A van has room for 6students and 2teachers . How many vans are needed for a total of 48students and 16 teachers?

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.

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8 0

1 year ago

Find the volume of the cylinder in terms of pi<br> H=6 r=3

Len [333]

Area of Base x Height

Area of a circle is PI x R squared

Radius is 3

Area of Base is 9Pi

9Pi x Height

Height is 6

9pi x 6 =

54 pi.

3 0

2 years ago

HELP

Serjik [45]

Answer:

A: 5+7+2.5=14.5/3=4.8333333

B: 6+12+3.5=21.5/3=7.16666666

4 0

2 years ago

Read 2 more answers

For a circle with a radius of 15 cm, what is the length of an arc intercepted by an angle measuring 120°?

slega [8]

Answer: 31.43 cm

Step-by-step explanation:

The length of an arc is calculated using the formula:

$\frac{theta}{360}$ X 2 $\pi$ r

where : theta is the angle in degree

r = radius

If the angle is given in Radian , the length can be calculated using the formula:

L = r∅

Since , the angle is given in degree , we will use the first formula.

L = $\frac{theta}{360}$ X 2 $\pi$ r

L = $\frac{120}{360}$ X 2 X π X 15

L = $\frac{1}{3}$ X 2 X $\frac{22}{7}$ X 15

L = $\frac{660}{21}$

L = 31.42857143

L ≈ 31.43 cm

5 0

3 years ago

Which of the following represents the factorization of trinomal below

My name is Ann [436]

A is the correct answer.......

Here is the work shown:

x^2-x-20

A is the correct answer because when using the distributive property it is the only example that results in x^2-x-20.

(x+4)(x-5)

x*x=x^2, x*-5=-5x, 4*x=4x, 4*-5=-20. Now combine all alike terms for your final answer. x^2-x-20..

please vote my answer brainliest. thanks!

5 0

2 years ago