Mathematics Question Thread

[jamonwindeyer]

Anyways, that's a 3-4U topic and 2U don't need to know it. I never did 3-4U but was taught by this 3U kid who dropped into my 2U class.

Thanks for the proof Kekemato! Just in case any 3 unit students read this and panic, it is only 4 unit students that could be expected to do this, only 4U learn integration by parts - 2U and 3U students could do it if they were asked to differentiate \(x\ln{x}-x\) first

Here is a guide for the fancy symbols

[sophiegmaher]

I really need some help on this question!!: "The area ln5/2 is rotated about the x-axis. Find the volume of the solid formed."
*the limits are when x=2 and x=5*
I feel like the answer is simple but I'm stuck.

[jamonwindeyer]

I really need some help on this question!!: "The area ln5/2 is rotated about the x-axis. Find the volume of the solid formed."
*the limits are when x=2 and x=5*
I feel like the answer is simple but I'm stuck.

Hey! So this one is interesting, because you are told the area but not the curve(s) being rotated - That's the tricky bit. You need to figure that out. Consider this:



So we know that whatever we integrate to get that area, our result is \(\ln{x}\) - Well that must be \(\frac{1}{x}\)! Our original integral to find that area must have been:



So therefore, to find the volume, we are doing:



And that is just a standard definite integral does that make sense?

[sophiegmaher]

And that is just a standard definite integral does that make sense?

Yes it does! However, the answers say the volume is 3/10 and I'm getting 21/100 ..?

[jamonwindeyer]

Yes it does! However, the answers say the volume is 3/10 and I'm getting 21/100 ..?

Perhaps some incorrect working?

[cxmplete]

Hi, how would you do questions 30 and 31 (sorry that they're such large questions but i'm realy stuck)?

[K9810]

Hi,

Can you please help me with this question?

[sophiegmaher]

Perhaps some incorrect working?

haha I think so, I didn't bring the x^2 to the top! Thank you!!

[jakesilove]

Hi, how would you do questions 30 and 31 (sorry that they're such large questions but i'm realy stuck)?

Hey! For the first question, we literally just sub in the relevant values;



From here, it gets a bit trickier. We need to find a nice pattern. Let's look at what happens in the third year, but without using the VALUE of the instalment, but rather using the relationship



Can you see a pattern? In the nth year, we find that



Now, letting n=20, we get $4306.38 (as required)

For the last part, we need to create a sum. This will look like




We use the sum of a geometric series to find that



Sub in n=20, and you get the correct answer out! Try using this approximate working out to get 31, and if you're still struggling we can walk you through it

[jakesilove]

Hi,

Can you please help me with this question?

Hey! First, we find the angle by using the length of an arc formula





Now, there is just a formula for the area of the minor segment. But, since it isn't on your formula sheet, let's derive it!

First, we find the area of the whole segment. Thankfully, that formula IS on your formula sheet, and is



Now, let's find the area of the TRIANGLE.



So, the area of the minor segment will be

[K9810]

Hey! First, we find the angle by using the length of an arc formula





Now, there is just a formula for the area of the minor segment. But, since it isn't on your formula sheet, let's derive it!

First, we find the area of the whole segment. Thankfully, that formula IS on your formula sheet, and is



Now, let's find the area of the TRIANGLE.



So, the area of the minor segment will be

Hey! Thanks for helping.
Can I directly use the formula for the minor segment 1/2*r^2(theta-sintheta)? Or do I have to do it separately like the way you showed me?

[jakesilove]

Hey! Thanks for helping.
Can I directly use the formula for the minor segment 1/2*r^2(theta-sintheta)? Or do I have to do it separately like the way you showed me?

If you know the formula, you can definitely just churn it out and get straight to the answer

[K9810]

If you know the formula, you can definitely just churn it out and get straight to the answer

Hey, sorry to bother you.
But when I used the minor segment formula I got

0.5(12)^2(pi/6-sinpi/6)=37.04

[jakesilove]

Hey, sorry to bother you.
But when I used the minor segment formula I got

0.5(12)^2(pi/6-sinpi/6)=37.04

Is your calculator in radians? Google tells me the answer is like 1.7

[K9810]

Is your calculator in radians? Google tells me the answer is like 1.7

Thank you so much!
I forgot to put it in radians