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So you have been given the domain of g. When it say map [1, 4] to [2, 6] this means [1, 4] is the domain and [2, 6] is the range of g. Actually the question does not explicitly state the domain of g but without making that assumption the question is not doable.

[1, 3.5]

So what you are describing is another way to approach the question. The key idea is establish an relation between "a" and "r" which they just happened to be able to do by dividing area_triangle/area_sector. To put it simply it is just one step of the calculation.

So you should first figure out what it is you don't understand. Is there particular line. Is there theorem that you have forgotten or not aware about. What about an axiom or definition.

This question should be straightforward if you understand it. All it is asking is what is the domain of f(g(x)).

The question is quite confusing still. r: smaller radius a: full area (not halved) a/2 = 1/2*r^2*pi/6 => a = r^2*pi/6 => sqrt(a) = r*sqrt(pi/6) There seems to be a mistake in the question.

So the first step would be figuring out what you don't understand regarding the solution. Also you have not defined "a". What is "a"?

So it does not matter what you don't know what to do. In university you can take a wide variety of subjects and figure out what specific field you want to go into. Maybe you could focus on areas you have no knowledge about that. E.g. biomedical or civil. Maybe IT is option. Or if nor IT maybe...

I didn't use latex

The syntax of piecewise function function is f(x) = { value1 condition1 { value2 condition2 { . { . { . { valueN conditionN The syntax means if condition1 is satisfied then f(x) will take upon the value of...

I see. The point I am trying to get cross it might be worth getting outside your comfort zone. Perhaps the subjects you find hard are actually easy. I actually never felt comfortable with science, however once I found the right resources I realised it was not hard at all.

ii reminds me of bernoulli inequality. But I am not sure if that is the way

Have you considered math or any science subjects?

telescoping sum.

Unfortunately, often when you want to solve a problem, you don't what approach to take. As a result you just need to give it go. I think key thing to look out for when going through question was trick used. E.g., proof by cases, was an additional theorem used as an lemma As a side note, you...

So there are two things you need to know. 1) the unit circle definition of the trigonometric functions 2) trig ratios for the special triangles https://www.youtube.com/playlist?list=PL0o_zxa4K1BVkRxCZubMPcCJ5Q5QwZdEM For 2) I have pasted a link. Refer to video 66, 67.

Stated simply, it is the intuitive idea that if there are a ways of doing something and b ways of doing another thing, then there are a · b ways of performing both actions. https://en.wikipedia.org/wiki/Rule_of_product

Most questions seem to be employing rule of product axiom. So as a first start apply the axiom.

I do not feel UTS was not honest about the degree me and my classmates. We were doing a data engineering degree. However the head teacher knew nothing about data engineering he seem to specialise in some other areas. The key aspect behind data engineering is ETL. This was never taught...

A lower SD means the data is spread less. If the data is spread less then this will likely mean you will get better estimate of the mean from a sample of data. Remember central limit theorem?