In the point-slope form of a line, (y-y1)=m(x-x1)
'm' represents the slope of the line.
(x1,y1) represents a given point on the line.
(x,y) represents any point on the line.
The equation of a straight line that passes through a particular point and is inclined at a specific angle to the x-axis can be found using the point slope form.
A straight line is represented using its slope and a point on the line using point slope form. This means that the point slope form is used to determine the equation of a line whose slope is "m" and passes through the point (x1,y1).
The point slope form's equation is (y-y1)=m(x-x1), where (x, y) is a randomly chosen point on the line and m is the slope.
Learn more about point-slope form here:
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Answer:
There's a lot of them.
There are many different ways to calculate
. 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}}}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B%5Cpi%7D%3D12%5Csum_%7Bk%3D0%7D%5E%7B%5Cinfty%7D%5Cfrac%7B%5Cleft%286k%5Cright%29%21%5Cleft%28545140134k%2B13591409%5Cright%29%7D%7B%5Cleft%283k%5Cright%29%21%5Cleft%28k%21%5Cright%29%5E3%5Cleft%28640320%5Cright%29%5E%7B3k%2B%5Cfrac%7B3%7D%7B2%7D%7D%7D)
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}](https://tex.z-dn.net/?f=%5Cfrac%7B426880%5Csqrt%7B10005%7D%7D%7B%5Cpi%7D%3D12%5Csum_%7Bk%3D0%7D%5E%7B%5Cinfty%7D%5Cfrac%7B%5Cleft%286k%5Cright%29%21%5Cleft%28545140134k%2B13591409%5Cright%29%7D%7B%5Cleft%283k%5Cright%29%21%5Cleft%28k%21%5Cright%29%5E3%5Cleft%28-262537412640768000%5Cright%29%5Ek%7D)
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,
can be used to calculate a fairly accurate pi, but a better rational approximation is
This fraction is actually accurate to 6 digits and it is the best approximation of
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.
We don't know how many cars James has but we know they have 't'. But we know Paul has 13 cars. The question asks if Paul hands over half of his cars to James how many would James have? Well, 13 / 2 = 6.5
If James right now has 't' cars then after Pauls give his cars, then James will have t + 6.5.
Hope this helps!