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March 29, 2024, 03:10:15 am

Author Topic: Mathematics Question Thread  (Read 1296776 times)  Share 

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RuiAce

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Re: Mathematics Question Thread
« Reply #915 on: November 13, 2016, 12:02:41 pm »
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so i got n=19

i couldn't get it any bigger becos the limit for file size
Snipping tool (automatically in Windows 7 and above) works miracles for captures; saves you having to use PrtScn to get a full screenshot

A quick check on WolframAlpha confirms that answer.

katnisschung

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Re: Mathematics Question Thread
« Reply #916 on: November 13, 2016, 12:04:12 pm »
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Thanks Ruiace
Yeah I should start using wolfram alpha more
get me out of here

katnisschung

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Re: Mathematics Question Thread
« Reply #917 on: November 13, 2016, 12:25:50 pm »
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A gp has 1st term 12
the terms of the sequence are all different and the sum of the 1st 2 two terms is equal to twice the third term

Find the 1st 3 terms of the sequence

So I interpreted this as
a=12
S2=2T3
So how do I know which formula to use for Sn becos I don't know what r is ? Or do I test them into both formulas
« Last Edit: November 13, 2016, 12:30:21 pm by katnisschung »
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RuiAce

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Re: Mathematics Question Thread
« Reply #918 on: November 13, 2016, 01:08:30 pm »
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A gp has 1st term 12
the terms of the sequence are all different and the sum of the 1st 2 two terms is equal to twice the third term

Find the 1st 3 terms of the sequence

So I interpreted this as
a=12
S2=2T3
So how do I know which formula to use for Sn becos I don't know what r is ? Or do I test them into both formulas


teapancakes08

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Re: Mathematics Question Thread
« Reply #919 on: November 13, 2016, 09:22:44 pm »
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Having trouble visualising this:

31. The track of a gramophone record is in the shape of a spiral curve and may be considered as a number of concentric circles of inner and outer radius 5.25cm and 10.5cm respectively. The record rotates at 33 1/3 rev/min and takes 18 minutes to play. Find the length of the track.

I'm presuming you have to use Sn = (n/2)(a+l) as it's possible to find both values by using C = 2πr (if I'm doing this correctly...), but the other values throw me off. Do I use d = st to help solve the question, or is there a entirely different way of solving it? The question also suggests to take π = 22/7, although I'm not sure what to do with it...any suggestions? Thanks to anyone who can help ^^
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jakesilove

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Re: Mathematics Question Thread
« Reply #920 on: November 13, 2016, 10:12:52 pm »
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Having trouble visualising this:

31. The track of a gramophone record is in the shape of a spiral curve and may be considered as a number of concentric circles of inner and outer radius 5.25cm and 10.5cm respectively. The record rotates at 33 1/3 rev/min and takes 18 minutes to play. Find the length of the track.

I'm presuming you have to use Sn = (n/2)(a+l) as it's possible to find both values by using C = 2πr (if I'm doing this correctly...), but the other values throw me off. Do I use d = st to help solve the question, or is there a entirely different way of solving it? The question also suggests to take π = 22/7, although I'm not sure what to do with it...any suggestions? Thanks to anyone who can help ^^

Weird question! Here's how I interpret it; if it takes 18 minutes to play, and the speed is 33 1/3 rev/min, then the number of revolutions will be (33.3333)*(18)=600 revolutions. So, we have 600 circles with radius' between 5.25cm and 10.5cm. That means that the radius will increase by (10.5-5.25)/600= 0.0525cm with each subsequent circle. This is a seriously weird question.

Our first circumference is 2π(5.25), then 2π(5.325) etc. etc. Clearly, this is increasing by 2*0.0525π with each circle, so that is going to be our value for d! We have n, a, l and d, so we can sum up the equation :)

Let me know if that all made sense!
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teapancakes08

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Re: Mathematics Question Thread
« Reply #921 on: November 13, 2016, 10:55:17 pm »
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Weird question! Here's how I interpret it; if it takes 18 minutes to play, and the speed is 33 1/3 rev/min, then the number of revolutions will be (33.3333)*(18)=600 revolutions. So, we have 600 circles with radius' between 5.25cm and 10.5cm. That means that the radius will increase by (10.5-5.25)/600= 0.0525cm with each subsequent circle. This is a seriously weird question.

Our first circumference is 2π(5.25), then 2π(5.325) etc. etc. Clearly, this is increasing by 2*0.0525π with each circle, so that is going to be our value for d! We have n, a, l and d, so we can sum up the equation :)

Let me know if that all made sense!

It seriously does...

My working out kind of looked like this:

full rev = speed*time
C = 2πr
a = 2π*5.25
l = 2π10.5

d (total revolutions) = speed*time
hence n = vt
n = 100/3 x 18
n = 600

...and then I pretty much plug in everything into Sn = (n/2) (a+l) and then BOOM. Answer. (Which is 296.88m for 2.d.p or 297m if you round it up to the nearest whole.)

To be honest the first thing that came to mind was physics, haha...

But yeah, it makes a lot more sense now - thanks so much for the clarifications ;D
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jakesilove

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Re: Mathematics Question Thread
« Reply #922 on: November 14, 2016, 11:19:26 am »
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It seriously does...

My working out kind of looked like this:

full rev = speed*time
C = 2πr
a = 2π*5.25
l = 2π10.5

d (total revolutions) = speed*time
hence n = vt
n = 100/3 x 18
n = 600

...and then I pretty much plug in everything into Sn = (n/2) (a+l) and then BOOM. Answer. (Which is 296.88m for 2.d.p or 297m if you round it up to the nearest whole.)

To be honest the first thing that came to mind was physics, haha...

But yeah, it makes a lot more sense now - thanks so much for the clarifications ;D

No problem! Glad I could help :)
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katnisschung

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Re: Mathematics Question Thread
« Reply #923 on: November 14, 2016, 05:03:00 pm »
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sighs.... series

show that three numbers a-d, a, a+d are in arithmetic progression. Hence find three
numbers in arithmetic sequence whose sum is -12 and whose product is 36
get me out of here

RuiAce

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Re: Mathematics Question Thread
« Reply #924 on: November 14, 2016, 05:27:59 pm »
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sighs.... series

show that three numbers a-d, a, a+d are in arithmetic progression. Hence find three
numbers in arithmetic sequence whose sum is -12 and whose product is 36





teapancakes08

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Re: Mathematics Question Thread
« Reply #925 on: November 14, 2016, 07:21:46 pm »
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Am enternally frustrated by this question:

40. The lengths of the sides of a right-angled triangle form the terms of an arithmetic sequence. If the hypotenuse is 15cm in length, what is the length of the other two sides?

I tried working it out using these two equations — 15^2 = a^2 + b^2 and 15 = 2b - a — but I have a sinking feeling that I'm looking at it the wrong way as when equating them I got irrational numbers, when the answers are definitely rational. Any suggestions for a less confusing (and potentially more efficient) way of solving this question?
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RuiAce

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Re: Mathematics Question Thread
« Reply #926 on: November 14, 2016, 08:04:40 pm »
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Am enternally frustrated by this question:

40. The lengths of the sides of a right-angled triangle form the terms of an arithmetic sequence. If the hypotenuse is 15cm in length, what is the length of the other two sides?

I tried working it out using these two equations — 15^2 = a^2 + b^2 and 15 = 2b - a — but I have a sinking feeling that I'm looking at it the wrong way as when equating them I got irrational numbers, when the answers are definitely rational. Any suggestions for a less confusing (and potentially more efficient) way of solving this question?




Remark on the note:

If we used a, a+b and a+2b, then we have a+2b=15 so a=15-2b
Then, 225 = a^2 + (a+b)^2 so 225 = (15-2b)^2 + (15-b)^2 which gives b=3 anyway.

teapancakes08

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Re: Mathematics Question Thread
« Reply #927 on: November 14, 2016, 08:49:10 pm »
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I think I might have made a carry-over error in this question:

"44. For a potato race, a straight line is marked on the ground from point A, and point B, C, D,... are marked on the line so that AB = BC = CD =...2 meters, and a potato is placed at each of the points B, C, D,.... A runner has to start from A and bring each potato by seperate journey back to a basket at A. Find the number of potatoes so that the total distance run during the race will be 480 meters."

(Sorry if the working out looks a bit iffy in some parts...^^;; )
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RuiAce

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Re: Mathematics Question Thread
« Reply #928 on: November 14, 2016, 09:21:52 pm »
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I think I might have made a carry-over error in this question:

"44. For a potato race, a straight line is marked on the ground from point A, and point B, C, D,... are marked on the line so that AB = BC = CD =...2 meters, and a potato is placed at each of the points B, C, D,.... A runner has to start from A and bring each potato by seperate journey back to a basket at A. Find the number of potatoes so that the total distance run during the race will be 480 meters."

(Sorry if the working out looks a bit iffy in some parts...^^;; )


A check on WolframAlpha showed that solving for n should give n as an integer, so looking at your final line I don't suspect there's been a mistake in algebra halfway through
« Last Edit: November 14, 2016, 09:27:13 pm by RuiAce »

teapancakes08

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Re: Mathematics Question Thread
« Reply #929 on: November 14, 2016, 09:49:03 pm »
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A check on WolframAlpha showed that solving for n should give n as an integer, so looking at your final line I don't suspect there's been a mistake in algebra halfway through

Got it ;D

Geh, I got stuck thinking it was like physics and started at zero. Actually, I got confused by the question stating A twice. Now that I think about it does make a lot more sense since it does indicate the the first run is the distance travelled from A to the next point (B) and back. Guess I wasn't paying much attention and jumped ahead to quickly...^^;;

Thanks for pointing that out ^^
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