A hore named northern dancer won the Kentucky derby with a time of exactly 2 minute. At thi contant rate, how long would it take Northern Dancer to run the Belmont take?

It is established that there is always a multiple of 4 between squares of consecutive even numbers.

Take two consecutive even integers into consideration.

If n is an integer, then

The first even number would then be 2n.

Let 2(n+1) be the next consecutive even number.

The following even numbers would follow:

2n, 2(n+1)

Each succeeding even number's square would be:

(2n)² = 2n ×2n = 4n²

[2(n+1)]² = (2n+2)² =(2n+2)(2n+2)

stretching out the brackets

= 4n² +4n +4n+4

[2(n+1)]² = 4n²+8n+4

We would choose values for n and calculate the difference between the squares of each consecutive even number in order to ascertain whether it is always a multiple of 4.

Let n = 1, 2, 3

For n= 1

4n² = 4(1)² = 4×1 = 4

4n²+8n+4 = 4(1)² + 8(1) + 4

= 4+8+4 = 16

The difference between consecutive even numbers' squares is equal to 16/4, or 12.

For n= 2

4n² = 4(2)² = 4×4 = 16

4n²+8n+4 = 4(2)² + 8(2) + 4

= 16+16+4 = 36

36-16 = 20 is the difference between the squares of two consecutive even numbers.

For n= 3

4n² = 4(3)² = 4×9 = 36

4n²+8n+4 = 4(3)² + 8(3) + 4

= 36+24+4 = 64

64-36 = 28 is the difference between the squares of two consecutive even numbers.

12 = 4×3

20 = 4×5

28= 4×7

We can see from the outcomes above that the numbers 12, 20, and 28 are multiples of 4.

As a result, a multiple of four always separates squares of succeeding even integers.

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Answer:

3/4

Step-by-step explanation:

[tex] \sqrt{ \frac{9 }{16?} \ } [/tex]

[tex] \sqrt{9 } [/tex]

=3

[tex] = 3[/tex]

[tex] \sqrt{16} [/tex]

[tex] = 4[/tex]

ans=3/4

These functions have restricted domains: f(x) is defined only for x >= 3 and g(x) is defined only for x < 3.

A function is a mathematical concept that assigns exactly one output (or "output value") to each input (or "input value"). It provides a way to describe the relationship between inputs and outputs and can be thought of as a machine that takes inputs and produces outputs. Functions can be represented using equations or graphs.

In mathematical terms, a function can be formally defined as a set of ordered pairs (x,y), where x is the input (independent variable) and y is the output (dependent variable). The output value for a given input value is unique, and a single input value cannot correspond to multiple output values.

Functions are widely used in mathematics, science, and engineering to model real-world phenomena and to describe mathematical relationships. There are many types of functions, including linear functions, polynomial functions, exponential functions, logarithmic functions, and trigonometric functions, among others.

The equation y = 2|x - 3| + 5 can be rewritten as two separate linear functions, f(x) and g(x), as follows:

f(x) = 2(x - 3) + 5, for x >= 3

g(x) = -2(x - 3) + 5, for x < 3

So, for x >= 3, y is given by the linear function f(x) = 2(x - 3) + 5, and for x < 3, y is given by the linear function g(x) = -2(x - 3) + 5.

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Answer:

one so that is the ansa mi

The numbers 61 (78 times), 32 (77 times), 21, 63 (73 times), 69 (71 times), and 23 are those that appear the most frequently in the New York lottery (70 times).

For instance, reports indicate that the most popular Powerball lottery numbers are 32, 41, 16, 22, 23, and 29. These are the top six MegaMillions numbers: 15, 24, 33, 1, 46, and 39.

According to data, the Powerball numbers that appeared the most frequently over the past seven years were 61 (78 times), 32 (77 times), 21, 63, 69, and 23.

The New York lottery's most frequent numbers are 61 (78 times), 32 (77 times), 21, and 63 (73 times).

The numbers 61 (78 times), 32 (77 times), 21, 63 (73 times), 69 (71 times), and 23 are those that appear the most frequently in the New York lottery (70 times).

Since 2005, a consultant at Ernst & Young has examined the Mega Millions lottery's chosen numbers. The outcomes:

most often winning combinations

14 On 48 winning tickets — 11.6%

36 On 48 winning tickets — 11.6%

48 On 47 winning tickets — 11.4%

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The most consistent player is Player A, with a standard deviation of 1.4.

To compare the variability of the two players' data, we can use either the interquartile range (IQR) or the standard deviation.

The interquartile range (IQR) is a measure of the spread of the data that takes into account the values of the first quartile (Q1), the median, and the third quartile (Q3). It is calculated as the difference between Q3 and Q1. A smaller IQR indicates that the data is more tightly clustered and, therefore, more consistent.

The standard deviation is a measure of the average spread of the data from the mean. A smaller standard deviation indicates that the data is more tightly clustered around the mean and, therefore, more consistent.

In this case, we can calculate the IQR and standard deviation for each player's data. After sorting the data and finding the quartiles, we get the following:

Player A:

Q1: 1.5

Median: 2

Q3: 3

IQR: 1.5

Standard deviation: 1.4

Player B:

Q1: 2

Median: 4

Q3: 5

IQR: 3.5

Standard deviation: 2.9

From the calculations, we can see that Player A has a smaller IQR (1.5) and a smaller standard deviation (1.4) compared to Player B (IQR = 3.5, Standard deviation = 2.9). This means that Player A's data is more tightly clustered around the median, indicating that he is more consistent in his performance.

Therefore, the correct answer is (C).

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--The given question is incomplete; the complete question is

"The table shows the number of goals made by two hockey players during the season's games.

Player A                  Player B

2, 3, 1, 3, 2, 2, 1, 3, 6  1, 4, 5, 1, 2, 4, 5, 5, 11

Which measure of variability is best for the data, and which player is more consistent?

A) Player A is the most consistent, with an IQR of 1.5.

B) Player B is the most consistent, with an IQR of 3.5.

C) Player A is the most consistent, with a standard deviation of 1.4.

D) Player B is the most consistent, with a standard deviation of 2.9."--

To find the volume of the solid using the slicing method, we need to find the area of each cross-sectional square and then multiply it by the length (or height) of the solid.

Let's call the height of the solid h and the side length of each square cross-section s. The radius of the base of the solid is 15, so the diameter of the base is 2 * 15 = 30. Half of the diameter is the chord of the semicircular base, and it's also equal to the side length of the square cross-section.

So, s = 30 / 2 = 15

Since the cross sections are squares, the height of the solid (h) is equal to the side length of the square (s).

Now we can find the area of each cross-sectional square:

A = s^2 = 15^2 = 225

Finally, to find the volume of the solid, we need to multiply the area of each cross-sectional square by the height of the solid:

V = A * h = 225 * 15 = 3375

So, the volume of the solid is 3375 cubic units.

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Let's call the height of the solid h and the side length of each square cross-section s. The radius of the base of the solid is 15, so the diameter of the base is 2 * 15 = 30. Half of the diameter is the chord of the semicircular base, and it's also equal to the side length of the square cross-section.

Now we can find the area of each cross-sectional square:

A = s^2 = 15^2 = 225

V = A * h = 225 * 15 = 3375

Answer:

Hindus from India invented zero to represent the idea of the power of the cosmos and universe as they expand into infinity. They called this the sunya which means empty in Sanskrit. The book Brahma Sphuta Siddhanta was published in c. 628 by Brahmagupta which defines zero as the subtraction of a number by itself, e.g. 5-5 =0.

The y values are also equal at x=-2. Thus, f(-2) = g(-2) is true. D is the right answer, thus.

Quantity and their permutations, relationships and associated tissues, shapes and their locales, and locations in which they are found are all components of the mathematics classroom. The relationship among a group of inputs, each of which has a productivity commission, is referred to by the term "function." A function is a relationship involving inputs and outputs where each input produces a single, unique result. Every function has an area and a codomain, often known like a scope. F is typically used to describe functions (x). An x is the input. Based on the following criteria, there are four primary categories of functions that are available: on functions, yet another functions, many-to-one functions, within functions, and on functions.

given

In the given graph, the two lines intersects at x = -2

And intersection point is that point , where the y values of the two graphs are equal .

That is  f(x) = g(x)

The y values are also equal at x=-2. Thus, f(-2) = g(-2) is true. D is the right answer, thus.

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For data at the interval​ level, we cannot calculate meaningful differences between data entries. The statement is false.

Interval:

The interval of a numerical value generally represents the maximum and minimum value between which the numerical value belongs, it is the amount of time that has passed between the beginning and end of the event which is also known as elapsed time.

The various ways of showing intervals are Inequalities, interval notations, and number lines, the amount of time between two given times is known as the time interval.

Data at the ordinal level can be qualitative or quantitative.  A true statement is​ "For data at the interval​ level, you can calculate meaningful differences between data​ entries."

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Mary paid $2.58 for one cup of coffee is  the correct answer.

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The factor for the Expression 7[tex]z^4[/tex]-5 + 10y³ + 20 is (y³ + 2)

A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:

Given:

7[tex]z^4[/tex]-5 + 10y³ + 20

Factorizing the expression

7[tex]z^4[/tex]-5 +10(y³ + 2)

So, the factor in the expression is (y³ + 2).

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The table you mentioned shows that the area of the bottom of the box, f(x), is equal to x2 when one side of the box is x feet long.

This can be written as f(x) = x2. You can also use this equation to calculate the area of the bottom of any rectangular box if you know the length of one of its sides. For example, if one side of the box is 4 feet then the area of the bottom of the box is f(4) = 42 = 16 square feet.

The bottom of the box refers to the bottom surface of a rectangular box. It is the surface that is parallel to the surface on which the box is resting. The area of the bottom of a box can be calculated by multiplying the length of one side of the box by the width of the other side. The bottom of the box can be used to hold items, and can also provide a stable platform for stacking items.

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When reviewing the rates for the reaction at a constant temperature CH4(g) +202 CO2(g) + 2 H2O(g): the magnitude is the same, but the sign is opposite.

Correct option: D

A chemical reaction's forward motion. It is frequently defined in terms of either the concentration of a reactant which is consumed in a period of time or the concentration of a product that is generated in a unit of time (amount per unit volume).

Methane concentration drops during the reaction, hence the rate of the reaction is equal to the rate at which methane is vanishing. It will have a negative value since methane concentration is falling during the process.

However, the rate of reaction is positive.

Therefore, while having opposing signs, the rates of reaction and methane's disappearance will be of equal size.

Hence option D is the correct answer.

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Answer: - 1/3

Step-by-step explanation:

To solve this algebraic expression, you will need to evaluate the equation like this:

13(9x + 3) = 3x + 1

117x + 39 =  3x + 1

117x + 39 - 39 =  3x + 1 - 39

117x = 3x - 38

117x - 3x = 3x - 38 - 3x

114x = -38

 x =  - 1/3

Therefore, the solution to this equation is -1/3. Hope this helps!

Adding and subtracting fractions with unlike denominators involves finding a common denominator, which is the least common multiple of the denominators of the fractions.

Once you have found the common denominator, you can convert each fraction so that it has the same denominator, and then you can add or subtract the numerators to find the final answer.

Here's an example word problem:

A baker has 3/4 of a bag of flour and 1/2 of another bag of flour. How much flour does the baker have in total?

To solve this problem, we need to find a common denominator for 3/4 and 1/2. The least common multiple of 4 and 2 is 4, so we can use 4 as the common denominator. We then convert each fraction so that it has a denominator of 4:

3/4 = (3 x 4) / (4 x 1) = 12/4

1/2 = (1 x 2) / (2 x 1) = 2/4

Now that both fractions have the same denominator, we can add their numerators to find the total:

12/4 + 2/4 = 14/4 = 3 1/2

So, the baker has 3 1/2 bags of flour in total.

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Since R is inversely proportional to A, the numerical value of A when R equal 9 is 2.

Proportional relationships are relationships between two variables where their ratios are equivalent.

Inversely proportional relation is expressed as;

R ∝ 1/A

then, R = k/A

Where k is the proportionality constant.

Given that;

First, we determine the proportionality constant.

R = k/A

12 = k/1.5

k = 18

Now, the value of A when R = 9 will be;

R = k/A

A = k/R

A = 18 / 9

A = 2

Therefore, the value of A is 2.

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The probability that the first child selected will be a girl is 0.5 or 50%.

The probability of a child being a boy or a girl is equal, as long as the parents are healthy and have no genetic conditions that affect the gender of the child. In general, the chance of having a boy or a girl is about 50-50.

However, it is important to understand that each individual birth is a random event and that the probability of having a boy or a girl is calculated over a large number of births.

This means that even though the overall probability of having a boy or a girl is equal, it is possible to have a run of several boys or several girls in a row.

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The constant is [tex]$y_0$[/tex] and the function is [tex]$y(t) = 4e^{-2t} + 2t - 9$[/tex].

The unique solution to the given initial value problem can be expressed as:

[tex]\begin{align}y(t) = 4e^{-2t} + 2t - 9 + y_0\end{align}[/tex][tex]\begin{align}y(t) = 4e^{-2t} + 2t - 9 + y_0\end{align}[/tex][tex]y(t) = 4e^{-2t} + 2t - 9 + y_0\end{align}[/tex]

where the constant is [tex]$y_0$[/tex] and the function is [tex]$y(t) = 4e^{-2t} + 2t - 9$[/tex].

To calculate the constant and the function, we solve the differential equation [tex]$y' = g(t)$[/tex] with the initial condition [tex]$y(0) = y_0$[/tex]. We start by differentiating both sides of the equation and rearranging to get the differential equation:

[tex]y' = g(t) \implies \frac{dy}{dt} = 4e^{-2t} + 2\end{align}[/tex]

Integrating both sides and using the initial condition gives us:

[tex]\int \frac{dy}{dt} dt &= \int (4e^{-2t} + 2)dt \\y &= 4e^{-2t} + 2t + c \\y(0) &= 4e^{-2(0)} + 2(0) + c \\y_0 &= 4 + c \\y(t) &= 4e^{-2t} + 2t - 9 + y_0\end{align}[/tex]

Therefore, the constant is [tex]$y_0$[/tex] and the function is [tex]$y(t) = 4e^{-2t} + 2t - 9$[/tex].

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Answer:

9.75

Step-by-step explanation:

7+2.75 =9.75

Answer:

a) 2

b)4

c) 8

To find the solution to a fractional power, you root the number with the denominator and the amount of times you times the number by itself is the numerator e.g. 16^3/4 is 8.

Hope this helps  

Answer:

a.) 2

b.) 4

c.) 8

Step-by-step explanation:

When an exponent is a fraction, you use the denominator as an exponent, then use the denominator as the root.

a.) [tex]8^{\frac{1}{3}}=\sqrt[3]{8^{1}}[/tex]

[tex]8=2*2*2[/tex]

[tex]\sqrt[3]{8}=2[/tex]

b.) [tex]8^{\frac{2}{3}}=\sqrt[3]{8^{2}}[/tex]

[tex]64=4*4*4[/tex]

 [tex]\sqrt[3]{64}=4[/tex]

c.) [tex]16^{\frac{3}{4}}=\sqrt[4]{16^{3}}[/tex]

[tex]4096=8*8*8*8[/tex]

[tex]\sqrt[4]{4096}=8[/tex]

The correct statement is:

Given a p-value of 0.02 and a significance level of 3%, you should reject the null hypothesis.

Given,

Four statements regarding p value and null hypothesis.

Now,

Depends on if the p-value is less or more than the significance level:

Hence the correct statement for this problem is given by:

Given a p-value of 0.02 and a significance level of 3%, you should reject the null hypothesis.

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Answer:

Step-by-step explanation:

Because all of the other sides are equal so it makes that equal

Answer:

Step-by-step explanation:

5

The builder has 17  grey bricks and 18 red bricks. The total weight of the bricks is 298 kilograms.

What is the system of equations?

Simultaneous equations, or a system of equations, Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution. A solution is not assured even then.

Assume that the builder has x number of red bricks and y number of gray bricks.

The weight of 1 red brick is 9 kilograms.

The weight of x red bricks is 9x kilograms.

The weight of 1 gray brick is 8 kilograms.

The weight of y red bricks is 8y kilograms.

The weight of x red bricks and y red bricks is 9x + 8y kilogram.

The total number of bricks is 35 whose weight is 298 kilograms.

According to the question,

x+y = 35 ......(i)

9x + 8y = 298 .....(ii)

Solve the equations by using the elimination method:

Multiply 9 with equation (i) and subtract equation (ii) from it:

9x+9y = 315

9x + 8y = 298

(-)  (-)       (-)

_______________

         y = 17

Putting y = 17 in equation (i)

x+17 = 35

x = 18

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The values of x and y are given as follows:

The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.

In this problem, we have that the right angle is bisected, and thus it is divided into two angles of 45º.

As the angle of 45º has the same value for the sine and the cosine, the sides of the triangle BDC have the same length, hence the value of x is given as follows:

x = 3.

Applying the Pythagorean Theorem, the value of y will be given as follows:

y² = 3² + 3²

y² = 2 x 9

[tex]y = 3\sqrt{2}[/tex]

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Answer:

[tex]x=\dfrac{9}{4}=2.25[/tex]

[tex]y=\dfrac{15}{4}=3.75[/tex]

Step-by-step explanation:

The altitude drawn from the vertex of the right angle perpendicular to the hypotenuse separates the hypotenuse into two segments. The ratio of the altitude to one segment is equal to the ratio of the other segment to the altitude.

[tex]\boxed{\sf \dfrac{altitude}{segment\:1}=\dfrac{segment\:2}{altitude}}[/tex]

From inspection of the given right triangle:

Therefore:

[tex]\implies \dfrac{BD}{CD}=\dfrac{AD}{BD}[/tex]

[tex]\implies \dfrac{3}{x}=\dfrac{4}{3}[/tex]

[tex]\implies 3 \cdot 3 = 4 \cdot x[/tex]

[tex]\implies9 = 4x[/tex]

[tex]\implies x=\dfrac{9}{4}[/tex]

The altitude drawn from the vertex of the right angle perpendicular to the hypotenuse separates the hypotenuse into two segments. The ratio of the hypotenuse to one leg is equal to the ratio of the same leg and the segment segment directly opposite the leg.

[tex]\boxed{\sf \dfrac{hypotenuse}{leg\:1}=\dfrac{leg\:1}{segment\;1}}\quad \sf and \quad \boxed{\sf \dfrac{hypotenuse}{leg\:2}=\dfrac{leg\:2}{segment\;2}}[/tex]

From inspection of the given right triangle:

Therefore:

[tex]\implies \dfrac{AC}{BC}=\dfrac{BC}{CD}[/tex]

[tex]\implies \dfrac{4+x}{y}=\dfrac{y}{x}[/tex]

[tex]\implies x(4+x)=y^2[/tex]

Substitute the found value of x:

[tex]\implies \dfrac{9}{4}\left(4+\dfrac{9}{4}\right)=y^2[/tex]

[tex]\implies y^2=\dfrac{225}{16}[/tex]

[tex]\implies y=\sqrt{\dfrac{225}{16}}[/tex]

[tex]\implies y=\dfrac{\sqrt{225}}{\sqrt{16}}[/tex]

[tex]\implies y=\dfrac{15}{4}[/tex]

a) The relative frequency distribution is 0.3212

b) The percentage of players that had a top speed less than 13.9 km/h = 0.007259 x 100 = 0.7259%

Given that,

Speed (km/hour) Number of players Relative frequency:

10 – 13.9

14 - 17.9

18 – 21.9

22 – 25.9

26 – 29.9

30 – 33.9

4

8

18

76

268

177 4/551=0.007259

8/551=0.01451

18/551=0.03266

76/ 551=0.1379

268/551 = 0.486

177/551=0.3212

Thus, The relative frequency distribution is 0.3212.

The percentage of players who had top speed between 14 and 17.9 km/h was = 0.01451 x100 = 1.451%

The percentage of players that had a top speed less than 13.9 km/h = 0.007259 x 100 = 0.7259%

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(a) Relative frequency distribution:

Speed (km/hr) Number of players Relative frequency

10-13.9 44 0.114

14-17.9 77 0.199

18-21.9 1414 0.368

22-25.9 5959 0.153

26-29.9 324324 0.084

30-33.9 181181 0.046

(b) Frequency histogram:

      |

      |

      |  X

      |  X

      |  X  X

      |  X  X

_______|__X__X

10     14     18     22     26     30

(c) Relative frequency histogram:

      |

      |

      |   X

      |   X

      |   X   X

      |   X   X

_______|___X___X

0.1   0.2   0.3   0.4   0.5   0.6   0.7

(d) Percentage of players with a top speed between 18 and 21.9 km/h:

0.368 * 100 = 36.8%

(e) Percentage of players with a top speed less than 13.9 km/h:

0.114 * 100 = 11.4%

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Answer:

y = -6

Step-by-step explanation:

We know the formula for slope is:

m = ( y2-y1)/(x2-x1)

We are given the two points using a variable and the slope.

-8 = (2-y)/(3-4)

-8 = (2-y)/(-1)

Multiply each side by -1.

8 = 2-y

Subtract 2 from each side.

8-2 = 2-y-2

6 = -y

Multiply by -1.

-6 =y

Answer:

y = -6

Step-by-step explanation:

The formula to find the slope is:

[tex]m = \frac{y_1 - y_2}{x_1-x_2}[/tex]

Given that,

( 4, y ) ⇒ ( x₁ , y₁ )

( 3, 2 ) ⇒ ( x₂ , y₂ )

m ( slope ) = -8

Accordingly, we have to find the value of y₁.

Let us find it now by making y₁ the subject.

[tex]\sf m = \frac{y_1 - y_2}{x_1-x_2} \\\\-8 = \frac{y_1 - 2}{4-3}\\\\-8 = \frac{y_1 - 2}{1}\\\\Multiply\:\:Both\:\:sides\:\:by\:\:1.\\\\-8=y_1-2\\\\Add \:\:2\:\:to\:\:both\:\:sides.\\\\-8+2=y_1\\\\-6=y_1=y[/tex]

Derivative of arcsin x is 1/√1-x²

The derivative of arcsin x is denoted by d/dx(arcsin x) (or) d/dx(sin-1x) (or) (arcsin x)' (or) (sin-1x)'. Its value is 1/√1 - x². We will prove it in two methods in the upcoming sections. The two methods are:

Using the chain rule

Using the first principles

Derivative of arcsin x Formula

The derivative of the arcsin function is,

d/dx(arcsin x) = 1/√1 - x² (OR)

d/dx(sin^-1x) = 1/√1 - x²

Derivative of Arcsin

d/dx(arcsinx) (or) d/dx(sin^-1x)

=1/√1-x²

arcsinx=1/√1-x²

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