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Understanding layout of a polynomail problem.

I have this question. I can see it is a basic polynomial. I know what a polynomial is and can do polynomial long division. I have been teaching myself with some help on here. The thing is I am not sure how to display the question in the polynomial format. I plotted these on a graph and I looks like it will take a little under 6 hours 45 mins. How do I express this mathematically?

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Re: Understanding layout of a polynomail problem.

I think it work something like this:

I am not sure if this makes any sense?

Re: Understanding layout of a polynomail problem.

This problem is not about polynomials, but about arithmetic progressions. The filling rate is an arithmetic progression (talk about how realistic this condition is). You need to find its sum to know how many liters are poured in n hours, then take the smallest n such that that volume is greater than or equal to the volume of the tank. The sum of an arithmetic series is a quadratic function in n, so equating it to the tank volume gives you a quadratic equation.

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Re: Understanding layout of a polynomail problem.

Im sorry,

This is how far I have get with it.

I don't quite understand. I need to work out what (s) is then if the 16x9x9 = greater than 1050 I am to replace that?

Can you lay this out a little more clearly please? Like from A to Z

Would appreciate it thanks

Re: Understanding layout of a polynomail problem.

You correctly have S(n) as a function of n: S(n) = (n/2)(2a_{1} + d(n-1)). You need to find the smallest n such that S(n) >= 1296 * 10^{3}. Substituting a_{1} = 150 and d = 200, we get the inequality

(n/2)(300 + 200(n-1)) >= 1296 * 10^{3}

n(150 + 100(n-1)) >= 1296 * 10^{3}

n(1.5 + n - 1) >= 12960 (by dividing the previous line by 100)

n(n + 0.5) >= 12960

n^{2} + 0.5n - 12960 >= 0.

The last line is a quadratic inequality. You can solve the corresponding equation and round up the largest root to an integer (if you think the problem requires an answer in whole hours).

The calculations above have to be double-checked.

Re: Understanding layout of a polynomail problem.

Everything you see makes sense now.

apart from

The last line is a quadratic inequality. You can solve the corresponding equation and round up the largest root to an integer (if you think the problem requires an answer in whole hours).

Can you elaborate please?

I know it sounds a bit stupid but I am just not clued up on the language that you guys use. You want me to find n^2 on the last line?

Re: Understanding layout of a polynomail problem.

Ok, after going backward I have discovered at because of the really poor layout of the lesson that have been allocated to me about this subject if not but of this work at the moment which I am supposed to be doing.