Mathematics Question Thread

[1937jk]

How do you solve,
Log₈x + log₄ x =10

[jakesilove]

How do you solve,
Log₈x + log₄ x =10

Hey! So, let's first recall that



Now, looks like we want to be working in 2s, so lets give that a crack



So, we are at the stage



We can simply rearrange our log, such that



and we're done!

[1937jk]

Hey! So, let's first recall that



Now, looks like we want to be working in 2s, so lets give that a crack



So, we are at the stage



We can simply rearrange our log, such that



and we're done!

Ohhhhhhh I see now! thank you so much!!!

[jakesilove]

Ohhhhhhh I see now! thank you so much!!!

No problem, always happy to help!

[1937jk]

Okay so another question,
Find any stationary points of the curve y= x + e^-x
I have the derivative
y'= 1 - e^-x
And so to find stationary points it equals zero
So e^-x = 1
I don't understand how to find x from this, if someone could please explain what I should know haha thanks!

[RuiAce]

Okay so another question,
Find any stationary points of the curve y= x + e^-x
I have the derivative
y'= 1 - e^-x
And so to find stationary points it equals zero
So e^-x = 1
I don't understand how to find x from this, if someone could please explain what I should know haha thanks!

[1937jk]

Oh of course! Thank you so much

[cxmplete]

how would you solve 6b?

[jamonwindeyer]

how would you solve 6b?

Hey! You would do an indefinite integral:



But we know at \(t=0\), we have no items yet, so:



Then just substitute \(t=10\) to get the answer of 110! Note you could also do a definite integral with limits 0 and 10, but this approach makes a little more sense on the surface, at least imo

[f_tan]

How do I work this out?

Mrs Caine contributes $1000 on the day of her son's birth, and increases her annual contribution by 6% each year. Her investment also earns 6% compound interest per annum. Fine the total value of Mrs Caine's investment on her son's third birthday (just before she makes her fourth contribution.)

Thank you!

[jamonwindeyer]

How do I work this out?

Mrs Caine contributes $1000 on the day of her son's birth, and increases her annual contribution by 6% each year. Her investment also earns 6% compound interest per annum. Fine the total value of Mrs Caine's investment on her son's third birthday (just before she makes her fourth contribution.)

Thank you!

Hey f_tan! We can just step through this one:

On the day of her sons birth, we have \($1000\).

After 1 year, we have gained 6% interest - Going up to \(1.06($1000)=$1060\).

We then make another annual contribution, which is 6% higher than the previous contribution of \($1000\). So we add \(1.06(1000)=$1060\) to that total, giving a total of \($2120\)! That's after the child's first birthday!

Continue this process - Apply 6% interest, then make an annual contribution of 6% greater than previous - You need to do it twice more to get to the third birthday, but remember not to add the final contribution!! Does this help?

[katnisschung]

hey hey!

could somebody pls check my answer
simple integration of e but mine seems to be wrong?

[jamonwindeyer]

JUST REALISED WE'VE HIT THE 100TH PAGE OF THIS THREAD!

Super exciting to see one of the first ever threads for the forum community of NSW reaching such a cool milestone

[jamonwindeyer]

hey hey!

could somebody pls check my answer
simple integration of e but mine seems to be wrong?

I think it is just the constants that are off!

[dadwwdnnnn]

Couple of Questions:

For my half yearlies, this question was in the practice HSC and I find get the answers:

Question 1: (Pretty sure its just algebra)



Question 2 e): (I have completed a-d)



Question 3: (Factorise)



Thanks for the help!,

Thomas