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@=)(= Note that csc is simply cosecant

-a-4b-5=-3 27a-36b-1=89 Next, a+4b=-2 3a-4b=10 From what is seen it is clear that a=2,b=-1

From this question you can also have 6+\alpha+\beta=10 9\alpha\beta=9 Simplifying gives \alpha+\beta=4 \alpha\beta=1 To find the roots instead of focusing on the product of roots let's have a look at the sum of roots. You see how the sum of roots is 4 right. Well note that x^{2}-4x+1 is a...

Let me ask you a question, what do you know if x=3 is a double root of the equation? If that is the case then you can have \left(x-3\right)^{2} is a root of the equation. Now you have this in the net we can now have x^{4}-10x^{3}+34x^{2}-42x+9=\left(x^{2}-6x+9\right)\left(...\right) What do we...

Well, since f'(x) > 0 then the function is always increasing. Since you are doing Mathematics Advanced this concept will be a very useful one in the topic that many HSC candidates struggle with Cumulative Density Function found in the last chapter. Keep this question in your back pocket it may...

Yes because once you have found the minimum turning point the function will only increase from the minimum turning point. If there is something lower than the minimum turning point you need to go back and check your calculations because there might be something lower.

Since you have shown that m=-12 and -20 then the style of attack would be to experiment with the fact that \alpha\beta+\alpha^{2}\beta+\beta^{2}\alpha=\alpha\beta+\alpha\beta\left(\alpha+\beta\right)=\alpha\beta\left(1+\alpha+\beta\right). First and foremost depending on the sum and product of...

For Q4 this is my interpretation of it. Since you have the juice and the water with 80% water and 20% juice. Well if 75% of the water is removed normally it would be 60% water removed but because there are two elements there the amount of water removed is half of that amount so in turn only...

Okay for Q1 10% of 350ml is just 35 ml but now what you have to do is to add water so that your 35ml that you had at the start is just 8%. Now this one can be done in two steps. 1. Find what is an eighth of 35ml and then multiply by 100 to get the new amount of cordial drink in the jug 2. Take...

This is simply the idea of less is more. As shorter quotes can allow you to come up with many ways to express it since they are open to interpretation and also very easy to memorise. Longer quotes can become a headache to remember when you think about them. All of this has to do with your...

A typical strategy is to think of collecting shells from the beach. At what point can you not hold your shells properly with the resources you have and your ability to hold them for a long period of time. It is at this point that you should just leave with what you have and make use of what you...

Have a look at the working out. If you need assistance someone will help interpret that information.

For this question -\tan{2x}\tan{x}=\frac{\cos{3x}-\cos{x}}{\cos{x}+\cos{3x}}, we can start working on this question knowing we need a 2x trig term and a x trig term. Now the mechanical step. \cos{3x}-\cos{x}=\cos{\left(2x+x\right)}-\cos{\left(2x-x\right)}...

1. Here are my hints. 10% of the drink is cordial and that you have 350mL of the drink at the start. First question what is 10% of 350mL, or you can go if 100 stands for 350 then what is 10 using the fact that percent is per a hundred. Then if we want that to be 8% only how much water do we need...

Do you mean we are given x+y\geq{2\sqrt{xy}}[/TEX]. Very important detail.

Do you need help for Q17?

I am not surprised by these two pathways because both of them are aimed at the fact that we still are dealing with COVID-19 which has not been eradicated yet from Australia so these pathways are very necessary. Actually, I kinda like these two pathways because they are very helpful as you are...

Wait Simpson’s method for 3U? I never seen that ever happen.

My question is "Does Dr Du write the NSW syllabus?" and be realistic when people write the syllabus they want to make sure teachers can finish teaching all their content in a whole year. But yeah I can see why some people might ask for it. I can also see why the cross product would be very...

Well simply put recall that \frac{a+b}{2}\geq{\sqrt{ab}}, \frac{c+d}{2}\geq{\sqrt{cd}} and with these two replace the x and y with them.