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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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Let ρ = x3 + xe−x for x ∈ (0, 1), compute the center of mass.
hram777 [196]

The center of mass is mathematically given as

\bar{x}=\left(\frac{44 e-100}{25 e-40}\right)\end{aligned}

<h3>What is the center of mass.?</h3>

Determine the center of mass in one dimension:

Represent the masses at the respective distances.

\begin{|c|c|} Masses \ & \ \ \ \ \ \ \ \ \ \ \ \ \ \ Located at \\\rho=x^{3}+x \cdot e^{-x} & \ \  \ \  x \in(0,1)$ \\\end

We calculate the total mass of the system.

\begin{aligned}m &=\int_{0}^{1} \rho \cdot d x \\& m =\int_{0}^{1}\left(x^{3}+x \cdot e^{-x}\right) \cdot d x \\&m =\left|\frac{x^{4}}{4}-(x+1) e^{-x}\right|_{0}^{1} \\&m =\left(\frac{5}{4}-\frac{2}{e}\right)\end{aligned}

Step 03: Calculate the moment of the system.

\begin{aligned}M &=\int_{0}^{1}(\rho \cdot x) \cdot d x \\& M=\int_{0}^{1}\left(x^{4}+x^{2} \cdot e^{-x}\right) \cdot d x \\&M =\left|\frac{x^{5}}{5}-\left(x^{2}-2 x+2\right) \cdot e^{-x}\right|_{0}^{1} \\&M=\left(\frac{11}{5}-\frac{5}{e}\right)\end{aligned}

we calculate the center of mass.

\begin{aligned}\bar{x} &=\left(\frac{M}{m}\right) \\& \bar{x}=\left\{\left(\frac{\left.11-\frac{5}{5}\right)}{\left(\frac{5}{4}-\frac{2}{e}\right)}\right\}\right.\\& \bar{x}=\left(\frac{11 e-25}{5 e}\right) \cdot\left(\frac{4 e}{5 e-8}\right) \\&\bar{x}=\left(\frac{44 e-100}{25 e-40}\right)\end{aligned}

Read more about the center of mass.

brainly.com/question/27549055

#SPJ1

8 0
2 years ago
What value of a make the equation 14-a=19-12
abruzzese [7]

14-a=19-12\\14-a=7\\a=14-7\\a=7

5 0
2 years ago
Read 2 more answers
evan has a job selling magazine and newspaper subscriptions. he earns $23 for each magazine subscription and $54 for each newspa
SashulF [63]
First we write the variables already defined:
 m = the number of magazine subscriptions sold
 n = the number of newspaper subscriptions sold
 We now write the system of inequations based on the following facts:
 "he earns $ 23 for each magazine subscription and $ 54 for each newspaper subscription that he sells. his goal is to make more than $ 642 per week"
 23m + 54n> 642
 "I have expectations to sell at least 10 subscriptions per week"
 m + n> = 10
 Answer: 
 A system of inequalities that models the given situation is: 
 23m + 54n> 642 
 m + n> = 10
5 0
3 years ago
The length of a rectangle is 6m more then the width. The area is 40m^2 . What is the length and the width?
erastova [34]

let the width of the rectangle be x

area of rectangle is l*b

x * (x + 6) = 40^2

x^2 + 6x = 40^2

x^2 + 6x = 1600

x + 6x =√1600

x + 6x = 40

7x = 40

x = 5.7

Hope you found this useful

4 0
3 years ago
5. On a recent day, the exchange rate for US dollars to British pounds
attashe74 [19]
250*0.62= 155

155 pounds is your answer.
8 0
3 years ago
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