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yKpoI14uk [10]
3 years ago
15

A regular heptagon has a radius of approximately 27.87 cm and the length of each side is 24.18 cm. What is the approximate area

of the heptagon rounded to the nearest whole number? Recall that a heptagon is a polygon with 7 sides.
Mathematics
2 answers:
kobusy [5.1K]3 years ago
5 0
If you know the side length, you don't need the radius to calculate the area.  The area for any regular polygon is:

A(n,s)=(ns^2)/(4tan(180/n)), where n=number of sides and s=length of sides.

The above is derived by dividing the polygon into n triangles...anyway, in this case:

A=(7*<span>24.18^2)/(4tan(180/7)

A=</span>1023.1767/tan(180/7)

A=2124.65 cm^2 (to nearest one-hundredth)
seraphim [82]3 years ago
4 0

Answer:

2124.65\text{ cm}^2.

Step-by-step explanation:

We have been given that a regular heptagon has a radius of approximately 27.87 cm and the length of each side is 24.18 cm.      

We will use area of a heptagon formula to find the area of our given heptagon.    

\text{Area of heptagon}=\frac{7}{4}*a^2*cot(\frac{180}{7}), where, a represents each side of heptagon.

Upon substituting a=24.18 cm we will get,

\text{Area of heptagon}=\frac{7}{4}*\text{(24.18 cm)}^2*cot(\frac{180}{7})

\text{Area of heptagon}=\frac{7}{4}*584.6724\text{ cm}^2*2.0765213965692558

\text{Area of heptagon}=7*146.1681\text{ cm}^2*2.0765213965692558

\text{Area of heptagon}=2124.648310021\text{ cm}^2\approx 2124.65\text{ cm}^2

Therefore, area of our given heptagon will be approximately 2124.65\text{ cm}^2.

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Suppose that one wishes to schedule vehicles from a central depot to five customer locations. The distance of making trips betwe
sladkih [1.3K]

Answer:

The routing suggested by the savings method is route (3,4)

Step-by-step explanation:

Savings for all trips (i, j), 1 ≤ i ∠ j ≤ 5

Total  number of trips to be commuted = 10 trips

S₁₂ = C₀₁ + C₀₂ - C₁₂ = 20 + 75 - 35 = 60

S₁₃ = C₀₁ + C₀₃ - C₁₃ = 20 + 33 - 5 = 48

S₁₄ = C₀₁ + C₀₄ - C₁₄ = 20 + 10 - 20 = 10

S₁₅ = C₀₁ + C₀₅ - C₁₅ = 20 + 30 - 15 = 35

S₂₃ = C₀₂ + C₀₃ - C₂₃ = 75 + 33 - 18 = 90

S₂₄ = C₀₂ + C₀₄ - C₂₄ = 75 + 10 - 58 = 27

S₂₅ = C₀₂ + C₀₅ - C₂₅ = 75 + 30 - 42 = 63

S₃₄ = C₀₃ + C₀₄ - C₃₄ = 33 + 10 - 40 = 3

S₃₅ = C₀₃ + C₀₅ - C₃₅ = 33 + 30 - 20 = 43

S₄₅= C₀₄ + C₀₅ - C₄₅ = 10 + 30 - 25 = 15

3 0
3 years ago
3-7=<br> 4-6=<br> 3+-6=<br> 4--1=<br> -5+-5=<br> -3+5=<br> -4-6=
kipiarov [429]

Answer:

Answers are below

Step-by-step explanation:

3 - 7 = -4

4 - 6 = -2

3 + -6 = -3

4 - - 1 = 5

-5 + -5 = -10

-3 + 5 = 2

-4 -6 = -10

Hope this helps!!

4 0
3 years ago
Determine the volume of the solid that lies between planes perpendicular to the x-axis at x=0 and x=4. The cross sections perpen
OverLord2011 [107]

Answer:

Volume = 16 unit^3

Step-by-step explanation:

Given:

- Solid lies between planes x = 0 and x = 4.

- The diagonals rum from curves y = sqrt(x)  to  y = -sqrt(x)

Find:

Determine the Volume bounded.

Solution:

- First we will find the projected area of the solid on the x = 0 plane.

                              A(x) = 0.5*(diagonal)^2

- Since the diagonal run from y = sqrt(x) to y = -sqrt(x). We have,

                              A(x) = 0.5*(sqrt(x) + sqrt(x) )^2

                              A(x) = 0.5*(4x) = 2x

- Using the Area we will integrate int the direction of x from 0 to 4 too get the volume of the solid:

                              V = integral(A(x)).dx

                              V = integral(2*x).dx

                               V = x^2

- Evaluate limits 0 < x < 4:

                               V= 16 - 0 = 16 unit^3

3 0
3 years ago
Suppose that a recent poll of American households about car ownership found that for households with a car, 39% owned a sedan, 3
Rama09 [41]

Answer:

The probability that of the 3 households randomly selected at least 1 owns a sports car is 0.1956.

Step-by-step explanation:

Let <em>X</em> = number of household owns a sports car.

The probability of <em>X</em> is, P (X) = p = 0.07.

Then the random variable <em>X</em> follows a Binomial distribution with <em>n</em> = 3 and <em>p</em> = 0.07.

The probability function of a binomial distribution is:

P(X=x) = {n\choose x}p^{x}[1-p]^{n-x}\\

Compute the probability that of the 3 households randomly selected at least 1 owns a sports car:

P(X\geq 1)=1-P(X

Thus, the probability that of the 3 households randomly selected at least 1 owns a sports car is 0.1956.

4 0
3 years ago
15 points!!
saveliy_v [14]

Answer:

b

Step-by-step explanation:

9x7.8x1/2x12

6 0
2 years ago
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