Mathematics Question Thread

[shellmekler]

Hi,

Can someone please help me with Q13d from the 2016 HSC exam?
To find the shaded area - I thought to find the area of the curve between 2 and 0 and then deduct the area of the triangle using 1/2bh but I might of integrated wrong? I am not sure.

Thanks in advance!

[envisagator]

The problem with what you did is that taking the intergral from 0 to 2 gives you the extra area under cos graph from 1 to 2, but what you are looking for is the area under cos curve from 0-1 so that you can subtract the area of the triangle between 0 and 1 to find the shaded area


I think you can take it from here, hope this helps

[Calley123]

Hey,
Please help with question Q4) b and c). This is part of the applications for sequence and series.

Thanks

[Calley123]

Please help again!
Still sequence and series questions.

[fun_jirachi]

Hey there!

Hey,
Please help with question Q4) b and c). This is part of the applications for sequence and series.

Thanks

For this one, b) is essentially the same as a), except you're plugging in 11 years instead of 1, 2 or 3 years.

c) for me is a little dodgy, might mean time, days years whatever, but im going to go ahead and assume it means how many years does it take to get 50k

so it takes 7 years to get to 50k, but if you really want to know how long it takes to get to 50k exactly, its just that 6.17 whatever whatever in years, around 2255 days, 54118 hours 3.247m minutes, and so on. just the question is really non specific, but i think that really the answer should be 7 ie. it takes 7 years to get to 50000 dollars

Please help again!
Still sequence and series questions.

and i dont think i can't help with this one, because you've just posted a statement with some information! what is the question? post it, and ill help you out

[Calley123]

Hey there!For this one, b) is essentially the same as a), except you're plugging in 11 years instead of 1, 2 or 3 years.

c) for me is a little dodgy, might mean time, days years whatever, but im going to go ahead and assume it means how many years does it take to get 50k

so it takes 7 years to get to 50k, but if you really want to know how long it takes to get to 50k exactly, its just that 6.17 whatever whatever in years, around 2255 days, 54118 hours 3.247m minutes, and so on. just the question is really non specific, but i think that really the answer should be 7 ie. it takes 7 years to get to 50000 dollarsand i dont think i can't help with this one, because you've just posted a statement with some information! what is the question? post it, and ill help you out

Thank you so much for doing part a! Sorry I thought I posted the question. Here it is now. Also please help me with question 10 !
Thanks in advance

[S200]

Isn't 10 just using the

compound interest formula?

Therefore...



EDIT:
You have to minus the principle. so \(\overbrace {{A-1400}}^ \text {Equals the interest...} \therefore ~$377\)

[fun_jirachi]

To start off I'd like to say cheers S200, saved me a bit of time there

Thank you so much for doing part a! Sorry I thought I posted the question. Here it is now. Also please help me with question 10 !
Thanks in advance

So hopefully you can see that for the nth apple where n is an integer, she runs 6n metres to get it ie. for the first one, she runs 6, 3m there and 3m back. Just note that for now.

a) To actually get to the k^th apple, she only needs to run 3k metres since the question doesnt mention anything about coming back.
b) And this is where we get into the fun stuff because its an arithmetic series, you're looking at the sum of the trips from the first apple to the k^th apple

c) now you just set S_k to equal 270.

Hope this helps!

[Calley123]

To start off I'd like to say cheers S200, saved me a bit of time there

So hopefully you can see that for the nth apple where n is an integer, she runs 6n metres to get it ie. for the first one, she runs 6, 3m there and 3m back. Just note that for now.

a) To actually get to the k^th apple, she only needs to run 3k metres since the question doesnt mention anything about coming back.
b) And this is where we get into the fun stuff because its an arithmetic series, you're looking at the sum of the trips from the first apple to the k^th apple

c) now you just set S_k to equal 270.

Hope this helps!

YASSSS Thanks

[Calley123]

HI,
Please help with Q11 d) and e).
Thanks

[RuiAce]

HI,
Please help with Q11 d) and e).
Thanks

This is an Extension 1 level question. Please post it in the relevant thread if you require help with it.

[ilikeapples]

Could someone please help me with this question: solve (3x^2 -2x)^0.5 = x^1.5

[Opengangs]

Could someone please help me with this question: solve (3x^2 -2x)^0.5 = x^1.5

We can simplify the left side if we recall the following property:

\[ (a^m)^n = a^{mn} \]
So if we raise both sides to the 1/0.5th power, we end up with:

\[ ((3x^2 - 2x)^{0.5})^2 = (x^{1.5})^2 \]

which simplifies down to:

\[ 3x^2 - 2x = x^3 \]

The rest should be fairly easy to simplify. If you have any questions, feel free to clarify

[S200]

Could someone please help me with this question: solve (3x^2 -2x)^0.5 = x^1.5

OG has given the index laws, so I'll just throw this up here...

This is equal to;                                         \(\sqrt{3x^2 -2x} = \sqrt{x^3} \)
square both sides and you have               \(3x^2-2x=x^3\)
Swing the \(x^3\) across and make a cubic...

[ilikeapples]

This seems like a really simple mc question but I keep getting the wrong answer: What is the distance from the point (p,q) to the line px+qy=0, could anyone help me out? (: