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3 years ago

What is Lim x → ∞ cos (x) ?

Mathematics

1 answer:

Sergeu [11.5K]3 years ago

6 0

Answer:

non existent

Step-by-step explanation:

Hello, please consider the following.

$\forall \ n \in \mathbb{N}\\\\cos((2n+1)\pi)=0\\\\cos(2n\pi)=1\\\\\text{So, there is no limit possible for } x \rightarrow +\infty$

Thank you.

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Nine tiles are numbered $\color[rgb]{0.35,0.35,0.35}1, 2, 3, \ldots, 9$. Each of three players randomly selects and keeps three

Eduardwww [97]

The probability that all three players obtain an odd sum is 3/14.

<h3>What is probability?</h3>

The probability is the ratio of possible distributions to the total distributions.

I.e.,

Probability = (possible distributions)/(total distributions)

<h3>Calculation:</h3>

Given that,

There are nine tiles - 1, 2, 3,...9, respectively.

A player must have an odd number of odd tiles to get an odd sum. That means he can either have three odd tiles, or two even tiles and an odd tile.

In the given nine tiles the number of odd tiles = 5 and the number of even tiles = 4.

The only possibility is that one player gets 3 odd tiles and the other two players get 2 even tiles and 1 odd tile.

So,

One player can be selected in $^3C_1$ ways.

The 3 odd tiles out of 5 can be selected in $^5C_3$ ways.

The remaining 2 odd tiles can be selected and distributed in $^2C_1$ ways.

The remaining 4 even tiles can be equally distributed in $\frac{4 ! \cdot 2 !}{(2 !)^{2} \cdot 2 !}$ ways.

So, the possible distributions = $^3C_1$ × $^5C_3$ × $^2C_1$ × $\frac{4 ! \cdot 2 !}{(2 !)^{2} \cdot 2 !}$

⇒ 3 × 10 × 2 × 6 = 360

To find the total distributions,

The first player needs 3 tiles from the 9 tiles in $^9C3=84$ ways

The second player needs 3 tiles from the remaining 6 tiles in $^6C_3=20$ ways

The third player takes the remaining tiles in 1 way.

So, the total distributions = 84 × 20 × 1 = 1680

Therefore, the required probability = (possible distributions)/(total distributions)

⇒ Probability = 360/1680 = 3/14.

So, the required probability for the three players to obtain an odd sum is 3/14.

Learn more about the probability of distributions here:

brainly.com/question/2500166

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3 0

2 years ago

Value of x after the statement "if P(x) then x 1" is executed where P(x): > 1

ziro4ka [17]

The values of x after the statement are:

b) If x=1, then the statement P(1)="1>1" is false, and thus the value of x is equal to 1 after the statement "P(x) then x := 1".
c) If x=2, then the statement P(2)="2>1" is true, and thus the value of x is equal to 1 after the statement "if P(x) then x := 1".

<h3>What is Discrete Mathematics?</h3>

This refers to the field of mathematics that studies mathematical structures and views them as discrete, rather than continuous and they include integers, statements, etc.

Therefore, if we consider the statement "if P(x) then x:=1" which is equivalent to "if x>1 then x:=1", then we can see that If x=1, then the statement P(1)="1>1" is false

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7 0

2 years ago

Please help me with this.

vitfil [10]

Answer:

15.6 inches

Step-by-step explanation:

Here we want to find the length of the missing side

Mathematically, we can use Pythagoras’ theorem

The theorem states that the square of the hypotenuse equals the sum of the squares of the two other sides

Let the missing side be x

18 is the side that faces right angle and this is the hypotenuse

Thus, we have ;

x^2 + 9^2 = 18^2

x^2 = 324 - 81

x^2 = 243

x = √(243)

x = 15.6 in

5 0

3 years ago

In 1967, New Zealander Burt Munro set the world record for an Indian motorcycle, on the Bonneville Salt Flats in Utah, with a ma

bagirrra123 [75]

Answer:49 sec

Step-by-step explanation:

Given

Maximum speed to reach is 183.58 mi/h

Length of course is 5 mi

acceleration rate is defined by 60mi/h in 4 sec

therefore acceleration(a) $=\frac{v-u}{t}$

$a=\frac{60\times 60\times 60}{4}$

$a=54\times 10^3 mi/h^2$

To reach a speed of 183.58mi/h with an acceleration of $54\times 10^3 mi/h^2$

Using equation of motion

v=u+at

$183.58=0+(54\times 10^3)t$

$t=\frac{183.58}{54\times 10^3}$

t=0.00339 hours

t=12.23 s reach maximum speed

To complete course it takes

$s=ut+\frac{1}{2}at^2$

$5=0+\frac{1}{2}\times 54\times 10^3 \times t^2$

t=0.01360 hour

or $t=48.98\approx 49 s$

7 0

3 years ago

Need help on solving this ?

katovenus [111]

For the first question, simply plug in the value of 3 into the polynomial question. The final answer is your volume of the hot water tub.

For the second question, you can figure out that x = -5 is not a real root because it does not touch or cross the x axis.

If it does it would be an solution.

4 0

3 years ago