OLDisGOLD

 𝙰𝙽𝚂𝚆𝙴𝚁 =  To solve a linear system of equations, you need to find the values of the variables that satisfy all of the equations in the system. There are several methods for solving linear systems, including substitution, elimination, and matrices. Here is an example of how to solve a linear system using the substitution method: Example: Solve the system of equations: Copy code 2x + y = 7 x - y = 1 Solve for one variable in terms of the other in one of the equations. Let's solve for y in the second equation: makefile Copy code x - y = 1 y = x - 1 Substitute this expression for y into the other equation and solve for x . Let's substitute y = x - 1 into the first equation: makefile Copy code 2x + y = 7 2x + (x - 1) = 7 3x - 1 = 7 3x = 8 x = 8/3 Substitute the value of x back into one of the equations to solve for y . Let's use the second equation: makefile Copy code x - y = 1 8/3 - y = 1 y = 5/3 Therefore, the solution to the system of equations is x = 8/3 and y = ...

      𝙰𝙽𝚂𝚆𝙴𝚁 =   There is  no single "father" of advanced English, as the development of advanced English is the result of centuries of evolution and contributions from countless individuals. However, there have been many influential figures throughout history who have  contributed to the development and spread of advanced English, including writers, scholars, linguists, and educators. Some notable figures in this regard include William Shakespeare, Samuel Johnson, Noah Webster, John Milton, Geoffrey Chaucer, and many others. Ultimately, the development of advanced English has been a collaborative effort that has involved contributions from many different individuals and communities over time.

 𝙰𝙽𝚂𝚆𝙴𝚁 =  It's difficult to answer this question definitively because it depends on various factors, such as the specific game you're playing, your skill level, the strategies you use, and even luck. In general, winning at any form of gambling involves a certain degree of luck, but skill and strategy can also play a role. In games like poker or blackjack, for example, players who are skilled and experienced in the game can have an advantage over less experienced players. They may be able to read their opponents, make better decisions, and manage their bankroll more effectively. However, even skilled players can lose in the short term due to variance and luck. In the long run, skill can often overcome these factors, but it's important to keep in mind that there is always an element of chance involved. In summary, winning at the Big Cash Game or any form of gambling can be challenging and requires a combination of luck, skill, and strategy. While there is no guaranteed...

 𝙰𝙽𝚂𝚆𝙴𝚁 =  One possible way to evaluate the integral ∫(1+x^2(1−x^2)1+x^4)^(-1/2)dx is by using trigonometric substitution. Let x = tanθ, so that dx = sec^2θdθ and 1 + x^2 = 1 + tan^2θ = sec^2θ 1 - x^2 = 1 - tan^2θ = cos^2θ 1 + x^4 = 1 + tan^4θ = sec^4θ Substituting these expressions in the integral yields: ∫(1+x^2(1−x^2)1+x^4)^(-1/2)dx = ∫(sec^2θcos^2θsec^4θ)^(-1/2)sec^2θdθ = ∫(cos^2θ)^(1/2)(sec^4θ)^(1/2)sec^2θdθ = ∫cosθsec^3θdθ We can evaluate this integral using integration by substitution: Let u = secθ, so that du = secθtanθdθ Substituting u and du, we have: ∫cosθsec^3θdθ = ∫du/u^3 = -1/(2u^2) + C Substituting back u = secθ, we get: ∫cosθsec^3θdθ = -1/(2sec^2θ) + C = -1/(2+2x^2(1-x^2)^(-1/2)) + C = -1/(2+2tan^2θsecθ) + C = -1/(2+x√(1-x^2)) + C Therefore, the solution to the integral is: ∫(1+x^2(1−x^2)1+x^4)^(-1/2)dx = -1/(2+x√(1-x^2)) + C.

 𝙰𝙽𝚂𝚆𝙴𝚁 =   The physical father of physics is often considered to be Sir Isaac Newton, a 17th-century English physicist and mathematician. Newton's groundbreaking work in mechanics and gravitation, as described in his book "Mathematical Principles of Natural Philosophy," laid the foundation for much of modern physics. He is also known for his work on optics, where he proposed that light is made up of particles, and his development of calculus. While Newton is widely considered to be one of the most influential physicists of all time, it is important to note that the development of physics was a collaborative effort involving many scientists and thinkers over centuries.

 ANSWER =  One way to prove this identity is by using complex analysis and the geometric series. First, we can use the formula for the sum of a geometric series to write: sum = 1 + e^(i pi/n) + e^(2i pi/n) + ... + e^((n-1)i*pi/n) Then, we can multiply both sides by e^(-i*pi/n) to get: e^(-i pi/n) * sum = e^(-i pi/n) + e^0 + e^(i pi/n) + ... + e^((n-2)i pi/n) + e^((n-1)i*pi/n) Next, we can subtract the second equation from the first to get: (1 - e^(-2i pi/n)) * sum = 1 - e^((n-1)i pi/n) Using the identity e^(ix) = cos(x) + i*sin(x), we can rewrite the left-hand side as: (1 - (cos(2 pi/n) - i sin(2*pi/n))) * sum = 1 - cos((n-1) pi/n) - i sin((n-1)*pi/n) Simplifying the left-hand side gives: 2*sin(pi/n) * sum = 1 - cos((n-1) pi/n) - i sin((n-1)*pi/n) Finally, we can solve for the sum by dividing both sides by 2*sin(pi/n) and using the identity cot(x) = 1/tan(x) = (cos(x)/sin(x)): sum = (1 - cos((n-1) pi/n)/2) * cot(pi/n) - i sin((n-1) pi/n)/(2 sin(pi/n)) Using the fact that e^(i*...