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14 pairwise different positive integers are written on the board. Their mean value is equal to 19. Let M be the largest of these numbers. Find the smallest possible value of M.
What is the smallest value of 9(a^2) + (b^2) +16(c^2) given that 3a-b+4c=16 and
(4/a) - (12/b) +(3/c) = 0
Ivan and 5 sportsmen took part in a final 100-meter dash (all sportsmen start running simultaneously). It is known that Ivan won the dash. At the moment when 9 seconds passed from the start, all sportsmen together ran 290 meters (and nobody finished the race yet). At the moment Ivan finished the dash, the other 5 sportsmen had to run a total of 100 meters. How many meters did Ivan run during 9 seconds? (During the dash, all runners move at a constant speed.)
Let f(x)=x^2+bx+c. It has turned out that equation f(x) = 2x - 7 has exactly one solution, and equation f(x)=21-6x also has exactly one solution. Find the largest value of parameter p such that equation f(x) has exactly one solution.
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?
The total sales for restaurant b was $450,000 more than restaurant b and the total sales were 550,000,000 what were the sales for the years
Now design two similar questions, which you will give your learners
f(x)= 2x x+2
