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because the two angles reflect eachother
a linear equation can be expressed in the form:\[y=mx+c\]which you have correctly drawn as a straight line graph
explain more please . thanks
now think of two linear equations - these would represent, say:\[y=m_1x+c_1\]and:\[y=m_2x+c_2\]
now, if these two lines intersect, then, at the point of intersection, the y-values of both must be equal - agreed?
therefore, we can say:\[m_1x+c_1=m_2x+c_2\]at the point of intersection
which is the same as saying:\[y=y\]
because y=y thats grate . amazing . tell if we have quadratic equations |dw:1346967366273:dw|
same applies for quads - except this time you will get two solutions for x instead of one that you got for the linear case
and each of these, in theory could give you two different y values
y1=x^2 +mx + c and y2=x^2 +mx + c
quads are usually written as:\[y=a_1x^2+b_1x+c_1\]and:\[y=a_2x^2+b_2x+c_2\]
so at the points of intersection we will have:\[a_1x^2+b_1x+c_1=a_2x^2+b_2x+c_2\]
which leads to a quadratic equation in x - solve to get the two values for x where these curves intersect
in general, we could have two curves defined by:\[y=f(x)\]and:\[y=g(x)\] |dw:1346967756823:dw|
and, at each point of intersection, the y and x values on each curve are equal
I hope I have explained it well enough for you - let me know if you require any more explanation
have outdone yourself
thx - and you are welcome my friend! :)
what is the highest think your done in maths??
think == thing?
:) I have studied for a PhD in Aeronautical Engineering. but that was many years ago. I now teach maths as a hobby because I still enjoy it.
WOW, thats great. can send you some of my question from time to time?
I'm not sure what you mean by "send", but if you mean message me now and then if no one else is helping you - then yes, by all means do - I'll be glad to help out when I can.
by that i meant , the message on the top left corner. thanks
ok - thats fine.
am going to do a lot of calculus. nice one
but bear in mind that I may not always respond immediately because I also moderate this site so please don't think I'm ignoring you in those cases. :)
thanks. I will be patient . :)
gr8! speak to you later then...