Solve this equation for me

[Afrobean]

Re: Solve this equation for me

Since when would this problem be Algebra 2 level stuff? I was doing this sort of work in seventh grade.

[rqm]

Re: Solve this equation for me

ya for real this is like end of pre-algebra stuff

[JKPolk]

Re: Solve this equation for me

lmao


How about some problems that are actually trickier to solve:

1. A stick of length one is split into two sticks at a random point that is uniformly distributed -- say X is the shorter stick and Y is the longer one. Find E(X) and Var(X), then find E(Y-X)^2

2. Leonid and Rubix are alternating rolling a pair of dice, stopping either when Leonid rolls the sum of 9 or when Rubix rolls the sum of 6. Assuming that Leonid rolls first, find the probability that Leonid has the final roll.

3. Easier one for ya -- you can buy a lottery ticket for $1. If you win, you get $5 back. You're determined to win twice at any cost. Each ticket has p = .125 of winning. What is the probability you get your second winning ticket on the sixth purchase? What's your expected profit or loss from this lottery in general?

Here's a hard one I doubt anyone here will get -- from one of my homeworks:

You have a system of N components. Each component will function, independently, with probability p. The total system of components will work if at least half of them are functioning. For what value of p is a 5-component system more likely to operate than a 3-component system? How about a (2k+1) component system over a (2k-1) component system?

Statistics is a world I'm glad I never had to enter.

What is the specific thrust of a turbojet engine with compressor pressure ratio 20, design Mach number 1.6, turbine inlet temp 1400K flying at 35,000 ft? Turbine and Compressor polytropic efficiency .95, isentropic effenciency .97, Gamma 1.4.

[iironiic]

Re: Solve this equation for me

Here's a hard one I doubt anyone here will get -- from one of my homeworks:

You have a system of N components. Each component will function, independently, with probability p. The total system of components will work if at least half of them are functioning. For what value of p is a 5-component system more likely to operate than a 3-component system? How about a (2k+1) component system over a (2k-1) component system?

do we win credits if we get the correct answer? lol

[MrRubix]

Re: Solve this equation for me

Probably not, especially not for that one since I just realized it can be Googled. The others, though, maybe.

[iironiic]

Re: Solve this equation for me

Probably not, especially not for that one since I just realized it can be Googled. The others, though, maybe.

Oh I was actually trying to solve that haha. Is the first one no values of p because you are left with a contradiction that p must be greater than 1?

EDIT: Oh crap... forgot about binomial coefficients... I fail hahah

[MrRubix]

Re: Solve this equation for me

No, lol

[Bluearrowll]

Re: Solve this equation for me

The answer is 42

[MrRubix]

Re: Solve this equation for me

I've gotta go for now but I'll give JKPolk's question a shot later -- looks like it's just a matter of throwing together some aerospace equations, but I only have a basic idea of how those variables would relate (and no idea where the gamma fits in). Also wtf is isosdmkflmdsklmfsdklopic efficiency.

[foilman8805]

Re: Solve this equation for me

Statistics is a world I'm glad I never had to enter.

I took my one quarter of mandated statistics for engineers and peaced the **** out. Not looking at that **** again.

What is the specific thrust of a turbojet engine with compressor pressure ratio 20, design Mach number 1.6, turbine inlet temp 1400K flying at 35,000 ft? Turbine and Compressor polytropic efficiency .95, isentropic effenciency .97, Gamma 1.4.

You're speaking my language, man!

@Rubix, Gamma is just the ratio of specific heat to specific volume, a common property for air. Rocket exhausts with fuel mixed into them are usually a gamma of 1.3.

EDIT: in an ideal situation, isentropic efficiency is 100%, meaning that it's entirely adiabatic and the process is reversible. Since we know that turbojets don't function at an ideal capacity in a real situation, the .97 is to make up for things like heat loss through the walls of the turbojet, etc.

[All_That_Chaz]

Re: Solve this equation for me

Industrial Econ from junior year undergrad.

Given Variables
N[H]=1
N[L]=5
P[H][q]=40-q
P[L][q]=20-2q
MC=1

Area of a trapezium: .5(a+b)c
S[H][q]= ((40+40-q)q/2 = 40q -.5q^2 for all q<=40, 800 for all q>40
S[L][q]= ((20+20-2q)q/2 = 20q - q^2 for all q<=10, 100 for all q>10

max(q[H],q[L],T[H],T[L]): N[H]T[H]+N[L]T[L]-MC(N[H]q[H]+N[L]q[L])
=> T[H]+5T[L]-(q[H]+5q[L])

subject to:
S[L][q[L]]-T[L]>=0; (PC-L)
S[H][q[H]]-T[H]>=0; (PC-H)
S[L][q[L]]-T[L]>=S[L][q[H]]-T[H]; (SS-L)
S[H][q[H]]-T[H]>=S[H][q[L]]-T[L]; (SS-H)

PC-L & SS-H => PC-H will hold as S[H][q]>S[L][q]
Assume all SS-L will hold

max(q[H],q[L],T[H],T[L]): T[H]+5T[L]-(q[H]+5q[L])
S[L][q[L]]-T[L]>=0; (PC-L)
S[H][q[H]]-T[H]>=S[H][q[L]]-T[L]; (SS-H)

=> T[L]=S[L][q[L]]; PC-L holds
=> T[H]=S[H][q[H]]-S[H][q[L]]+T[L]
T[H]=S[H][q[H]]-S[H][q[L]]+S[L][q[L]]; SS-L holds

=> max(q[H],q[L]): S[H][q[H]]-S[H][q[L]]+S[L][q[L]]+5S[L][q[L]]-(q[H]+5q[L])
=> max(q[H],q[L]): 40q[H]-.5q[H]^2-40q[L]-.5q[L]^2+120q[L]-6q[L]^2-(q[H]+5q[L])

FOC[q[H]]: 40-q[H]-1=0 => q[H][*]=39
FOC[q[L]]: -40-q[L]+120-12q[L]-5 => q[L][*]=(75/13)

Prices
T[L][*]=S[L](75/13)=20(75/13)-(75/13)^2=82.1
T[H][*]=S[H](39)-S[H](75/13)+S[L](75/13)
=(40(39)-.5(39^2)-(40(75/13)-.5(75/13)^2)+(20(75/13)-(75/13)^2)
=799.5-214.13+82.1
=667.47

SS-L holds
S[L][q[L][*]]-T[L][*]>=S[L][q[H][*]]-T[H][*]; (S[L][q[H][*]]=100 for q>10)
0>=100-667.47=-567.47 yayz!

Profits
pi=N[H]T[H]+N[L]T[L]-MC(N[H]q[H]+N[L]q[L])
pi=1(667.47)+5(82.1)-1(1(39)+5(75/13))
pi=1077.97-67.85
pi=$1010.12


suck it, rubix.

[leonid]

Re: Solve this equation for me

1. E(X)=1/4, Var(X)=7/48, [E(Y-X)]^2=1/4 ??

[MrRubix]

Re: Solve this equation for me

Leonid: E(X) is right, Var(X) isn't, and neither is E(Y-X)^2

I can tell you're close on Var(X), you probably just made a tiny mistake somewhere

[iironiic]

Re: Solve this equation for me

I'm currently preparing for the Putnam Math Competition... anyone else?

[MrRubix]

Re: Solve this equation for me

You do not prepare for the Putnam -- the Putnam prepares YOU