Very quick maths question

[almoststew1990]

I have the following formula that is written exactly like the below:

L = A/V + B +C.V + D.V2

What do the dots between C and V and between D and V2 mean?

I have read this as:

L = A/V + B + (C*V) + (D*[V^2])

Is this correct

 

[Destination]

One would assume so, but that stupid full case 2 on the end could be intrepetede as a 2, althought unlikely.

 

[Hagar]

Could be V and V2 are different variables, not V and V squared?

period generally means multiply.

 

[Luckystrike123]

The dots mean multiply, as writing x would imply that there is an x variable rather than a multiplication.

Also I would take V2 as a different value for V. eg velocity1 = 10mph, velocity2 = 15mph.

That is unless of course it is a squared like you have written below (V^2).

 

[danza]

Is this one of those crap Facebook maths questions?

 

[Mynight]

Why would anyone write a formula like that .

Not a very helpful post I know sorry.

 

[almoststew1990]

Thanks for clarifying the periods.

The variables are listed as a b c d v. V is average speed and there is only one speed used. So v2 is either v squared or v*2 and they're the same thing anyway.

This comes from Government WebTAG Cost Benefit Analysis guidance. That is how they've listed it in Excel and the supplimentary guidance document.

 

[DR_Pingu]

Why would anyone write a formula like that .

Not a very helpful post I know sorry.

Because it takes so much longer to write it out nice and neat on a PC than it would by hand on paper, but still equals the same thing.

The dots = "multiply"

8.7 = 8 x 7 = 56

EDIT: [anything] squared would have the symbol "^2" next to it, i.e. 2^2 = 2 squared = 4. It denotes what power the number is to, so 3^3 = 27, 4^5 = 1024, etc.

Hope that clears everything up for you.

^^^ Having looked again I know it doesn't because the V and V2 is written so stupidly... At a glance I'd class it as 2*V, as you'd pretty much always Get V1 & V2 if there were 2 velocities; whoever has written that is a joke.

 

[Mynight]

Because it takes so much longer to write it out nice and neat on a PC than it would by hand on paper, but still equals the same thing.

The asterisks = "multiply"

8*7 = 8 x 7 = 56

EDIT: [anything] squared would have the symbol "^2" next to it, i.e. 2^2 = 2 squared = 4. It denotes what power the number is to, so 3^3 = 27, 4^5 = 1024, etc.

Hope that clears everything up for you.

That's what I would have expected but using "." instead of an asterisks or leaving out the ^ just seems weird when it's only a couple keystrokes longer to write. It's mainly the is it V^2 or V*2 that's making me think WTH.

 

[snail1]

I read it as v^2 with the series going Av^-1 + Bv^0 + Cv^1 + Dv^2, i.e. the power of v is increasing in each term. There is a name for this kind of series which escapes me.

 

[tbyeah]

I read it as v^2 with the series going Av^-1 + Bv^0 + Cv^1 + Dv^2, i.e. the power of v is increasing in each term. There is a name for this kind of series which escapes me.

+1

Geometric progression I think it is

 

[DR_Pingu]

That's what I would have expected but using "." instead of an asterisks or leaving out the ^ just seems weird when it's only a couple keystrokes longer to write. It's mainly the is it V^2 or V*2 that's making me think WTH.

Dots are used pretty commonly in higher level maths, just not like that - as in like a full stop - they're usually like in the middle of the 'height', like • as in 4•7 = 28. I just think whoever wrote out that, whatever their level of qualification, is genuinely a joke.

 

[DR_Pingu]

+1

Geometric progression I think it is

There's also arithmetic progression too, but you're quite right - in my head geometric would be the correct one to use here although we don't know the actual question

 

[Mynight]

Argh fair enough. Didn't take A level maths and I don't remember it from GCSEs.

After snails explanation I'm going to bow out .

 

[D D Danneh]

Dots are used pretty commonly in higher level maths, just not like that - as in like a full stop - they're usually like in the middle of the 'height', like • as in 4•7 = 28. I just think whoever wrote out that, whatever their level of qualification, is genuinely a joke.

This, if it's written with the dot at the bottom that's just poor form. Dots are frequently used when talking about multiplying vectors to differentiate between different types, because you can multipy elementwise (dot product): if A = (a1, a2, a3) and B = (b1, b2, b3), A.B = (a1b1, a2b2, a3b3), and you have the cross product AxB = (a2b3 - a3b2, a3b1 - b3a1, a1b2 - b2a1).

Personally I've never seen dots used when talking about multiplying single elements.

 

[almoststew1990]

You lot have got me worried now what with Geometric progression and whatnot!

For context, this is for calculating the fuel efficiency of vehicles:

Fuel Consumption is estimated using a function of the form: L= a/v + b + c.v + d.v2
Where:

L = consumption of fuel Liters per km;
v = average speed kph;
a, b, c, d = parameters defined for each vehicle category.

For "Petrol Car" category:
a= 1.11932
b= 0.04400
c= -0.00008
d= 0.000002

It appears logical that the period is just "multiply" on the basis that at its heart this is just speed * variable to get the fuel effeciency. Even if this does mean that 100kph is apparently less fuel effecient by a significant margin than 10kph, which is very wrong?

 

[tbyeah]

There's also arithmetic progression too, but you're quite right - in my head geometric would be the correct one to use here although we don't know the actual question

Arithmetic is a+(n)d, geometric is ad^(n) (or a+d^(n)). I think?

 

[DR_Pingu]

Arithmetic is a+(n)d, geometric is ad^(n) (or a+d^(n)). I think?

Let me get my notes out - did this at BTEC last year and HNC this year lol :3

EDIT:

a, a+d, a+(n-1)d <--- continues like that. a = first term, d = common difference, a+d = 2nd term, then continues as a+(n-1)d

Geo Prog is:

a, ar, ar^2, ar^3.... ar^(n-1) <--- again, continues like that. a = first term, r = common ratio, as above regarding 2nd term then continuing.

 

[D D Danneh]

It appears logical that the period is just "multiply" on the basis that at its heart this is just speed * variable to get the fuel effeciency. Even if this does mean that 100kph is apparently less fuel effecient by a significant margin than 10kph, which is very wrong?

Correct, if V is simply velocity (well, speed), then this is just referring to multiplication.

As for fuel efficiency, this is correct, since the drag force on a moving object is proportional to the speed squared, travelling at twice the speed will require four times the force to maintain the speed, yet the journey will take half the time, so the fuel used will be double (completely ignoring the non-ignorable other factors like acceleration, junctions, etc).

 

[DR_Pingu]

Correct, if V is simply velocity (well, speed), then this is just referring to multiplication.

As for fuel efficiency, this is correct, since the drag force on a moving object is proportional to the speed squared, travelling at twice the speed will require four times the force to maintain the speed, yet the journey will take half the time, so the fuel used will be double (completely ignoring the non-ignorable other factors like acceleration, junctions, etc).

Velocity is correct, not speed, just sayin'

And what you've said makes sense, managing to put the formula into theoretic, just a shame the gimp who wrote it for Stew couldn't just bloody write it as it should be written. Having done a few calculations too it would suggest that that'd be the correct formula (although outcomes are the same [increase in efficiency to a certain point then decreases], just the answer is slightly different due to the squaring)