Other Math Answers

(History of Math) Solve the following problem from tablet YBC 6967: A number exceeds its reciprocal by 7. Find the number and the reciprocal. (In this case, that two numbers are “reciprocals” means that their product is 60.) 

(history of math) In 1936, a group of Old Babylonian tablets was lifted at Susa (about 200 miles from Babylon). On this tablet, The ratio of the perimeter of a regular hexagon to the circumference of the circumscribed circle is given as 0; 57, 36. What approximation of π does this lead to?

1.   For each m ≥ 1 and n ≥ 1, if m is even and n is odd, then m + n² or _m² + n is prime.

1000 chips are situated in a row. Each of the chips is either black or white. It is known that whatever two white chips are considered, the number of chips between them is not equal to 12 (possibly it is 0). What is the largest possible number of white chips in the row?

a. Solve the equation x³+x²−16x+ 20 = 0 by Cardan’s method.

b. Locate the root of f(x) = x¹⁰ −1 between 0 and 1.3 using the Bisection method correct to three decimal places.

c. Prove that the convergence order of the Secant method is 1.618.

d. Use the iteration method to find the root of the equation e^x = 5x correct to three decimal places.

e. The bacteria concentration in reservoirs as C = 4e^−2t+e^−0.1t, using Newton Raphson method, calculate the time required for the bacteria concentration to be 0.5. Correct up to 7 decimal places.