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Mice21 [21]
3 years ago
11

What is the measure of an interior angle in a regular octagon?

Mathematics
1 answer:
Degger [83]3 years ago
7 0

Answer:

135°

Step-by-step explanation:

(n-2) * 180 =

(8-2) * 180=

6*180= 1080

1080: 8 = 135

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Save me the headache
maxonik [38]

(9\sin2x+9\cos2x)^2=81

Taking the square root of both sides gives two possible cases,

9\sin2x+9\cos2x=9\implies\sin2x+\cos2x=1

or

9\sin2x+9\cos2x=-9\implies\sin2x+\cos2x=-1

Recall that

\sin(\alpha\pm\beta)=\sin\alpha\cos\beta\pm\cos\alpha\sin\beta

If \alpha=2x and \beta=\dfrac\pi4, we have

\sin\left(2x+\dfrac\pi4\right)=\dfrac{\sin2x+\cos2x}{\sqrt2}

so in the equations above, we can write

\sin2x+\cos2x=\sqrt2\sin\left(2x+\dfrac\pi4\right)=\pm1

Then in the first case,

\sqrt2\sin\left(2x+\dfrac\pi4\right)=1\implies\sin\left(2x+\dfrac\pi4\right)=\dfrac1{\sqrt2}

\implies2x+\dfrac\pi4=\dfrac\pi4+2n\pi\text{ or }\dfrac{3\pi}4+2n\pi

(where n is any integer)

\implies2x=2n\pi\text{ or }\dfrac\pi2+2n\pi

\implies x=n\pi\text{ or }\dfrac\pi4+n\pi

and in the second,

\sqrt2\sin\left(2x+\dfrac\pi4\right)=-1\implies\sin\left(2x+\dfrac\pi4\right)=-\dfrac1{\sqrt2}

\implies2x+\dfrac\pi4=-\dfrac\pi4+2n\pi\text{ or }-\dfrac{3\pi}4+2n\pi

\implies2x=-\dfrac\pi2+2n\pi\text{ or }-\pi+2n\pi

\implies x=-\dfrac\pi4+n\pi\text{ or }-\dfrac\pi2+n\pi

Then the solutions that fall in the interval [0,2\pi) are

x=0,\dfrac\pi4,\dfrac\pi2,\dfrac{3\pi}4,\pi,\dfrac{5\pi}4,\dfrac{3\pi}2,\dfrac{7\pi}4

5 0
3 years ago
Read 2 more answers
Mrs. Hernanadez is covering the top of a kitchen shelf that is26 3/8 inches long and 15 1/2 inches wide. She incorrectly measure
miss Akunina [59]

Answer:

The  calculation of Mrs. Hernanadez will affect by 1.375 inches lesser.

Step-by-step explanation:

Given:

Length of the Kitchen shelf = 26 3/8 inches

Width of the Kitchen Shelf =  15 1/2 inches

Incorrect measurement of the length of the kitchen shelf = 25 inches

Solution:

The Actual length of the kitchen shelf is 26\frac{3}{8}

But she measured as 25 inches

So the error in the measurement will be

=>Correct length of the shelf - Incorrect length of the shelf

=> 26\frac{3}{8} - 25

Coverting the mixed fraction to fraction,

=> \frac{211}{8} - 25

=> 26.375 - 25

=>1.375

5 0
3 years ago
Hgehergergherhgerhgergergergergerger
telo118 [61]
Hsiabwbshhdbevejsjsbsvs
4 0
3 years ago
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Total consumption of fruit juice in a particular country in 2006 was about 1.85 billion gallons. The population of that country
Eduardwww [97]

Given :

Population of country in 2006 , P = 300 million.

Consumption of fruit juice in 2006 by while population, C = 1.85 billion.

To Find :

The average number of gallons of fruit juice consumed per person in the country in​ 2006.

Solution :

We know, 1 billion = 1000 million.

C = 1.85 billion = 1850 million.

Now, average umber of gallons of fruit juice consumed per person in the country in​ 2006 is :

c =\dfrac{C}{P}\\\\c=\dfrac{1850}{300}\ gallons/person\\\\c=6.17 \ gallons/person

Hence, this is the required solution.

4 0
3 years ago
What does this mean 31>28
Alona [7]

Answer:

31 is greater than 28

Step-by-step explanation:

That is how you read it: 31 is greater than 28

8 0
3 years ago
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