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Try to express b as a function f(y) where y=q/p and f(y)=27y+70(1/y). We can speak about the greatest value of b for q/p<0. If q/p>0...

You are right. There are the local maximum and the local minimum. In my opinion, the question only holds for q/p<0.

This question makes no sense to me. If ##p, q## are fixed, then that determines ##b##. There is no question of maximising ##b## in...

You are right. Given the problem as stated, there is no maximum value for ##b##.

Thank you very much for the explanation JimWhoKnew, Gavran, PeroK, FactChecker

I have posted the full question so I don't know about this Sorry but why should we consider the case where the quadratic must have one...

Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then...

I understand. Thank you very much for the help and explanation DaveE, nasu, Steve4Physics

Say we have a transverse wave, moving in the +x direction, along a string. There are 2 very different types of graph and it’s easy to...

Yes.

Imagine that you are measuring the wave height at some arbitrary position on the x-axis. As the waves move towards you, which wave peak...

I answered A but the answer key is B. I thought since the wave is moving to the right, P started first compared to Q (the crest of P is...

I understand. Thank you very much for all the help and explanation PeroK, BvU, WWGD, DaveC426913, JimWhoKnew, Gavran

How about this: Starting with 5 identical balls, there is a total of 5!=120 arrangements. Now consider the distinction. Then: By...

For more complicated problems than this one in the original post the formula is $$...