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3 years ago

6

Mathematics

2 answers:

3241004551 [841]3 years ago

8 0

Answer:

The product is greater than 4

tamaranim1 [39]3 years ago

4 0

The product is greater than 4

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Given the following three arithmetic sequences : 1, 3, ... and 1, 4, ... and 1, 5, ... A number is randomly selected from 1 to 1

ladessa [460]

Answer:

0.333

Step-by-step explanation:

The first sequence starts at 1 and has a common difference of 2. It will include every odd number in the range.

The second sequence starts at 1 and has a common difference of 3. It will include odd numbers and the even numbers 4, 10, 16, .... That is, all even numbers of the form 6n -2 will be included. The last one corresponds to the largest value of n such that ...

6n -2 ≤ 1000

6n ≤ 1002

n ≤ 167

That is, 167 even numbers will also be excluded.

The third sequence starts at 1 and has a common difference of 4. Every number in this sequence is also a number in the first sequence.

So the numbers in these sequences include all 500 odd numbers and 167 even numbers, for a total of 667 numbers. The probability that a randomly chosen number is not in one of these sequences is ...

(1000 -667)/(1000) = 333/1000 = 0.333 . . . . p(not a sequence term)

8 0

3 years ago

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

PLEASEE HELP!! Find the area of the kite.

aev [14]

Answer:

Step-by-step explanation:

Area of kite is Area of triangles. Area is 6+3=9

6 0

3 years ago

What is the arc length if

dem82 [27]

Answer:

A. 8π / 3

Step-by-step explanation:

6 0

3 years ago

Write an expression for the area of the shaded region in its simplest form. Show all of your steps.

patriot [66]

The area of the shaded region will be the area of the rectangle minus the area of the white square inside of it:

((x+10)(2x+5)) - ((x+1)(x+1))

First, FOIL both of the areas separately:

(2x^2 + 5x + 20x + 50) - (x^2 + x + x + 1)

Simplify within the parentheses by adding like terms:

(2x^2 + 25x + 50) - (x^2 + 2x + 1)

Now, subtract one equation from the other:

2x^2 + 25x + 50
-x^2 - 2x - 1
= x^2 + 23x + 49

This will be the equation for the area.

3 0

3 years ago