Answer:
√10
Step-by-step explanation:
√(x2-x1)^2+(y2-y1)^2=√10
Answer:
Area = 530 cm^2
Step-by-step explanation:
<em>f(3) = 13</em>
- Step-by-step explanation:
<em>f(x) = 2x + 7</em>
<em>replace </em><em>x</em><em> with </em><em>3</em>
<em>f(3) = 2×3 + 7</em>
<em>= 6 + 7</em>
<em>= 13</em>
The center of mass is mathematically given as
![\bar{x}=\left(\frac{44 e-100}{25 e-40}\right)\end{aligned}](https://tex.z-dn.net/?f=%5Cbar%7Bx%7D%3D%5Cleft%28%5Cfrac%7B44%20e-100%7D%7B25%20e-40%7D%5Cright%29%5Cend%7Baligned%7D)
<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](https://tex.z-dn.net/?f=%5Cbegin%7B%7Cc%7Cc%7C%7D%20Masses%20%5C%20%26%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20Located%20at%20%5C%5C%5Crho%3Dx%5E%7B3%7D%2Bx%20%5Ccdot%20e%5E%7B-x%7D%20%26%20%5C%20%5C%20%20%5C%20%5C%20%20x%20%5Cin%280%2C1%29%24%20%5C%5C%5Cend)
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}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7Dm%20%26%3D%5Cint_%7B0%7D%5E%7B1%7D%20%5Crho%20%5Ccdot%20d%20x%20%5C%5C%26%20m%20%3D%5Cint_%7B0%7D%5E%7B1%7D%5Cleft%28x%5E%7B3%7D%2Bx%20%5Ccdot%20e%5E%7B-x%7D%5Cright%29%20%5Ccdot%20d%20x%20%5C%5C%26m%20%3D%5Cleft%7C%5Cfrac%7Bx%5E%7B4%7D%7D%7B4%7D-%28x%2B1%29%20e%5E%7B-x%7D%5Cright%7C_%7B0%7D%5E%7B1%7D%20%5C%5C%26m%20%3D%5Cleft%28%5Cfrac%7B5%7D%7B4%7D-%5Cfrac%7B2%7D%7Be%7D%5Cright%29%5Cend%7Baligned%7D)
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}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7DM%20%26%3D%5Cint_%7B0%7D%5E%7B1%7D%28%5Crho%20%5Ccdot%20x%29%20%5Ccdot%20d%20x%20%5C%5C%26%20M%3D%5Cint_%7B0%7D%5E%7B1%7D%5Cleft%28x%5E%7B4%7D%2Bx%5E%7B2%7D%20%5Ccdot%20e%5E%7B-x%7D%5Cright%29%20%5Ccdot%20d%20x%20%5C%5C%26M%20%3D%5Cleft%7C%5Cfrac%7Bx%5E%7B5%7D%7D%7B5%7D-%5Cleft%28x%5E%7B2%7D-2%20x%2B2%5Cright%29%20%5Ccdot%20e%5E%7B-x%7D%5Cright%7C_%7B0%7D%5E%7B1%7D%20%5C%5C%26M%3D%5Cleft%28%5Cfrac%7B11%7D%7B5%7D-%5Cfrac%7B5%7D%7Be%7D%5Cright%29%5Cend%7Baligned%7D)
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}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%5Cbar%7Bx%7D%20%26%3D%5Cleft%28%5Cfrac%7BM%7D%7Bm%7D%5Cright%29%20%5C%5C%26%20%5Cbar%7Bx%7D%3D%5Cleft%5C%7B%5Cleft%28%5Cfrac%7B%5Cleft.11-%5Cfrac%7B5%7D%7B5%7D%5Cright%29%7D%7B%5Cleft%28%5Cfrac%7B5%7D%7B4%7D-%5Cfrac%7B2%7D%7Be%7D%5Cright%29%7D%5Cright%5C%7D%5Cright.%5C%5C%26%20%5Cbar%7Bx%7D%3D%5Cleft%28%5Cfrac%7B11%20e-25%7D%7B5%20e%7D%5Cright%29%20%5Ccdot%5Cleft%28%5Cfrac%7B4%20e%7D%7B5%20e-8%7D%5Cright%29%20%5C%5C%26%5Cbar%7Bx%7D%3D%5Cleft%28%5Cfrac%7B44%20e-100%7D%7B25%20e-40%7D%5Cright%29%5Cend%7Baligned%7D)
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The way to convert counts into relative frequencies in a Two Way Relative Frequency Table is to divide the count by the total number of items
<h3>What is a Frequency Table?</h3>
This refers to the depiction of the number of times in which an event occurs in the form of a table.
Hence, when a two-way frequency table is used, it shows the visual representation of the possible relationship between different sets of data.
Please note that your question is incomplete as you did not provide the frequency table needed and also the trends and generalizations to find, so a general overview was given.
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