- #1
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Homework Statement
line m2-to-m is 3km longer than line m1-to-m
what are lengths for ##M~~M_2## and ##M~~M_1##
Homework Equations
pythagorean theorem hopefully can be used
The Attempt at a Solution
use the picture to your advantage in hopefully creating a valid system of equations. With which, X and Y can both be solved.
However the question only asked really what was (X-3) and what was (X). Y should hopefully only be used as an intermediary variable to that purpose(?)
system of equations is as follows:
$$y^2~+~ 5.6^2~= ~x^2$$
$$(18-y)^2 ~+ ~5.6^2~ = ~(x-3)^2$$
The top equation can be reduced into following form...
##x= \sqrt{y^2+5.6^2}##
the lower equation can be reduced into the form of...
##y^2~-36y~+346.36= x*(x-6)##
insert top equation into the lower equation. Hopefully this was correct because on pen-paper-style it took an entire page, really...
##35y^2 -630y +2724.89=0##
from calculator
y = 10.7736967
y= 7.226303295
We can test these Y's and hopefully to ascertain whether or not the system is true.
I think that with the top value of Y (y ~ 10.773 ...)
the originatl system of equations seems to work ok.
testing can be done with calculator for example with assigning variables with some values such as
y=10.7736967
from the top equation we plug in the y value, and calculate that x should be equal to about 12.14218022with that x value, you can plug it into the lower equation and it should hold true.
so it looks like length of x = 12.14218022 km
it looks like length of (x-3) = 9.142180224 km