# Please can you help me with this maths problem?Watch

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#1
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.
0
2 years ago
#2
(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 which means that for some constant .

Increasing the length by 40% means we get and you want to manipulate this equation to get for some constant 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.
1
2 years ago
#3
(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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#4
(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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2 years ago
#5
(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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#6
(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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2 years ago
#7
(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!
0
#8
(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
0
2 years ago
#9
What is the final answer then 40%?
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2 years ago
#10
18.3
0
2 years ago
#11
What does RHS mean?
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2 years ago
#12
i got 15.5% but good lord am i rusty on this ****.. aha

Someone approve the official answer i'm curious
0
1 year ago
#13
i am still sooo confused on this topic :/
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1 year ago
#14
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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9 months ago
#15
3 litres and 400 ml .how can i do the one in militres
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7 months ago
#16
Omg thank you 🙏 this helped me so much 🤝🤝🙏🙏😊😊
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