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Apr 9, 2014 · Having the answers in back is often a hindrance more than a help. In high school freshman year my answers were typically more exact than the textbook's, because the textbook used 3.14 3.14 as an approximation for π π. But much more to the point, in real life, you must personally confirm your answer.
- The Riemann Hypothesis
- The Collatz Conjecture
- The Erdős-Strauss Conjecture
- Equation Four
- Goldbach's Conjecture
- Equation Six
- The Whitehead Conjecture
- Equation Eight
- The Euler-Mascheroni Constant
- Equation Ten
Equation: σ (n) ≤ Hn +ln (Hn)eHn 1. Where n is a positive integer 2. Hn is the n-th harmonic number 3. σ(n) is the sum of the positive integers divisible by n For an instance, if n = 4 then σ(4)=1+2+4=7 and H4 = 1+1/2+1/3+1/4. Solve this equation to either prove or disprove the following inequality n≥1? Does it hold for all n≥1? This problem is ref...
Equation: 3n+1 1. where n is a positive integer n/2 2. where n is a non-negative integer Prove the answer end by cycling through 1,4,2,1,4,2,1,… if n is a positive integer. This is a repetitive process and you will repeat it with the new value of n you get. If your first n = 1 then your subsequent answers will be 1, 4, 2, 1, 4, 2, 1, 4… infinitely....
Equation: 4/n=1/a+1/b+1/c 1. where n≥2 2. a, b and c are positive integers. This equation aims to see if we can prove that for if n is greater than or equal to 2, then one can write 4*n as a sum of three positive unit fractions. This equation was formed in 1948 by two men named Paul Erdős and Ernst Strauss which is why it is referred to as the Erdő...
Equation: Use 2(2∧127)-1 – 1 to prove or disprove if it’s a prime number or not? Looks pretty straight forward, does it? Here is a little context on the problem. Let’s take a prime number 2. Now, 22 – 1 = 3 which is also a prime number. 25 – 1 = 31 which is also a prime number and so is 27−1=127. 2127 −1=170141183460469231731687303715884105727 is a...
Equation: Prove that x + y = n 1. where x and y are any two primes 2. n is ≥ 4 This problem, as relatively simple as it sounds has never been solved. Solving this problem will earn you a free million dollars. This equation was first proposed by Goldbach hence the name Goldbach's Conjecture. If you are still unsure then pick any even number like 6, ...
Equation: Prove that (K)n = JK1N(q)JO1N(q) 1. Where O = unknot (we are dealing with knot theory) 2. (K)n = Kashaev's invariant of K for any K or knot 3. JK1N(q) of K is equal to N-colored Jones polynomial 4. We also have the volume of conjecture as (EQ3) 5. Here vol(K) = hyperbolic volume This equation tries to portray the relationship between quan...
Equation: G = (S | R) 1. when CW complex K (S | R) is aspherical 2. if π2 (K (S | R)) = 0 What you are doing in this equation is prove the claim made by Mr. Whitehead in 1941 in an algebraic topology that every subcomplex of an aspherical CW complexthat is connected and in two dimensions is also spherical. This was named after the man, Whitehead co...
Equation: (EQ4) 1. Where Γ = a second countable locally compact group 2. And the * and r subscript = 0 or 1. This equation is the definition of morphism and is referred to as an assembly map. Check out the reduced C*-algebrafor more insight into the concept surrounding this equation.
Equation: y=limn→∞(∑m=1n1m−log(n)) Find out if y is rational or irrational in the equation above. To fully understand this problem you need to take another look at rational numbers and their concepts. The character y is what is known as the Euler-Mascheroni constant and it has a value of 0.5772. This equation has been calculated up to almost half o...
Equation: π + e Find the sum and determine if it is algebraic or transcendental. To understand this question you need to have an idea of algebraic real numbersand how they operate. The number pi or π originated in the 17th century and it is transcendental along with e. but what about their sum? So Far this has never been solved.
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- Calculating Gas Mileage. One of the best real-life applications of algebra is the ability to figure out how far you can drive with a specific number of gallons of gas.
- Calculating the Length of a Trip. Okay so you know how far you are going to get on a gallon of gas. But how long will it take you to get there? If you know how fast you are travelling, and you know how far away your destination is, you can determine the amount of time it will take!
- Financial Planning. I credit my own financial literacy to my understanding of algebra and mathematics in general. Understanding algebra helped my family build our bank account, stay out of debt, and ensure that we always have enough money for our purchases before we make them.
- Budgeting. Another important part of being financially literate is understanding how to set up a budget that balances your monthly expenses and income.
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Algebra questions on functions, systems of equations, zeros of polynomials, rational functions, quadratic functions, logarithmic and exponential functions, with solutions and answers are presented.
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Find below a wide variety of hard word problems in algebra. Most tricky and tough algebra word problems are covered here. If you can solve these, you can probably solve any algebra problems.
