Projects And Homeworks of a school Student

 Here are the first 10000 digits of pi calculated by my own program You can also use it and calculate by your own to custom decimal places from  https://projectandwork.blogspot.com/2023/05/blog-post.html?m=1 Enjoy!!! 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798609437027705392171762931767523846748184676694051320005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235420199561121290219608640344181598136297747713099605187072113499999983729780499510

 Python program to calculate π Chundnovsky's formulae: `\frac{426880\sqrt{10005}}{\pi}=` `\sum _{k=0}^{\infty}\frac{(6k)!(13591409+545140134k)}{(3k)!(k!)^3(-640320)^{3k}}` #made by Raxit Gupta import decimal  import math  #we use Chundnovsky's formulae def compute_pi(n):   decimal.getcontext().prec = n + 3   C = 426880 * decimal.Decimal(10005).sqrt()   K = decimal.Decimal(6)   M = decimal.Decimal(1)   X = decimal.Decimal(1)   L = decimal.Decimal(13591409)   S = L   # For better precision, we calculate to n+3 and remove the last two digit   for i in range(1, n+3):     M = decimal.Decimal(M* ((1728*i*i*i)-(2592*i*i)+(1104*i)-120)/(i*i*i))     L = decimal.Decimal(545140134+L)     X = decimal.Decimal(-262537412640768000*X)     S += decimal.Decimal((M*L) / X)     return str(C/S)[:-2] n=int(input("Enter decimal places:")) P=compute_pi(n) print(P)           if there is any mistake, please comment!

As humans, we have explored a lot of the world's islands, but there are still some fascinating and unexplored places that remain a mystery. These islands are not just a mystery because humans have never set foot on them, but they also hold some of the world's most intriguing secrets. Here are some of the most interesting islands in the world that humans have never reached: Bouvet Island : This uninhabited island is located in the South Atlantic Ocean, and it's considered the most remote island in the world. The island is covered in glaciers and has a rugged terrain that makes it nearly impossible to reach. Bouvet Island is also home to an active volcano that last erupted in 2016. Its is a territoryof Norway. Sentinel Island : This island is located in the Bay of Bengal and is home to the Sentinelese tribe, one of the world's last uncontacted tribes. The island is so isolated that it's illegal to go within three miles of it, and the tribe has been known to attack any

  The viral problem: I these days of social media, even an easy problem of 5th standards are confusion peoples. Here is one of the problem gone viral in February 2023. The problem is: "Klein reads 30 pages of a book on Monday and `\frac{1}{8}` of the book on Tuesday. He completed the remaining `\frac{1}{4}` on the book on Wednesday. How many pages are there in the book?"   Peoples are saying that even geniuses can't solve it!!! I don't think so. Let's try together and let me know in the comment of you were able to solve it. Let's solve it! Solution: Let's assume that total number of pages in the book are `p`. On Monday=30 On Tuesday=`\frac{p}{8}` On Wednesday=`\frac{p}{4}` A.T.Q, `\rightarrow 30+\frac{p}{8}+\frac{p}{4}=p` `\rightarrow \frac{240+p+2p}{8}=p` `\rightarrow 240+3p=8p` `\rightarrow 240=5p` `\rightarrow p=\frac{240}{5}` `\rightarrow p=48` Hence, solved that p=48 Please support me by adding comments!!!

The Illuminati, a secret society that is believed to have existed for centuries, has captured the imagination of people around the world. Its members are said to be among the most powerful and influential people in the world, controlling governments, financial institutions, and even the entertainment industry. But what is the truth behind this enigmatic organization, and why do so many people believe in its existence? Despite the lack of concrete evidence, rumors and conspiracy theories about the Illuminati persist, with many people convinced that they are a real force in the world. The symbols associated with the Illuminati - the all-seeing eye, the pyramid, and the double-headed eagle - have become part of popular culture, appearing in movies, music videos, and even on the back of the US dollar bill. But what do these symbols mean, and why are they associated with the Illuminati? Some people believe that they represent the Illuminati's control over the world, while others see the

Run the following program and enter the desired decimal places of `\pi`. You would get your result .

 With the popularity of national parks like Yellowstone and Yosemite, it's easy to forget about the many other breathtaking parks that deserve just as much attention. From coast to coast, there are several lesser-known national parks waiting to be explored and appreciated. Here's a list of some of the most beautiful, yet unsung, national parks in the United States: Isle Royale National Park, Michigan Located in the middle of Lake Superior, this remote and rugged island is a true gem for nature lovers. The park is home to a diverse array of wildlife, including moose, wolves, and a variety of bird species. Visitors can explore the island by hiking, camping, or even kayaking. Congaree National Park, South Carolina This unique park is one of the largest intact expanses of old-growth bottomland hardwood forest in the world. Visitors can hike the boardwalk trails to see towering trees, discover diverse plant life, and observe various species of wildlife. Dry Tortugas National Park, F

 Ice cream is a sweet treat that never goes out of style. However, for those who are looking for something different, there are ice cream flavors that go beyond the usual chocolate, vanilla, and strawberry. Here are some of the world's most unusual ice cream flavors that you need to try: Wasabi - This spicy ice cream is a popular flavor in Japan. Wasabi ice cream is made with real wasabi paste, giving it a sharp, hot flavor that will awaken your taste buds. Garlic - Garlic ice cream may sound strange, but it's a must-try for those who love savory flavors. It's creamy, slightly sweet, and has a strong garlic flavor that will linger in your mouth. Bacon - Bacon ice cream is the perfect combination of salty and sweet. It's made with real bacon bits and has a rich, smoky flavor that will have you hooked. Black Licorice - This flavor is not for everyone, but it's definitely unique. Black licorice ice cream is made with real licorice extract and has a distinctive, ani

As human beings, we often take for granted the incredible capabilities of our bodies. From the complex system of bones and muscles that allow us to move and perform physical tasks, to the intricate network of nerves and synapses that allow us to think and feel, our bodies are truly remarkable machines. One aspect of our physiology that is particularly fascinating is the human brain. This three-pound organ is the control center of the body, responsible for everything from regulating heart rate and breathing to controlling our emotions and decision-making processes. Despite its small size, the brain is incredibly complex and powerful, containing billions of neurons and trillions of connections. Scientists are still working to fully understand all of the functions and capabilities of the brain, but some of its known functions include: • Perception : The brain receives and processes information from our senses, allowing us to see, hear, touch, taste, and smell the world around us. • Moveme

In a ∆ABC, CA=CB. D and E are points on AB such that AD=DE=EB. If C=120° find `\angle CED` First the figure is CA=CB and AD=DE=EB: Now, let's construct a line segment CP perpendicular to AB to C: Now, by the property of isoscleles triangle, its altitude is its median. So CP divided angle C in two halfs and also bisects AB. So AP=PB Now, in `\triangle CDP` and `\triangle CEP`: CP=CP (given) `\angle CPD `=`\angle CPE`=90° DP=PE (as AP=PB and AD=EB. So AP-AD=AD-EB hence DP=PE) `\therefore  \triangle CDP \cong \triangle CEP`...........(i) But DP+PE=DE Now let AD=DE=EB=2x Then DP=PE=x Also, `\angle PCA =\angle PCB =60`° `also ~ \angle PCD=\angle PCE=\alpha`......from(i) Now, let's focus on `\triangle PCB` as follows: Here, `tanC=\frac{PB}{PC}` `\rightarrow tan60`°=`\frac{3x}{PC}` `\rightarrow \frac{3x}{\sqrt{3}}=PC` Now in `\triangle PCE=` `\rightarrow tan \alpha =\frac{PE}{PC} ` `\rightarrow  tan \alpha =\frac{x}{\frac{3x}{\sqrt{3}}}` `\rightarrow tan \alpha =\frac{\sqrt{3} x}{3x}`

 T rex dino game   write you scores in comment!! .

  AKASH CLASS 10 MODULE MATHEMATICS (1+2) PDF Hello guys, Here I am posting Akash's module book PDF of class 10 Mathematics . This book is really very high-level book and information for foundations, NTSE, Olympiads and CBSE board exams.  The PDF is below of this page. You can also  Akash module of Biology, Chemistry , Physics and Social Science Free   PDF in my blog  https://projectandwork.blogspot.com  . If you like this, please just leave a nice comment:)

  AKASH CLASS 10 MODULE CHEMESTRY (1+2) PDF Hello guys, Here I am posting Akash's module book PDF of class 10 Chemistry. This book is really very high-level book and information for foundations, NTSE, Olympiads and CBSE board exams.  The PDF is below of this page. You can also  Akash module of Biology, Maths, Physics and Social Science Free   PDF in my blog  https://projectandwork.blogspot.com  . If you like this, please just leave a nice comment:)

  AKASH CLASS 10 MODULE PHYSICS (1+2) PDF Hello guys, Here I am posting Akash's module book PDF of class 10 Physics. This book is really very high-level book and information for foundations, NTSE, Olympiads and CBSE board exams.  The PDF is below of this page. You can also  Akash module of Biology, Maths, Chemistry and Social Science Free   PDF in my blog  https://projectandwork.blogspot.com  . If you like this, please just leave a nice comment:)

AKASH CLASS 10 MODULE BIOLOGY (1+2) PDF Hello guys, Here I am posting Akash's module book PDF of class 10 Biology. This book is really very high-level book and information for foundations, NTSE, Olympiads and CBSE board exams.  The PDF is below of this page. You can also Akash module of Physics, Maths, Chemistry and Social Science Free   PDF in my blog https://projectandwork.blogspot.com  . If you like this, please just leave a nice comment:) Thank you...

 These are three activities on obtaining different conditions of solution for pair of linear equations in two variable. These are: To obtain the condition for no solutions of given pair of linear equation. T o obtain the condition for unique solutions of given pair of linear equation. To obtain the condition for no solutions of given pair of linear equation. Hope it helped you

Project on PI Hi This is a project on π-world's mysterious number.   

 Python program to calculate π Chundnovsky's formulae: `\frac{426880\sqrt{10005}}{\pi}=` `\sum _{k=0}^{\infty}\frac{(6k)!(13591409+545140134k)}{(3k)!(k!)^3(-640320)^{3k}}` import decimal  import math  #we use Chundnovsky's formulae def compute_pi(n):       decimal.getcontext().prec=n+1      A=426880*decimal.Decimal(10005).sqrt()      B=6      C=1      D=1      E=13591409      F=E      for i in range(1,n):           C=C*((1728*i*i*i)-(2592*i*i)+(1104*i)-120)/(i*i*i)           E+=545140134           D*=0-262537412640768000           F+=decimal.Decimal(C*E)/D      pi=A/F      return pi n=int(input("Enter decimal places:")) P=compute_pi(n) print(P)           if there is any mistake, please comment!

Euler's continued Fraction Formula: If `r_i` are complex numbers and `x` is defined by: ` x=1+\sum_{i=1}^{\infty}r_{1}r_{2}\cdot r_(i)=1+\sum_{i=1}^\infty  (\prod_{j=1}^{i}r_{j})` Then this equality can be proved by induction:  `x=\frac{1}{1-\frac{r_1}{1+r_1-\frac{r_2}{1+r_2-\frac{r_3}{1+r_3-\ddots}}}}` Its prove will be posted later...

  Find   x , if \displaystyle \begin{array}{|l}4^{\frac{x}{y}+\frac{y}{x}}=32\\ \log_3(x-y)+\log_3(x+y)=1\end{array} 4 y x ​ + x y ​ = 32 lo g 3 ​ ( x − y ) + lo g 3 ​ ( x + y ) = 1 ​ Solution: Checking if the system is defined for two variables is a hard task, so we shall find the eventual solutions to the system and check directly if the system is defined for them. We shall only write  \displaystyle \begin{array}{|l}x+y>0\\x-y>0\end{array} x + y > 0 x − y > 0 ​  for now. \displaystyle \begin{array}{|l}\frac{x}{y}+\frac{y}{x}=log_432\\log_3(x^2-y^2)=1\end{array} y x ​ + x y ​ = l o g 4 ​ 32 l o g 3 ​ ( x 2 − y 2 ) = 1 ​ \displaystyle \begin{array}{|l}\frac{x}{y}+\frac{y}{x}=\frac{1}{2}log_232\\x^2-y^2=3\end{array} y x ​ + x y ​ = 2 1 ​ l o g 2 ​ 32 x 2 − y 2 = 3 ​ \displaystyle \begin{array}{|l}\frac{x^2+y^2}{xy}=\frac{5}{2}\\x^2-y^2=3\end{array} x y x 2 + y 2 ​ = 2 5 ​ x 2 − y 2 = 3 ​ \displaystyle \begin{array}{|l}x^2+y^2=\frac{5}{2}xy\\x^2-y^2=3\end{array} x 2 + y 2 = 2