evaluate log(35×49 over 40÷56)

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