Hello, happy Friday, I am just here with some geometry questions.

Mathematics

1 answer:

Marina86 [1]3 years ago

6 0

Answer:

$x=12$

Step-by-step explanation:

Notice that the segment bisects the obtuse angle.

Then by the Angle Bisector Theorem:

$\displaystyle \frac{x-4}{6}=\frac{x}{9}$

Cross-multiply:

$6(x)=9(x-4)$

Distribute:

$6x=9x-36$

So:

$-3x=-36$

Therefore:

$x=12$

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<h2>Answer:</h2>

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<h2>Step-by-step explanation:</h2>

Archimedes was a brilliant mathematician. This man rose the formula of the volume of a sphere by comparing this shape to a cylinder. The volume of a sphere is hard to calculate by comparing this object to a cube. So Archimedes imagined cutting a sphere into two halves, called hemispheres. So an hemisphere gave him a flat surface, which is easier to work with. Therefore, if he'd find the volume of a hemisphere, then he'd multiply the result by 2 and would get the volume of a sphere. Then he imagined a hemisphere within a cylinder as the one shown below. Also, he imagined a cone within the same cylinder. <em>What did he find? </em>He found that the volume of the hemisphere should be equal to the volume of the cylinder minus the volume of the cone:

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