Answer:
d
Step-by-step explanation:
hope this helped!!!!!
Answer:
6 times whatever x is would be greater that -54
Answer: he would receive a rebate of $1677.5
Step-by-step explanation:
A General Motors buyer-incentive program offered a 5.5% rebate on the selling price of a new car. This means that if the selling price of the new car is $x, the rebate (in dollars) that a customer would receive is
5.5/100 × x = 0.055 × x = 0.055x
Therefore, for a customer who purchased a $30,500 car under this program, the rebate that he would receive is
0.055 × 30500 = $1677.5
The center of mass is mathematically given as
![\bar{x}=\left(\frac{44 e-100}{25 e-40}\right)\end{aligned}](https://tex.z-dn.net/?f=%5Cbar%7Bx%7D%3D%5Cleft%28%5Cfrac%7B44%20e-100%7D%7B25%20e-40%7D%5Cright%29%5Cend%7Baligned%7D)
<h3>What is the center of mass.?</h3>
Determine the center of mass in one dimension:
Represent the masses at the respective distances.
![\begin{|c|c|} Masses \ & \ \ \ \ \ \ \ \ \ \ \ \ \ \ Located at \\\rho=x^{3}+x \cdot e^{-x} & \ \ \ \ x \in(0,1)$ \\\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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I think it’s the third one and the last two. I’m sorry if it’s wrong