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3 years ago

Wha is the area of this

Mathematics

1 answer:

Korvikt [17]3 years ago

6 0

Octagon, stop sign.

Eight isoscles triangles. It looks like we're told the side is 9.9 and the height to the side (also called the apothem) is 12.

So each isosceles triangle has area (1/2)(9.9)(12) and we have eight of them,

area = 8(1/2)(9.9)(12) = 475.2

Answer: 475.2

Usually we wouldn't be told 9.9 -- this is the baby version. We know each of those isoscles triangles has unique angle 360/8=45 degrees, so the apothem and half the side of the octagon are a right triangle with acute angle 22.5 degrees.

The area of the right triangle with long leg 12, short leg x,

tan 22.5 = x/12 or

x = 12 tan 22.5

Twice that is what we're told is 9.9; let's check:

2x = 24 tan 22.5 = 9.941125496954282

The area of the little right triangle is

(1/2) 12 × 12 tan 22.5

and there are 16 of these

16 (1/2) 12 × 12 tan 22.5 ≈ 477.174

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A certain circle can be represented by the following equation. x^2+y^2+18x+14y+105=0 What is the center of the circle? What is t

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Answer:

See below.

Step-by-step explanation:

Recall the equation for a circle:

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We need to turn the given equation into the above format. We do this by completing the square.

First, group them:

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For the first section, complete the square for $x^2+18x$ :

$x^2+18x+81-81$

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Do the same for the second:

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$y^2+14y+49-49$

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All together:

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Step-by-step explanation:

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3 years ago

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Answer:

The symphonic choir can record a maximum of 14 songs.

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We know that the album cannot be more than 72 minutes long, and the jazz choir records a total of $7 (3min) = 21$ song minutes.

If we call $c$ the number of songs the symphonic choir records , and each song is 3.5 minute long, then the song minutes for the symphonic choir are $3.5c$ ; therefore, we have the inequality

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$3.5c\leq 51$

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3 years ago