Mathematics Question Thread

[RuiAce]

This question is from the log and Exponential Functions, a two unit topic but I think its for 3U students...
Sorry

Even if it's for 3U students that doesn't address the main problem.

there are two regions that could be implied by this information.

[gumscape]

Hello! How do I do this question?

what are the equations of the vertical asymptotes of y=1/2sex(2x-1)

Thank you!!!

[RuiAce]

You might wanna fix your typo.

Note that the 1/2 in front does not change the asymptotes.

[owidjaja]

Hey,
I've been kinda stuck with this question because I keep getting the same answer but it's different to the answers. Is there something I did wrong in my working out? (Still haven't figured out how to embed images so I'll try via Google Drive Link)

Thanks in advance!

[RuiAce]

Hey,
I've been kinda stuck with this question because I keep getting the same answer but it's different to the answers. Is there something I did wrong in my working out? (Still haven't figured out how to embed images so I'll try via Google Drive Link)

Thanks in advance!

Presumably everything else was just an error carry through, because I think the factorisation might be wrong. I’m on my phone right now but when I plugged into Wolfram I got -2x^2-5x+3=-(2x-1)(x+3)

[owidjaja]

Hey guys,
I need help with the following question:
Consider the function x^2=8y. Tangents are drawn at the points A(4,2) and B(-4,2) and intersect on the y-axis. Find the area bounded by the curve and the tangents.

Thanks in advance.

[jamonwindeyer]

Hey guys,
I need help with the following question:
Consider the function x^2=8y. Tangents are drawn at the points A(4,2) and B(-4,2( and intersect on the y-axis. Find the area bounded by the curve and the tangents.

Thanks in advance.

Hey hey!! This is a big question, the first few steps laid out are:

- Rearrange the equation to make \(y\) the subject
- Differentiate the function
- Determine the gradients of the function at the two points of interest using the derivative
- Use these gradients and the point-gradient formula to find the equations of the two tangents

Equations are

At this point, you have the equation of the parabola and two lines. The area enclosed between them can be split in half, one from \(x=-4\) to \(x=0\) (the y-axis), and one from \(x=0\) to \(x=4\). You need to then find each of those using an integral! The first half, for example, would be:



And the second half:



Calculate those and add them up! The tricky bit about this is really just sequencing your actions, and then visualising how to divide that area you get as a result - Hopefully you are able to form a sketch because that helps heaps! I wanted to put one but Imgur is failing on me for some reason anyways, hopefully this helps add some clarity, but definitely skipped the bulk of it. If you let me know where you are having trouble specifically I can help some more!

[Aaron12038488]

 The limiting sum of  a geometric series is 20. what series might this be? (Give 2 possible answers)
Cheers

[owidjaja]

Hey guys,
So the question I need help in is: The parabola y= (x+2)^2 is rotated about the x-axis from x=0 to x=2. Find the volume of the solid formed.
I attached my working out because I'm not sure where I went wrong. The answer is supposed to be 992/5 π u^3.

Thanks in advance.

[Sine]

Hey guys,
So the question I need help in is: The parabola y= (x+2)^2 is rotated about the x-axis from x=0 to x=2. Find the volume of the solid formed.
I attached my working out because I'm not sure where I went wrong. The answer is supposed to be 992/5 π u^3.

Thanks in advance.

Hey owidjaja,
you made an error i've done before ahah . You didn't use the 0 when evaluting the intergral .maybe thinking it cancels down to 0? Anyway you should have a line of working (3rd line) saying pi[(4)^5/5 - (2)^5/5].

Hopefully this makes sense

[jamonwindeyer]

The limiting sum of  a geometric series is 20. what series might this be? (Give 2 possible answers)
Cheers

Hey mate! If the limiting sum is 20:



Choose values of \(a\) and \(r\) that make this true! For example, \(a=10\) and \(r=0.5\)

[RuiAce]

The limiting sum of  a geometric series is 20. what series might this be? (Give 2 possible answers)
Cheers

Will just add a comment: This question is open ended, because there's actually an infinite number of possible answers.

Perhaps the most convenient way of doing this is to use the formula (as stated above), and just put any random values of \(r\) into it (such that \( |r|<1 \) of course), and then solve for \(a\) in both cases.

[Mate2425]

Hi could i please get some help with the question below regarding exponentials and logs and also with the setting out of the x and y intercepts thank you!
 
b) Sketch, showing any stationary points and inflexions:
Y = (log e x - 1 )^3

[Opengangs]

Hi could i please get some help with the question below regarding exponentials and logs and also with the setting out of the x and y intercepts thank you!
 
b) Sketch, showing any stationary points and inflexions:
Y = (log e x - 1 )^3

Hey, Mate2425!




----

[cnimm2000]

Hi guys,
i was doing this series and applications hsc question:
2007 Q3
Can you please let me know if i have the correct answers pls.
thank you
i) Tn = 750 + 100 (n-1)
ii) 1650 m
iii) 12 000 m
iv) 20 days