Question

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.

Answer 1

using geometry? maybe you mean using purely algebra?

Answer 2

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

Answer 3

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

Answer 4

it's not that simple lol..try it

Answer 5

that is giving negative x.

since these are two straight lines, there should be two values that satisfy the given condition right ?

Answer 6

i mean two values of x

Answer 7

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

Answer 8

no positive values only -4802

Answer 9

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..

Answer 10

humm.. lets say x axis is time

Answer 11

at t=0, y2 is 343 more than y1

Answer 12

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

Answer 13

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

Answer 14

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

Answer 15

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

Answer 16

are you sure you entered the correct equations?

Answer 17

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

Answer 18

i am going for lunch.. brb

Answer 19

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..

Answer 20

sure there must be some explanation...

Answer 21

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..

Answer 22

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

Answer 23

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.

Answer 24

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 :)

Answer 25

yw