OT: maths challenge...doing my head in!
NGale
Posts: 1,866
ok not on topic in anyway I know, but this is doing my head in so perhaps some of you could point me in the right direction seeing as Jake won't and he's at work!
Quartz Vibrates at 2.5 million pulses per second, caesium vibrates at 9 162 631 770 per second. Calculate how many more times per second caesium vibrates than quartz
Quartz Vibrates at 2.5 million pulses per second, caesium vibrates at 9 162 631 770 per second. Calculate how many more times per second caesium vibrates than quartz
Officers don't run, it's undignified and panics the men
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916,013,1770 more times per secondB'Twin Sport 1
FCN 7 =4, +2(non cycling clothes) +1(beard)0 
Or 9162631770/2500000?
Casesium vibrates around 3665x as fast?
ish0 
bails87 wrote:Isn't it just:
9,162,631,770 minus 2,500,000 equals 9,160,131,770
This0 
take the speed of ceasium and subtract the speed of quartz to find the difference.
gives you 916,013,1770 or 3665 times faster than quartz0 
Get yourself a wind up watch  then it don't matterNobody told me we had a communication problem0

916,013,1770 is correct if question is how many more times per second does it vibrate.
3665 is correct if question is how many times faster does it vibrate.
I believe the question was the former so if forced to choose that's what I would go with. You could argue the second one is correct although you are on thin ground. If this was an exam I'd be tempted to answer both and explain why I did so due to potential ambiguity in the original question. True story I once got 101% on maths exam for doing exactly that and pointing out two answers were correct depending on how you read the question. The irony was not lost on me even at 15!
Chris
Genesis Equilibrium  FCN 3/4/50 
yay! i won the internets raceB'Twin Sport 1
FCN 7 =4, +2(non cycling clothes) +1(beard)0 
Question is, why are you asking the question? A quartz clock operates using an entirely different principle to an atomic (e.g. cesium) clock, doesn't it?0

oooh this is fun
another one for you.
Estimate the following variables without using a calculator, showing all stages of your calculation and any assumptions made.
z= sqrt (R3+(2pi f l ) 2) given pi=3.142, R= 4X10pwr3, f=75 and L=981Officers don't run, it's undignified and panics the men0 
42Nobody told me we had a communication problem0

NGale wrote:oooh this is fun
another one for you.
Estimate the following variables without using a calculator, showing all stages of your calculation and any assumptions made.
z= sqrt (R3+(2pi f l ) 2) given pi=3.142, R= 4X10pwr3, f=75 and L=981
I guess the random '2' at the end means to square the previous term (given this is an impedance calculation)
so the second term is 2 * pi * 75 * 981 is ~ 6 * 75 * 1000 = 450000 or 4.5E5. The square of that is going to be >> than the value of R (4E3) so can be ignored, therefore z = 4.5E5
What do I win?
BTW I would have thought it should have been Z= sqrt(R^2 + (2pi fL)^2) but the argument still holds as the square of 4.5E5 is still >> than the square of 4E3...Invacare Spectra Plus electric wheelchair, max speed 4mph0 
NGale wrote:oooh this is fun
another one for you.
Estimate the following variables without using a calculator, showing all stages of your calculation and any assumptions made.
z= sqrt (R3+(2pi f l ) 2) given pi=3.142, R= 4X10pwr3, f=75 and L=981
r= 4x10pwr3 = 4,000
2pi = 6.284
fl = 75x981 = 4905+68670 = 73,575
2pi fl = (6 x 73,575 = 451,460) + approx (.3 x73,575 = 22,573) = 474,033
(2pi f l ) 2) = 2 x 474,033 = 948,066
(R3+(2pi f l ) 2) = 4,000 + 948,066 = 953,066
now the hard part
sqrt(953,066)
1000x1000 = 1,000,000
Need to get a bit lower
950 x 950 = 47,500 + 855,000 = 902,500
Need a bit more
I'd go for 975 as an estimate.
Chris
Genesis Equilibrium  FCN 3/4/50 
OptimisticBiker wrote:NGale wrote:oooh this is fun
another one for you.
Estimate the following variables without using a calculator, showing all stages of your calculation and any assumptions made.
z= sqrt (R3+(2pi f l ) 2) given pi=3.142, R= 4X10pwr3, f=75 and L=981
I guess the random '2' at the end means to square the previous term (given this is an impedance calculation)
so the second term is 2 * pi * 75 * 981 is ~ 6 * 75 * 1000 = 450000 or 4.5E5. The square of that is going to be >> than the value of R (4E3) so can be ignored, therefore z = 4.5E5
What do I win?
BTW I would have thought it should have been Z= sqrt(R^2 + (2pi fL)^2) but the argument still holds as the square of 4.5E5 is still >> than the square of 4E3...
Bracket in the wrong place for that, it's only double (2pi f l ) as per the op.
Chris
Genesis Equilibrium  FCN 3/4/50 
Sketchley wrote:OptimisticBiker wrote:NGale wrote:oooh this is fun
another one for you.
Estimate the following variables without using a calculator, showing all stages of your calculation and any assumptions made.
z= sqrt (R3+(2pi f l ) 2) given pi=3.142, R= 4X10pwr3, f=75 and L=981
I guess the random '2' at the end means to square the previous term (given this is an impedance calculation)
Bracket in the wrong place for that, it's only double (2pi f l ) as per the op.
if could be written (using the same spacing as the OP)
z= sqrt(R3+(2pi f l ) * 2)
or
z= sqrt(R3+(2pi f l ) ^ 2)
I read it as the latter cos I'm an electronic engineer by training and the *2 makes no sense.... just as there is no variable R3, but R so I would assume R3 really meant R^2 (with a typo) since this is the calculation for the total impedance of a series resistor and inductorInvacare Spectra Plus electric wheelchair, max speed 4mph0 
Yep, I'll go with that.0

There a mistake in my calculation, bonus point if you can spot it, but it doesn't make a huge difference I'd still go for same estimate of 975.
OptimisticBiker no way can you interpret that as ^2 given that R= 4X10pwr3 appears later.
Chris
Genesis Equilibrium  FCN 3/4/50 
Sketchley wrote:There a mistake in my calculation, bonus point if you can spot it, but it doesn't make a huge difference I'd still go for same estimate of 975.
OptimisticBiker no way can you interpret that as ^2 given that R= 4X10pwr3 appears later.
and you would lose marks for the step
(R3+(2pi f l ) 2) = 4,000 + 948,066 = 953,066
for not recognising that 4000 << 948066 and therefore can be discounted...
also for reducing pi to 6.3 (1 sig place) but keeping the fL term as 73575 rather than estimating to say 74000
also .3 * 73575 =~ 22000 not 22573
but otherwise its not badInvacare Spectra Plus electric wheelchair, max speed 4mph0 
(R3+(2pi f l ) 2) = 4,000 + 948,066 = 953,066
should be
(R3+(2pi f l ) 2) = 4,000 + 948,066 = 952,066Commuter: Forme Vision Red/Black FCN 4
Weekender: White/Black  Cube Agree GTC pro FCN 30 
Torvid wrote:(R3+(2pi f l ) 2) = 4,000 + 948,066 = 953,066
should be
(R3+(2pi f l ) 2) = 4,000 + 948,066 = 952,066
Thank you for being the only poster who can consistently put commas in the right place in numbers. Does my nut in that one.
[/pedant]1985 Mercian King of Mercia  work in progress (Hah! Who am I kidding?)
Pinnacle Monzonite
Part of the antigrowth coalition0 
rjsterry wrote:Torvid wrote:(R3+(2pi f l ) 2) = 4,000 + 948,066 = 953,066
should be
(R3+(2pi f l ) 2) = 4,000 + 948,066 = 952,066
Thank you for being the only poster who can consistently put commas in the right place in numbers. Does my nut in that one.
[/pedant]
That would be Sketchley's doing i was raised to do it but in the day of CSV files and other excel imports, it's best to just mash all the numbers together otherwise it goes a bit wrong.Commuter: Forme Vision Red/Black FCN 4
Weekender: White/Black  Cube Agree GTC pro FCN 30 
Torvid wrote:rjsterry wrote:Torvid wrote:(R3+(2pi f l ) 2) = 4,000 + 948,066 = 953,066
should be
(R3+(2pi f l ) 2) = 4,000 + 948,066 = 952,066
Thank you for being the only poster who can consistently put commas in the right place in numbers. Does my nut in that one.
[/pedant]
That would be Sketchley's doing i was raised to do it but in the day of CSV files and other excel imports, it's best to just mash all the numbers together otherwise it goes a bit wrong.
I only did it as it makes the maths easier to do in your head as original question said no calculators.
Chris
Genesis Equilibrium  FCN 3/4/50 
however now that i have had time to sit down and look at the puzzle
sqrt((4,000*3)+((2*3.142)*75*981)*2)
sqrt(12,000+((6.284)*75*981)*2)
sqrt(12,000+((471.3*981)*2)
sqrt(12,000+((462,345.3)*2)
sqrt(12,000+924,690.6)
sqrt(936,690.6)
967.8 give or take a couple or remaindersCommuter: Forme Vision Red/Black FCN 4
Weekender: White/Black  Cube Agree GTC pro FCN 30 
Torvid wrote:however now that i have had time to sit down and look at the puzzle
sqrt((4,000*3)+((2*3.142)*75*981)*2)
sqrt(12,000+((6.284)*75*981)*2)
sqrt(12,000+((471.3*981)*2)
sqrt(12,000+((462,345.3)*2)
sqrt(12,000+924,690.6)
sqrt(936,690.6)
967.8 give or take a couple or remainders
Be honest did you use a calculator?
I was a bit out in places but 975 was a pretty good estimate without a calculator. Happy with that.
Chris
Genesis Equilibrium  FCN 3/4/50 
Sketchley wrote:Torvid wrote:however now that i have had time to sit down and look at the puzzle
sqrt((4,000*3)+((2*3.142)*75*981)*2)
sqrt(12,000+((6.284)*75*981)*2)
sqrt(12,000+((471.3*981)*2)
sqrt(12,000+((462,345.3)*2)
sqrt(12,000+924,690.6)
sqrt(936,690.6)
967.8 give or take a couple or remainders
Be honest did you use a calculator?
I was a bit out in places but 975 was a pretty good estimate without a calculator. Happy with that.
no but i did use 2 pages of A4 got an A in pure. and a B in mechanical maths alevel more years ago than I care to think about now.Commuter: Forme Vision Red/Black FCN 4
Weekender: White/Black  Cube Agree GTC pro FCN 30 
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As to what the equation is for i have no clue 981 could be acceleration due to graviy but at the same time a quick google says part of it is an inductance calculation so i'm lost.Commuter: Forme Vision Red/Black FCN 4
Weekender: White/Black  Cube Agree GTC pro FCN 30 
NGale wrote:oooh this is fun
another one for you.
Estimate the following variables without using a calculator, showing all stages of your calculation and any assumptions made.
z= sqrt (R3+(2pi f l ) 2) given pi=3.142, R= 4X10pwr3, f=75 and L=981
Isn't it easier to simplify the equation first, doing so I get N+1I've added a signature to prove it is still possible.0 
Torvid wrote:Sketchley wrote:Torvid wrote:however now that i have had time to sit down and look at the puzzle
sqrt((4,000*3)+((2*3.142)*75*981)*2)
sqrt(12,000+((6.284)*75*981)*2)
sqrt(12,000+((471.3*981)*2)
sqrt(12,000+((462,345.3)*2)
sqrt(12,000+924,690.6)
sqrt(936,690.6)
967.8 give or take a couple or remainders
Be honest did you use a calculator?
I was a bit out in places but 975 was a pretty good estimate without a calculator. Happy with that.
no but i did use 2 pages of A4 got an A in pure. and a B in mechanical maths alevel more years ago than I care to think about now.
Good job you could always use a (graphical) calculator in maths mechanics eh?
I LOVED mechanics.0