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3 years ago

10

A stop sign is a regular octagon. The standard stop sign has a 16.2 inch radius. The area of a standard stop sign is ___________

____
square inches. Please round your answer to the nearest whole number

1 answer:

juin [17]3 years ago

7 0

The area of standard stop sign regular octagon is 742.3 squared inches, if the standard stop sign has a 16.2 inch radius.

Step-by-step explanation:

The given is,

Radius of standard stop sign is 16.2 inch radius

Step:1

The regular octagon is equal to the 16 right angled triangle,

Angle of right angle triangle = $\frac{360}{16}$ = 22.5°

Ref attachment,

From the OAB right angle triangle,

Trigonometric ratio,

sin ∅ = $\frac{Opp}{Hyp}$

Where, ∅ = 22.5°

Hyp = Radius = 16.2 inches

Ratio becomes,

sin 22.5°= $\frac{b}{16.2}$

b = (0.374607)(16.2)

b = 6.19947 inches

Trigonometric ratio,

cos ∅ = $\frac{Adj}{Hyp}$

Where, ∅ = 22.5°

Hyp = Radius = 16.2 inches

Adj = h

Ratio becomes,

cos 22.5°= $\frac{h}{16.2}$

h = (0.9238795)(16.2)

h = 14.967 inches

Step:2

From the triangle OAC,

Area, $A = \frac{1}{2} (Height )( Base)$

Where, Height = 14.967 inches

Base = b + x = 6.19947 + 6.19947

= 12.3989 inches

From the values equation becomes,

A = $\frac{1}{2} (14.967)(12.39894)$

A = 92.7875 Squared inches

Step:3

The octagon is equal to sum of 8 triangles

Area of octagon = 8 × Area of triangle

= 8 × 92.7875

= 742.3 squared inches

Result:

The area of standard stop sign regular octagon is 742.3 squared inches, if the standard stop sign has a 16.2 inch radius.

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3 years ago

Read 2 more answers

Determine formula of the nth term 2, 6, 12 20 30,42

nalin [4]

Check the forward differences of the sequence.

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$b_n = a_{n+1} - a_n$

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Let $\{c_n\}$ be the sequence of differences of $\{b_n\}$ ,

$c_n = b_{n+1} - b_n$

and we see that this is a constant sequence, $\{c_n\} = \{2, 2, 2, 2, \ldots\}$ . In other words, $\{b_n\}$ is an arithmetic sequence with common difference between terms of 2. That is,

$2 = b_{n+1} - b_n \implies b_{n+1} = b_n + 2$

and we can solve for $b_n$ in terms of $b_1=4$ :

$b_{n+1} = b_n + 2$

$b_{n+1} = (b_{n-1}+2) + 2 = b_{n-1} + 2\times2$

$b_{n+1} = (b_{n-2}+2) + 2\times2 = b_{n-2} + 3\times2$

and so on down to

$b_{n+1} = b_1 + 2n \implies b_{n+1} = 2n + 4 \implies b_n = 2(n-1)+4 = 2(n + 1)$

We solve for $a_n$ in the same way.

$2(n+1) = a_{n+1} - a_n \implies a_{n+1} = a_n + 2(n + 1)$

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$a_{n+1} = (a_{n-2} + 2(n-1)) + 2((n+1)+n) \\ ~~~~~~~ = a_{n-2} + 2 ((n+1) + n + (n-1))$

$a_{n+1} = (a_{n-3} + 2(n-2)) + 2((n+1)+n+(n-1)) \\ ~~~~~~~= a_{n-3} + 2 ((n+1) + n + (n-1) + (n-2))$

and so on down to

$a_{n+1} = a_1 + 2 \displaystyle \sum_{k=2}^{n+1} k = 2 + 2 \times \frac{n(n+3)}2$

$\implies a_{n+1} = n^2 + 3n + 2 \implies \boxed{a_n = n^2 + n}$

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2 years ago

bekas [8.4K]

The percent off the store should display is 27.0%

The initial percent off given to Matt = 20%

The additional percent off given to Matt = 7%

The percent off the store should display is the total percent off given to their product. That is, the addition of the first and second percent off.

The total percent off the store gave to Matt is calculated as;

= 20% + 7%

= 27%

To the nearest tenth of a percent = 27.0%

Thus, the percent off the store should display is 27.0%

Learn more here: brainly.com/question/16956055

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