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Rufina [12.5K]
3 years ago
11

Someone please help me with this question

Mathematics
1 answer:
alexira [117]3 years ago
5 0
Is there another part of this?
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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
A small airplane can fly 12 miles in 3 minutes. At this rate, how far can the airplane fly in 1 hour?
Sidana [21]

Answer:

The airplane can fly up to 240 miles in a hour

Step-by-step explanation:

Cross multiply

(12)(60)=3x

720=3x

Divide 3 on both sides

x=240

7 0
3 years ago
Read 2 more answers
Please help me! I’m desperate!
earnstyle [38]
What numbers are inside both circles?
The answer is A.
6 0
3 years ago
Read 2 more answers
A pair of boots has an original price of $95. they are on sale for 35 percent off. what number can you multiply $95 by to equal
Alex Ar [27]
Multiply it by .35
.35 is equal to %35.
4 0
3 years ago
Find the value of the expression if x=-7
LUCKY_DIMON [66]

Answer: -16

Step-by-step explanation:

49 would be the result of -7 squared. Due to the fact it is negative, it would cancel out to be positive.

For the numerator, 49-1 is equivalent to 48.

48/x+4

-7+4 = -3

48/-3

= -16

5 0
3 years ago
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