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 2 years ago
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
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.

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

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.1ya solving equations... algebra is ok.. . :)

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

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

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.1that is giving negative x. since these are two straight lines, there should be two values that satisfy the given condition right ?

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.1i mean two values of x

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

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

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1340005766066:dw

shubhamsrg
 2 years ago
Best ResponseYou've already chosen the best response.0why 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..

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.1humm.. lets say x axis is time

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.1at t=0, y2 is 343 more than y1

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

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.1since y1 is increasing much faster than y2, at some point y1 reaches y2

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.1after some more time, y1 value reaches double the y2 also right ?

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.1i need to know the time at which y1 reaches twice the value of y2. hope my question is making sense...

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

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.1there should be two values for x.. goes from \[\infty \to + \infty\]

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.1i am going for lunch.. brb

shubhamsrg
 2 years ago
Best ResponseYou've already chosen the best response.0well 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..

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.1sure there must be some explanation...

shubhamsrg
 2 years ago
Best ResponseYou've already chosen the best response.0y1/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..

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

telliott99
 2 years ago
Best ResponseYou've already chosen the best response.1Much 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.

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.1i 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 :)
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