Recent content by 000

Homework Statement Say we have an infinite sequence of natural numbers A such that no K subsequences can be found adjacent such that the average of the elements in any subsequence is equal for all K subsequences. Sorry about my poor description, an example would be that {2, 3, 4, 1} wouldn't...

f(x) must always be larger than x, are there any asymptotic functions that fit that criteria?

Homework Statement There exists a function f(x) such that the indefinite integral of 1/f(x) as x-> infinity diverges, and f(x) >= x for all values of x. Prove this function must be a linear polynomial. Homework Equations None that I know of.The Attempt at a Solution No idea where to start.

The gravitational potential energy is dependent on the square of the height, correct?

Sorry, there was a mistake in the question. What I meant to say was how much work must be done in order achieve height 'h'.

Could you clarify?

Homework Statement A rocket is launched at a planet of 600km radius, 5.29e22 kg mass, and 9.8068 m/s^2 surface gravity such that it reaches a maximum height 'h' with work 'x'. What is the value of 'x'? Ignore air resistance, and gravity is dependent on height. Homework Equations Unsure of...