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anonymous
 one year ago
hey @parthkohli
anonymous
 one year ago
hey @parthkohli

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0when i say 30 i mean 40

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.3what does "reducing the length of the curve" mean? I mean you can draw the shortest possible path from (10,10) to (30,0) that also happens to be a straight line.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yea but it needs to be smooth

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.3what does that mean? a linear function is a polynomial too. what exactly do you mean by smooth?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0mena no rough edges and its curve

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0like continuous function

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0is there function that looks like the black line i drew

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.3so you need a polynomial function that makes a smooth transition and is also the shortest

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so it has curve to smothly attach to another track but at the smae shorter length

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0but at the same time *

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.3what's the context of this question? it's really specific

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i have done the question let me send the link

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0but what i am trying to figure out is the shorter length than this

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.3sorry, my OS stopped working.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so on xy plane i want a function that give me length <27.37

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1443516744812:dw

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.3You're permitted to use calculators right?\[g(x) = ax^4 + bx^3 + cx^2 + dx + e\]\[10^4 a + 10^3 b + 10^2 c + 10 d + e = 10\]\[30^4 a + 30^3 b + 30^2 c + 30 d + e=0\]\[\int_{10}^{30} g(x)dx=200\]\[4a(10)^3 + 3b(10)^2 + 2c(10) + d(10) =0\]Now the last one is tricky.

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.3You know how to calculate arc length using integrals right?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yea but i use wolfram alpha normaly u mind using it sending the link plz

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.3Because you really are looking to minimise arclength given the above constraints.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok wait do i do the same steps as i did for my previous function find a,b,c,d

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and then put them in an expression and use arc length to get length

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.3I think Wolfram is gonna have some good fun with this one.

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.3Here, you have a, b, c, d and e.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yea kinda forgot about e

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0thank you so much for ur help

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.3I'm curious to see how you'll input so much into Wolfram. It's scary.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0what if i find an expression then too

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.3sorry, the last equation is\[4a(10^3) + 3b(10^2 ) + 2c(10) + d = \color{red}1\]

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.3wow the expression is way too long... you'll have to be subscribe to pro

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i have subscribe pro

baru
 one year ago
Best ResponseYou've already chosen the best response.1@ParthKohli for arguments sake, (specifics not necessary) i would write the function for arc length squared lets call it L=f(a b c d e) now what?to minimize, we need to substitute variables in terms of each other so that they represent their interdependencies right? how will you do that? you have four other equations ? or am i way off, and talking crap?

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.3yes  we have four equations. in the arc length function, we'll eliminate four variables and will be left with a function that is in terms of only one variable.

baru
 one year ago
Best ResponseYou've already chosen the best response.1is that a general thing, as in if there are n unknowns and (n1) equations we can bring it down to 1 variable?

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.3I suppose. Let's take a smaller example.\[f(x,y,z) = x+yz\]\[x=y+1\]\[z = x\]\[f(x,y,z) =x+(x1)  (x) = 3x  1\]

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.3Three variables, two equations. Now we can minimise the function with onevariable very easily.

baru
 one year ago
Best ResponseYou've already chosen the best response.1@ParthKohli one other thing, i get why you have picked an equation with 5 unknowns since we have 5 pieces of information, but the equation could just as easily been \[ax^7 + bx^6 +cx^5 +dx +e\] or something else equally arbitrary so why specifically have you chosen the one that you have?

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.3that is a very good observation, one that I did give some thought to but skipped. unfortunately, it may be impossible to find *the* polynomial that satisfies the above constraints because the degree may go as high as... anything we want it to reach. the degreeseven polynomial you wrote may not be the best degreeseven polynomial to satisfy the conditions because it's missing some terms and unless we're sure while solving for the seventhdegree that those terms turn out to be zero, we'll never be sure. so choose a degreefour polynomial adds certainty to what we get  we can be sure that we'll get the best fourthdegree polynomial. of course there are polynomials much better than that one, but we can only go as far as we can look.

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.3ultimately, we're looking for a polynomial that resembles a straightline the most in the region x = 10 to x = 30, so we can add as many terms as we like, but we can't go that far  can we?

baru
 one year ago
Best ResponseYou've already chosen the best response.1ah..makes sense. thanks a lot!!

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.3by the way, we still can approach this problem through multivariable calculus for polynomials that have more terms than five. that way, we can get an even closer polynomial.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0hey its not making sense

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.3thanks for the question  I really had to think about it to come up with an answer.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.05 variables how do i get values for 5 unknown variable

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.3plug it into WolframAlpha

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i only have 4 equation

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i found a ,b, c ,d but not e

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.3were you able to find a, b, c, d in terms of e?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[0.0001852x ^{4}0.01246x ^{3}+0.2076x ^{2}0.01555x+e\]

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.3wait what? you were able to uniquely determine a, b, c, d?!

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.3it's not a 4x4 equation so

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yea i thought so help plz

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.3plug the stuff into Wolfram and it should give you all other variables in terms of one variable

baru
 one year ago
Best ResponseYou've already chosen the best response.1@ayeshaafzal221 where did you find this question?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0its my practise question for exams

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.3what did it return?

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.3you don't have a Wolfram pro subscription do you?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0even on my ipad not working

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.3there's this data entry or something feature which you can use

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0or u know the values i have found cant i just sub it into any equation and get the e value

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.3no, you can't do that. it's not a 4x4 equation so you most likely input the wrong equations.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yea true i am gonna go old fashion , and do em manually

baru
 one year ago
Best ResponseYou've already chosen the best response.1@ParthKohli , when you say multivariable calculus approach: are you talking about Lagrange multipliers?(i've just reached this topic)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@ParthKohli srry i am disturbing u again when u say we have five variables and one of them was minimum arc length what do u mean?
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