Please can you help me with this maths problem? Watch

Ioniccopperflame
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A pendulum of length L cm has time period T seconds. T is directly proportional to the square root of L. The length of the pendulum is increased by 40%. Work out the percentage increase in the time period.
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RDKGames
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(Original post by Ioniccopperflame)
A pendulum of length L cm has time period T seconds. T is directly proportional to the square root of L. The length of the pendulum is increased by 40%. Work out the percentage increase in the time period.
So we are told that T \propto \sqrt{L} which means that T=k\sqrt{L} for some constant k.

Increasing the length by 40% means we get aT=k\sqrt{1.4L} and you want to manipulate this equation to get aT=a(k\sqrt{L}) for some constant a where the RHS is as we had in the first place, and the LHS is multiplied by the same thing as the RHS- this multiple will tell you by what percentage the time increases.
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Lauren-x-
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(1) You could also square both sides to get T2 is proportional to L.

Increasing L by 40% is the same as multiplying by 1.4.

Because it is T2 is proportional to L, then (aT) 2 is proportional to 1.4L...

a2T2 is proportional to 1.4L.

Then you know a2=1.4 (from (1) we know that T2 is proportional to L).

You can then see what the % increase is, in the same way as an increase by 40% is 1.4.

Though RDKGames' help was much clearer than mine haha!
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Ioniccopperflame
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(Original post by Lauren-x-)
(1) You could also square both sides to get T2 is proportional to L.

Increasing L by 40% is the same as multiplying by 1.4.

Because it is T2 is proportional to L, then (aT) 2 is proportional to 1.4L...

a2T2 is proportional to 1.4L.

Then you know a2=1.4 (from (1) we know that T2 is proportional to L).

You can then see what the % increase is, in the same way as an increase by 40% is 1.4.

Though RDKGames' help was much clearer than mine haha!
I sort of understand but can you explain where a and 1.4L come from please?
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Daydreamer3
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(Original post by Ioniccopperflame)
I sort of understand but can you explain where a and 1.4L come from please?
It says that its increased by 40% so to find the percentage increase multiplier you do 100% + 40% = 140/100 to get 1.4.

This question was in your test wasnt it ? aha
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Ioniccopperflame
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(Original post by Daydreamer3)
It says that its increased by 40% so to find the percentage increase multiplier you do 100% + 40% = 140/100 to get 1.4.

This question was in your test wasnt it ? aha
What about the letter a? Where does that come from?
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Lauren-x-
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(Original post by Ioniccopperflame)
What about the letter a? Where does that come from?
The letter a is just something to represent the percentage increase (the answer to the question) in the form of a decimal. It could be any letter you want - you could've chosen x,y,k or any other letter of the alphabet!
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Ioniccopperflame
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(Original post by Lauren-x-)
The letter a is just something to represent the percentage increase (the answer to the question) in the form of a decimal. It could be any letter you want - you could've chosen x,y,k or any other letter of the alphabet!
Thank you
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Butterfly567
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What is the final answer then 40%?
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bidmas
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18.3
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Joshkkkk
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What does RHS mean?
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Konanabanana
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i got 15.5% but good lord am i rusty on this ****.. aha

Someone approve the official answer i'm curious
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PepeTheFroggi
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i am still sooo confused on this topic :/
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Tutortutor
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T ∝√L
So T=k√L

We are told Let L = 1 represent the original length of pendulum

Therefore T=k√1 So T=k You now have to build the second equation: L has undergone a 40% increase T has undergone an x % increase (because they don't tell us)

So we can write for the increase: xT = k √1.4

BUT WE ALREADY KNOW THAT T=K , so we can sub K into the T to get a formula for x wrt k ( and the ks cancel)

so xk = k √1.4 (cancel ks)

x = √1.4 = 1.183 or 18.3% increase 3sf
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meglarahman
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3 litres and 400 ml .how can i do the one in militres
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Hahjdidndndj
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Omg thank you 🙏 this helped me so much 🤝🤝🙏🙏😊😊
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