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tigry1 [53]
3 years ago
5

What is the exact circumference of the circle?

Mathematics
1 answer:
cestrela7 [59]3 years ago
4 0

Hello!

What is the exact circumference of the circle?

A.

10π feet  

B.

20π feet  

C.

40π feet  

D.

60π feet

Solving: Using the data  (Circle with center A and diameter of 20 feet labeled).

diameter = 2*radius

20 = 2*r

2\:r = 20

r = \dfrac{20}{2}  

\boxed{r = 10\:ft}

Formula: (Circle length)

\boxed{C = 2* \pi *r}

Now, replace in the circumference length formula:

C = 2\:\pi *r

C = 2\:\pi *10

\boxed{\boxed{C = 20\:\pi\:ft}}\end{array}}\qquad\quad\checkmark

Answer:  

B.  20π feet

\underline{The\:exact\:circumference\:of\:the\:circle\:is\:\:20\:\pi\:ft}

______________________________

I Hope this helps, greetings ... Dexteright02! =)

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Answer:

The distance between the pirate and the treasure can be found from the following relationship between ΔEAF and ΔABC;

\overline{AE}/\overline{AB} =  \overline{FA}/\overline{AC} = \overline{EF}/\overline{BC}

Step-by-step explanation:

From the question diagram, we have two triangles, ΔEAF and ΔABC;

The ratio of the lengths of the sides \overline{AE}/\overline{AB} =  \overline{FA}/\overline{AC}

∠EAF and ∠BAC are vertical angles, therefore ∠EAF = ∠BAC

Therefore, ΔEAF and ΔABC are similar triangles by Side-Angle-Side, SAS, rule of similarity which states that two triangles that have ratios of a pair of their corresponding sides and the two sides also form equal angles within each triangle, then the two triangles are similar

Therefore, the ratio of the each pair of corresponding sides of the two triangles are equal

We have;

\overline{AE}/\overline{AB} =  \overline{FA}/\overline{AC} = 50 ft. /(100 ft.) =  \overline{EF}/\overline{BC} = \overline{EF}/120 ft.

\overline{EF} = 120 ft. × 50 ft./(100 ft.) = 60 ft.

\overline{EF} = 60 ft.

The distance between the pirate and the treasure, \overline{EF} = 60 ft.

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