## ganeshie8 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. one year ago one year ago

1. shubhamsrg

using geometry? maybe you mean using purely algebra?

2. ganeshie8

ya solving equations... algebra is ok.. . :)

3. shubhamsrg

just set y1 = 2y2 make substitutions and solve for x

4. lgbasallote

it's not that simple lol..try it

5. ganeshie8

that is giving negative x. since these are two straight lines, there should be two values that satisfy the given condition right ?

6. ganeshie8

i mean two values of x

7. shubhamsrg

ok leme try 3x/7 = 4x/7 + 686 yes it gives -ve x it has no +ve solution i'd guess..

8. Arthur_Bonnouvrier

no positive values only -4802

9. ganeshie8

|dw:1340005766066:dw|

10. shubhamsrg

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..

11. ganeshie8

humm.. lets say x axis is time

12. ganeshie8

at t=0, y2 is 343 more than y1

13. Arthur_Bonnouvrier

just enter the equation y1=2*(y2) and you'll see that there is only one value which is -4802.

14. ganeshie8

since y1 is increasing much faster than y2, at some point y1 reaches y2

15. ganeshie8

after some more time, y1 value reaches double the y2 also right ?

16. ganeshie8

i need to know the time at which y1 reaches twice the value of y2. hope my question is making sense...

17. Arthur_Bonnouvrier

are you sure you entered the correct equations?

18. ganeshie8

there should be two values for x.. goes from $-\infty \to + \infty$

19. ganeshie8

i am going for lunch.. brb

20. shubhamsrg

well yes,,there'll be 2 values,,we didnt take the co-ordinates 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..

21. ganeshie8

sure there must be some explanation...

22. shubhamsrg

y1/y2 = 3x/(2x + 2401) =k(say) 3x = 2kx + 2401k =>x = 2401k/(3-2k) 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..

23. shubhamsrg

maybe k is ratio of magnitudes by default,, :|

24. telliott99

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 x-axis 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.

25. ganeshie8

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 :)

26. telliott99

yw