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nikitadnepr [17]
3 years ago
9

What is the measurement to the calculation to figure the numbers of pi

Mathematics
1 answer:
AlexFokin [52]3 years ago
4 0

Answer:

There's a lot of them.

There are many different ways to calculate \pi. The ones used by computers to generate tons of digits are usually infinite series.

The series that has been prominent in recent records for the most digits of pi is the Chudnovsky algorithm.

The algorithm is this:

\frac{1}{\pi}=12\sum_{k=0}^{\infty}\frac{\left(6k\right)!\left(545140134k+13591409\right)}{\left(3k\right)!\left(k!\right)^3\left(640320\right)^{3k+\frac{3}{2}}}

For faster performance, it can be simplified to this:

\frac{426880\sqrt{10005}}{\pi}=12\sum_{k=0}^{\infty}\frac{\left(6k\right)!\left(545140134k+13591409\right)}{\left(3k\right)!\left(k!\right)^3\left(-262537412640768000\right)^k}

Other algorithms have been used, but right now this is the one that is being used to set the recent records.

There are also some approximations that are used because they are very easy to calculate.

first, \frac{22}{7} can be used to calculate a fairly accurate pi, but a better rational approximation is \frac{355}{113} This fraction is actually accurate to 6 digits and it is the best approximation of \pi in simplest form and with a denominator below 30,000.

There are several other approximations and if you want to learn more I would recommend looking at the Wikipedia page which has tons of algorithms for pi.

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An artist created the sculpture shown with concrete. The radius of the bottom hemisphere is double that of the top hemisphere. F
klemol [59]

<u>Answer:</u>

Vt = 4071.5 ft^3

<u>Step-by-step explanation:</u>

Givens:

  • R = 12
  • R = 2r => r = 6

Equations

  1. V = (4/3)(pi)r^3

Find: Vt (Total Volume)

Vt = (1/2)V1 + (1/2)(V2)

Vt = (1/2)(V1 + V2)                 <em>[Factor out (4/3) and (pi) from volumes]</em>

Vt = (1/2)(4/3)(pi)(R^3 + r^3)  <em>[Sub in Values]</em>

Vt = 4071.5 ft^3

5 0
3 years ago
The ages of three children in a family can be expressed as consecutive integers. The square of the age of the youngest child is
tensa zangetsu [6.8K]

Answer: 10, 11, & 12

<u>Step-by-step explanation:</u>

Let x represent the age of the youngest child.  

Their ages are consecutive so,

Youngest: x

Middle: x + 1

Oldest: x + 2

The age of the Youngest squared (x²) equals 8 times the Oldest [8(x + 2)] plus 4.

x² = 8(x + 2) + 4

x² = 8x + 16 + 4

x² = 8x + 20

x² - 8x - 20 = 0

(x - 10)(x + 2) = 0

x - 10 = 0     or      x + 2 = 0

  x = 10       or          x = -2

Since age cannot be negative, x = -2 is not valid

So, the Youngest (x) is 10

the Middle (x + 1) is 11

and the Oldest (x + 2) is 12

4 0
3 years ago
Cooling towers are used to remove or expel heat from a process. A cooling tower's walls are modeled by x squared over 324 minus
olchik [2.2K]

The width of the cooling tower at the base of the structure will be A. 36 meters.

<h3>How to calculate the width?</h3>

From the information given, the towers walls are modeled by x²/324 - (y² - 90)²/1600.

Therefore, the width of the cooling tower at the base of the structure will be:

= 2 × ✓324

= 2 × 18

= 36

In conclusion, the width is 36 meters.

Learn more about width on:

brainly.com/question/25855344

#SPJ1

3 0
1 year ago
△QRS is rotated about point P to △Q′R′S′ . Which statements are true about the pre-image and image?
yuradex [85]

Note that rotation will not affect the shape and size of an object.

Rotation with respect to a point preserves the corresponding sides and the corresponding angles of the original image.

Hence, the statements

The corresponding angle measurements in each triangle between the pre-image and the image are preserved and

The corresponding lengths, from the point of rotation, between the pre-image and the image are preserved

are true.

3 0
3 years ago
The midpoint of UV is point W. What are the coordinates of point V?
madreJ [45]

Since you don't provide the coordinates of the point W, I will help you in a general form anyway. In the Figure below is represented the segment that matches this problem. We have two endpoints U and V. So, by using the midpoint formula we may solve this problem:

Midpoint=W=W(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2})=W(x_{3}, y_{3}) \\ \\ where:\\ \ U=U(x_{1}, y_{1}) \ and \ V=V(x_{2}, y_{2}) \\ \\ and: \\ x_{3}=\frac{x_{1}+x_{2}}{2} \\ y_{3}=\frac{y_{1}+y_{2}}{2}

Therefore:

x_{2}=2x_{3}-x_{1} \\ y_{2}=2y_{3}-y_{1}

So we know x_{3} \ and \ y_{3} but we also must know x_{1} \ and \ y_{1}

Finally, knowing the points U and W we can find the endpoint V.

7 0
3 years ago
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