Mathematics Question Thread

[jamonwindeyer]

ahaha thanks ruiace
im such an idiot 

Definitely not! We're glad we can help you out too, don't ever feel less intelligent by asking questions. It is only unintelligent to keep questions to yourself

[anotherworld2b]

thank you for your help
I was able to do q5 a and b but i wasnt able to do part c. Could i get some help with it please?

I reuploaded the question from before hopefully its clearer. I am not sure what i need to find

I also wanted to ask in exams is there a particular way to write the domain and range of a function?

15 degrees comes from the question itself, that looks okay to me!

For the circles one, you are finding two minor segments. The minor segment in circle 1 and the minor segment in circle 2, the formula should be something like this:



The radii are in the question; you've found the angles already! What this formula does is takes the area of the sector, and subtracts the area of the triangle, leaving only the area of the minor segment. So you don't need to find the areas of the triangles separately like you did in your earlier working; if you know this formula, you can just substitute it into here!

Unfortunately I can't see that diagram for the last question properly, too small

[asd987]

Hi,
can someone explain how to do part iii of Q15c of the 2016 hsc exam. thanks

[RuiAce]

Hi,
can someone explain how to do part iii of Q15c of the 2016 hsc exam. thanks

[jamonwindeyer]

thank you for your help
I was able to do q5 a and b but i wasnt able to do part c. Could i get some help with it please?

I reuploaded the question from before hopefully its clearer. I am not sure what i need to find

I also wanted to ask in exams is there a particular way to write the domain and range of a function?

Sorry I missed this! For that reuploaded question, draw the lines BF and AG. Those lines will intersect at some point, call it X. You want angle AXF! Hint, you'll only need the dimensions of the rectangle closest to us to get this question right

For Part C of that question, good start on finding the distance travelled! What you need to consider is the bigger, non right angled triangle, formed by the points F, Farmhouse and End on your diagram! The angle on the left of the triangle, is 90+15=105 degrees. You are going to need to do some work on that triangle. Do the following:

1- Find the distance between the plane and the farmhouse using the cosine rule
2- Find the angle in the bottom left corner of the triangle, the one formed at the farmhouse.

Then, once you have that smaller angle, the angle of elevation you want is just the complementary angle to that, so just subtract 90 degrees

That's a rough process, let me know how you go!

For domain and range, you can use either inequalities: \(x>5, y\le7\), or set notation, \(\left(5, \infty\right), \left(-\infty, 7\right]\), I'm not sure what is preferred in WACE but for NSW it is the former!

[asd987]

Hi, can i get some help with part iii of the 2015 hsc Q15b

[Jakeybaby]

Hi, can i get some help with part iii of the 2015 hsc Q15b

\begin{equation}\text{ } \\ 15~{b}~\text{iii} \\ {\frac{AB}{DF}}={\frac{AC}{DC}}~\text{(corresponding sides)} \\ \text{But }{D}~\text{is the midpoint of }AC \\ \therefore~{\frac{AB}{DF}}~=~{\frac{2}{1}} \\ AB~=~2DF \\ \therefore~AE~+~EB~=~2DF~① \\ \text{ } \\ \text{Now } \\ EB~=~EF~{\left({e}{q}{u}{a}{l}~\right.}\text{sides in Isos Triangle)} \\ EB~=~DF~+~{E}\Delta{B}~=~DF~+~AE~{\left({\operatorname{sin}{{c}{e}}}~AE~=~ED \right)} \\ \therefore~DF~=~EB~-~AE~② \\ \text{ } \\ \text{From }①~\text{and }② \\ AE~+~EB~=~2{\left(EB-AE \right)} \\ AE~+~EB~=~2EB~-~2AE \\ 3AE~=~EB \\ \text{ }\end{equation}

[RuiAce]

\begin{equation}\text{ } \\ 15~{b}~\text{iii} \\ {\frac{AB}{DF}}={\frac{AC}{DC}}~\text{(corresponding }\sigma\delta{s} \\ \text{But }{D}~\text{is the midpoint of }AC \\ \therefore~{\frac{AB}{DF}}~=~{\frac{2}{1}} \\ AB~=~2DF \\ \therefore~AE~+~EB~=~2DF~① \\ \text{ } \\ \text{Now } \\ EB~=~EF~{\left({e}{q}{u}{a}L~\right.}\text{sides in Isos Triangle)} \\ EB~=~DF~+~{E}\Delta{B}~=~DF~+~AE~{\left({\operatorname{sin}{{c}{e}}}~AE~=~ED \right)} \\ \therefore~DF~=~EB~-~AE~② \\ \text{ } \\ \text{From }①~\text{and }② \\ AE~+~EB~=~2{\left(EB-AE \right)} \\ AE~+~EB~=~2EB~-~2AE \\ 3AE~=~EB \\ \text{ }\end{equation}

This is some...interesting...LaTeX... 

[Jakeybaby]

This is some...interesting...LaTeX... 

I just used FX Equation 5 and then copied as LaTeX haha, as I don't know how to write in LaTeX myself

[Yasminpotts1105]

"Find the radius and height, correct to 2 decimal places, of a cylinder that holds 200cm^3, if its surface area is to be a minimum."

[RuiAce]

"Find the radius and height, correct to 2 decimal places, of a cylinder that holds 200cm^3, if its surface area is to be a minimum."

[Jakeybaby]

I'm always too slow haha

[Yasminpotts1105]

How do we differentiate something like y = 1/(x^2 + 2) or even something with just x in the numerator and an integer in the denominator?

[RuiAce]

How do we differentiate something like y = 1/(x^2 + 2) or even something with just x in the numerator and an integer in the denominator?

Do you mean an integer in the numerator and x in the denominator?

[Yasminpotts1105]

With x in the denominator we just bring it to the numerator and make it have a negative index don't we? I'm just confused at the moment with how to differentiate something like x/3