2006-11-26 15:21:27 · 8 answers · asked by Eric 2 in Science & Mathematics ➔ Mathematics
numbers are 25, taken twice.
way to prove it is to write x*(50-x), take a derivative and set it to zero.
2006-11-26 15:23:44 · answer #1 · answered by Anonymous · 1⤊ 0⤋
Consider breaking 50 in to 49 and 1. The product is 49. Try 48 and 2 - it is 96. You soon find that the as the two numbers that add up to 50 become nearly equal the product goes to the maximum. Therfore the biggest product is when the number 50 is formed by 25 and 25. (25x25=625 is the biggest product).
You use the term number (not integer) in your question. So, had it been a sum that is not an even number like 50 (say 53 or 54.6), the constituent numbers forming such an odd number (or a decimal number like 54.6) would be its decimal quotient of division by 2.0.
2006-11-26 15:35:35 · answer #2 · answered by Inquirer 2 · 0⤊ 0⤋
Use brute force ....
sum of 50 = 1 + 49, 2+48, 3+ 47.... 25+25....
then you will observe that the largest number pair is 25 x 25. this should give you the largest product .
2006-11-26 15:25:52 · answer #3 · answered by Matthew N 5 · 0⤊ 0⤋
As long as the numbers need not be distinct, the answer is 25 and 25. As an illustration, use the areas of rectangles and squares, where half the perimeter equals 50. A rectangle with a side measuring 1 and a side measuring 49 gives an area of 49. A side of 2 and a side of 48 gives an area of 96. Continuing, we notice the greatest area occurs where the two sides are the same; that is, we have a square.
2006-11-26 15:28:25 · answer #4 · answered by Dan 3 · 0⤊ 0⤋
Im pretty sure its 25 and 25 the number in the exact middle because as you increas one number and decrease and number so they add up to 50 the product shrinks so 25 and 25 is 625 and 24 and 26 is 624 and all the way down 49 and 1 is 49!
2006-11-26 15:25:50 · answer #5 · answered by Ravioli 2 · 0⤊ 0⤋
call the 1st variety X, so the 2d variety is 50-X. you elect X(50-X) to be a optimum. X(50-X) = 50X - X^2. to remedy this with Calculus, take the 1st spinoff that's 50-2X and remedy for X to get X=25. with out Calculus, discover the two roots via factoring into X(50-X) which yields X=0 and X=50. the answer is halfway between the roots for the reason which you have a quadratic function. desire that helps!
2016-12-29 13:12:28 · answer #6 · answered by ? 3 · 0⤊ 0⤋
25 + 25 = 50
25 * 25 = 625
2006-11-26 15:24:50 · answer #7 · answered by cw 3 · 0⤊ 0⤋
25 & 25
25+25=50
25*25=625
2006-11-26 15:31:09 · answer #8 · answered by yupchagee 7 · 0⤊ 0⤋