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ganeshie8
Group Title
There are two straight lines
y1 = (3/7)x
y2 = (2/7)x + 343
Find "At what POSITIVE value of x, y1 reaches twice of y2 "
i am struggling with this problem from an hour... pls help using geometry only. no calculus pls.
 2 years ago
 2 years ago
ganeshie8 Group Title
There are two straight lines y1 = (3/7)x y2 = (2/7)x + 343 Find "At what POSITIVE value of x, y1 reaches twice of y2 " i am struggling with this problem from an hour... pls help using geometry only. no calculus pls.
 2 years ago
 2 years ago

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shubhamsrg Group TitleBest ResponseYou've already chosen the best response.0
using geometry? maybe you mean using purely algebra?
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.0
ya solving equations... algebra is ok.. . :)
 2 years ago

shubhamsrg Group TitleBest ResponseYou've already chosen the best response.0
just set y1 = 2y2 make substitutions and solve for x
 2 years ago

lgbasallote Group TitleBest ResponseYou've already chosen the best response.0
it's not that simple lol..try it
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.0
that is giving negative x. since these are two straight lines, there should be two values that satisfy the given condition right ?
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.0
i mean two values of x
 2 years ago

shubhamsrg Group TitleBest ResponseYou've already chosen the best response.0
ok leme try 3x/7 = 4x/7 + 686 yes it gives ve x it has no +ve solution i'd guess..
 2 years ago

Arthur_Bonnouvrier Group TitleBest ResponseYou've already chosen the best response.0
no positive values only 4802
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.0
dw:1340005766066:dw
 2 years ago

shubhamsrg Group TitleBest ResponseYou've already chosen the best response.0
why 2 solns.. see 1st eqn gives a line passing through (0,0) and slope = 3/7 2nd eqn gives a line passing through (0,343) ,slope =2/7 and both lines are increasing.. its easy to conclude then,,why only ve x will work..
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.0
humm.. lets say x axis is time
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.0
at t=0, y2 is 343 more than y1
 2 years ago

Arthur_Bonnouvrier Group TitleBest ResponseYou've already chosen the best response.0
just enter the equation y1=2*(y2) and you'll see that there is only one value which is 4802.
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.0
since y1 is increasing much faster than y2, at some point y1 reaches y2
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.0
after some more time, y1 value reaches double the y2 also right ?
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.0
i need to know the time at which y1 reaches twice the value of y2. hope my question is making sense...
 2 years ago

Arthur_Bonnouvrier Group TitleBest ResponseYou've already chosen the best response.0
are you sure you entered the correct equations?
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.0
there should be two values for x.. goes from \[\infty \to + \infty\]
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.0
i am going for lunch.. brb
 2 years ago

shubhamsrg Group TitleBest ResponseYou've already chosen the best response.0
well yes,,there'll be 2 values,,we didnt take the coordinates into account earlier,,setting y1=2y2 will yield another solution,,but that also gives ve x.. hmmn there must be some explanation,,i'll get back to it..
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.0
sure there must be some explanation...
 2 years ago

shubhamsrg Group TitleBest ResponseYou've already chosen the best response.0
y1/y2 = 3x/(2x + 2401) =k(say) 3x = 2kx + 2401k =>x = 2401k/(32k) so for k=3/2,,x is undefined,,k > 3/2,,x gets ve.. k<3/2,,x is +ve.. maybe this is satisfactory,,since 2>3/2,,x had to be ve.. but why is x ve for k = 2// hmm..
 2 years ago

shubhamsrg Group TitleBest ResponseYou've already chosen the best response.0
maybe k is ratio of magnitudes by default,, :
 2 years ago

telliott99 Group TitleBest ResponseYou've already chosen the best response.1
Much later.. I sketched the graph. It's clear that the two lines must cross. Since the relative slope (y1 grows faster than y2) is 1/7, that happens at 7 (343) = x = 2401. There, y1 = 3 (343) and y2 = 2 (343) + 343 = 1029. However, since y2 is moving away from the xaxis with a slope of 2/7, and y1 only grows faster than y2 by 1/7, I think there is no way y1 can ever be twice y2. Instead, at any x > 2401, (I think) y2 will be 2/3 of the way to y1 up from 1029. HTH.
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.0
i had trouble understanding this few days back... i guess i get it finally.. frm ur explanation i see : for (y1 = 3/7x) to reach twice the value of function (y2 = 2/7x+343)  is same as  asking for a slope of 4/7... but y1 is slow  its growing at 3/7 only.... so y1 can never reach twice y2.... . !! thank you :)
 2 years ago
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