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lesya [120]
3 years ago
12

What is the area of a regular heptagon with side length of 6 meters and a distance from the to the vertex of 6 meters? round you

r answer to the nearest tenth
Mathematics
1 answer:
Ahat [919]3 years ago
8 0
Apothem = side length / 2*tan(180 / number of sides)
apothem = side length / 2*tan (180 / 7)
apothem = 6 / (2*tan( <span> <span> <span> 25.7142857143</span></span></span>))
apothem = 6 / 2*0.48157
<span><span><span>apothem = 6.2296239384 </span> </span> </span>

Polygon area = (# of sides * side length * apothem) / 2
Polygon area = ( 7 * 6 * <span>6.2296239384) / 2
</span><span><span><span>Polygon area = 130.8221027064 </span> </span> </span> 



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11/12 of the disk space on a
svet-max [94.6K]

Answer:

2 whole number 1 out of 4

Step-by-step explanation:

11/12 x 3

11/4 = 2remainder 3

2 whole number 3 out of 12

When u reduce it will be 2 whole number 1 out of 4

8 0
3 years ago
What is the sum of the first 51 consecutive odd positive integers?
Angelina_Jolie [31]
We call:

a_{n} as the set of <span>the first 51 consecutive odd positive integers, so:

</span>a_{n} = \{1, 3, 5, 7, 9...\}

Where:
a_{1} = 1
a_{2} = 3
a_{3} = 5
a_{4} = 7
a_{5} = 9
<span>and so on.

In mathematics, a sequence of numbers, such that the difference between two consecutive terms is constant, is called Arithmetic Progression, so:

3-1 = 2
5-3 = 2
7-5 = 2
9-7 = 2 and so on.

Then, the common difference is 2, thus:

</span>a_{n} = \{ a_{1} , a_{1} + d, a_{1} + d + d,..., a_{1} + (n-2)d+d\}
<span>
Then:

</span>a_{n} = a_{1} + (n-1)d
<span>
So, we need to find the sum of the members of the finite series, which is called arithmetic series:

There is a formula for arithmetic series, namely:

</span>S_{k} = ( \frac{a_{1} +  a_{k}}{2}  ).k
<span>
Therefore, we need to find:
</span>a_{k} =  a_{51}  

Given that a_{1} = 1, then:

a_{n} = a_{1} + (n-1)d = 1 + (n-1)(2) = 2n-1

Thus:
a_{k} = a_{51} = 2(51)-1 = 101

Lastly:

S_{51} = ( \frac{1 + 101}{2} ).51 = 2601 

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