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3 years ago

If you continue adding fractions according to this pattern when will you reach a sum of 2?

Mathematics

1 answer:

mr Goodwill [35]3 years ago

6 0

Answer:

You will never be able to reach the sum of 2

Step-by-step explanation:

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Suppose that the length of a side of a cube X is uniformly distributed in the interval 9

Nastasia [14]

Answer:

$f(v) = \left \{ {{\frac{1}{3}v^{-\frac{2}{3}}\ 9^3 \le v \le 10^3} \atop {0, elsewhere}} \right.$

Step-by-step explanation:

Given

$9 < x < 10$ --- interval

Required

The probability density of the volume of the cube

The volume of a cube is:

$v = x^3$

For a uniform distribution, we have:

$x \to U(a,b)$

and

$f(x) = \left \{ {{\frac{1}{b-a}\ a \le x \le b} \atop {0\ elsewhere}} \right.$

$9 < x < 10$ implies that:

$(a,b) = (9,10)$

So, we have:

$f(x) = \left \{ {{\frac{1}{10-9}\ 9 \le x \le 10} \atop {0\ elsewhere}} \right.$

Solve

$f(x) = \left \{ {{\frac{1}{1}\ 9 \le x \le 10} \atop {0\ elsewhere}} \right.$

$f(x) = \left \{ {{1\ 9 \le x \le 10} \atop {0\ elsewhere}} \right.$

Recall that:

$v = x^3$

Make x the subject

$x = v^\frac{1}{3}$

So, the cumulative density is:

$F(x) = P(x < v^\frac{1}{3})$

$f(x) = \left \{ {{1\ 9 \le x \le 10} \atop {0\ elsewhere}} \right.$ becomes

$f(x) = \left \{ {{1\ 9 \le x \le v^\frac{1}{3} - 9} \atop {0\ elsewhere}} \right.$

The CDF is:

$F(x) = \int\limits^{v^\frac{1}{3}}_9 1\ dx$

Integrate

$F(x) = [v]\limits^{v^\frac{1}{3}}_9$

Expand

$F(x) = v^\frac{1}{3} - 9$

The density function of the volume F(v) is:

$F(v) = F'(x)$

Differentiate F(x) to give:

$F(x) = v^\frac{1}{3} - 9$

$F'(x) = \frac{1}{3}v^{\frac{1}{3}-1}$

$F'(x) = \frac{1}{3}v^{-\frac{2}{3}}$

$F(v) = \frac{1}{3}v^{-\frac{2}{3}}$

So:

$f(v) = \left \{ {{\frac{1}{3}v^{-\frac{2}{3}}\ 9^3 \le v \le 10^3} \atop {0, elsewhere}} \right.$

8 0

3 years ago

the graph to the right represents mario’s mile time in minutes, y, based on the number of hours he spends training in hours , x

sveta [45]

Answer: it is 13+13=26

Step-by-step explanation:

I don’t care.

3 0

2 years ago

Big Ben (the clocktower) in London has a circumference of 72.22 feet and an area of 415.27 feet^2. What is the diameter AND radi

Mashutka [201]

Answer:

Diameter = 23 Radius = 11.5

Step-by-step explanation:

Divide the circumference by π, or 3.14 for an estimation. The result is the circle's diameter.

diameter = 23

Divide the diameter by 2.

There you go, you found the circle's radius

7 0

2 years ago

What are the values of x in the equation x(x-6)=4(x=6)?

Klio2033 [76]

X=6....6(6-6)=4(6=6) 6(0)=0....0=\=4 6=6

7 0

3 years ago

In circle O, the measure of ABC is 68. what is the measure of AC?

mixer [17]

Answer:
A.
Step-by-step explanation:
We have been given a diagram. We are asked to find the measure of angle ABC.
First of all, we will find measure of major arc AC by subtracting 146 from 360 degrees.

Now, we will use tangent-tangent angle theorem to solve for ABC.
Tangent-Tangent angle theorem states that angle formed by two tangents outside a circle is half the difference of intercepted arcs.

Therefore, the measure of angle ABC is 34 degrees and option A is the correct choice.

4 0

3 years ago