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Learn how to solve the definite integral of 1/x * (x/(1-x)) from 0 to 1. This step-by-step guide demonstrates simplifying the integrand, applying integration rules, and evaluating the limits to reveal the integral diverges to positive infinity.

A bonus of Rs 21000 is shared between 3 managers and 7 salespeople. A salesperson claims they would get 25% more if the bonus was shared equally. Is the salesperson correct? The answer is no, they would get about 16.67% more.

This math problem involves solving for the value of 3^X - 3^Y, given that 3^X ÷ 3^Y = 3 and 3^X + 3^Y = 12. The solution involves using the properties of exponents to simplify the equations and solve for the values of 3^X and 3^Y, ultimately leading to the answer of 6.

This math problem asks you to add four mixed numbers: 15 2/7 + 23 3/4 + 7 5/7 + 5 1/4. The solution involves finding a common denominator, converting the mixed numbers to improper fractions, adding the fractions, and simplifying the result. The answer is 52.

This problem involves solving for the value of P in the equation 125^(3P-4) = √5. The solution involves simplifying both sides of the equation, expressing them with the same base, and then equating the exponents to solve for P. The final answer is P = 25/18.

This math problem involves simplifying the expression 8^(-1/2) / √2. The solution involves using exponent rules and simplifying square roots to arrive at the final answer of 1/4 or 0.25.

This step-by-step solution demonstrates how to solve the equation 7√(3x - 5) = 28, arriving at the answer x = 7.

This math problem asks to solve for the value of T² + M, given the equations T + M = 6 and T - M = 2. The solution involves solving for T and M using the first two equations and then substituting the values into the third equation to find the answer: T² + M = 18.

This problem solves the equation 2^(x+1) - 3^x = 0 for x using logarithmic properties. The solution is x = 1 / (log₂(3) - 1), which is approximately 2.7095.

Solve the math problem 13 - 2 × 3! and find the answer. The solution is 1.

Solve for the value of √x + 1/√x given that x = 7 + 4√3. The solution reveals a surprising simplification, resulting in an answer of 4.

Solve the math problem 5 + 1 x 5. The correct answer is 10, following the order of operations.

Solve the math problem 60 ÷ 6 x 2. The answer is 20.

Solve for 'c' in the equation f = (a-c)(b-d)/(ac-bd). The solution is c = (ab - ad - fbd)/(fa + b - d).

This proof demonstrates that Bessel functions of different orders, $J_n(x)$ and $J_{n+m}(x)$, have no common zeros except at x=0. The proof uses the Bessel differential equation, recurrence relations, and a proof by contradiction to show that assuming a common zero leads to a contradiction.

Discover why no two integers can be the same distance from the square root of 2. This math problem explores the concept of irrational numbers and distance, proving that integers and the square root of 2 cannot share equidistant points.

Discover the elegant solution to the Basel Problem, a mathematical puzzle that asks for the sum of the reciprocals of all squared integers. Learn how the infinite series 1/1² + 1/2² + 1/3² + ... surprisingly equals π²/6.

Discover how many times you need to roll a six-sided die and get a "6" before you can confidently declare the die is biased. Learn about the limitations of small sample sizes and the importance of statistical analysis in determining probability.

This math problem explores the additive identity property. The equation (-2 + 2) + (-2 + 2) + (-2 + 2)... = 0 is true because each set of parentheses simplifies to zero, and adding zero repeatedly results in zero.

Solve the weekend math challenge: What is 16 to the power of zero? The answer is 1, based on the rule that any number raised to the power of zero equals 1.

This math problem calculates the total cost of a box of 50 dental floss picks, priced at 2 yuan each. The solution reveals the total cost to be 100 yuan.

Find the derivative of the polynomial function f(x) = 3x³ - 2x² + x - 5. The solution, using the power rule of differentiation, is f'(x) = 9x² - 4x + 1.

This math problem involves calculating the latest time Jeff can leave his house to get to work on time, considering his commute from Bexleyheath to Bluewater, including walking times to and from bus stops. The solution requires analyzing a bus timetable and performing simple time calculations.

Find out how long it takes a train to travel from London St Pancras to Paris, departing at 0618 and arriving at 0947. The answer is 209 minutes.

Natalie drives from London to Sheffield, leaving at 9:15 am. After a 2.5-hour drive, she takes a 20-minute break and then drives for another 85 minutes. Find out what time Natalie arrives in Sheffield. Solution: Natalie arrives in Sheffield at 1:40 pm.

Find out what time a 98-minute film ends if it starts at 7:45 pm. The film finishes at 9:23 pm.

Find out what time Hayley arrived at her friend's house after leaving home at 10:40 am, walking 14 minutes to the shop, spending 10 minutes there, and then walking 22 minutes to her friend's house. Solution: Hayley arrived at her friend's house at 11:26 am.

Find the difference, in minutes, between 2 hours 25 minutes and 1 1/2 hours. The solution is 55 minutes.

Find the difference, in minutes, between 55 minutes and 1 3/4 hours. The answer is 50 minutes.

Learn how to convert hours to minutes with this simple example: 4 hours equals 240 minutes.