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jeka57 [31]
3 years ago
6

You and your friend Sam are going to paint your 300 square feet room together.

Mathematics
1 answer:
Elza [17]3 years ago
4 0
Fraction that Sam painted in 1 min is:
10/25=2/5
Fraction that you painted in 1 min:
5/25=1/5

Fraction pained by both in 1 min:
1/5+2/5=3/5 ft²/min
Time taken to paint 50 ft² will be:
time=3/5×50=30 min
Thus we conclude that Sam was wrong.

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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

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8 0
2 years ago
Solve for a side triangles please help it’s urgent please answer
rodikova [14]

Answer:

AC ≈ 2.87

Step-by-step explanation:

Using the sine ratio in the right triangle

sin35° = \frac{opposite}{hypotenuse} = \frac{AC}{AB} = \frac{AC}{5}

Multiply both sides by 5

5 × sin35° = AC , thus

AC ≈ 2.87 ( to the nearest hundredth )

7 0
2 years ago
Use powers to rewrite these problems: Example: 5 x 5 = 52
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5 × 3 = 15, so 3 quarters of 20 is 15.
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