ATAR Notes: Forum
VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Mathematical Methods CAS => Topic started by: melanie.dee on November 06, 2007, 09:26:46 pm
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this one really is simple, but i dont know how to do anything involving e
anyway its asking for the x coordinate of intersection of the graphs of 2 equations. the equations are..
e^2x and 6 - e^x
there is a graphy, but i dont think you need it to solve that.
is it just when the two equations equal eachother. but then, how do i transpose that to find x, cos i dont know what you're allowed to do with e, and the rules and such
e^2x = 6 - e^x .. or is this completely retarded?
then how do i finish it
ahhh help please!
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Yup you're pretty much there!
e^2x = 6 - e^x
e^2x + e^x - 6 = 0
Let A = e^x
so A^2 + A - 6 = 0
A_______-2
A_______+3
So A = 2, or A = -3
But A = e^x
so e^x = 2 or e^x = -3
but e^x is always positive so discard the solution e^x = -3
now go with e^x = 2
and x = log_e(2)
:)
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^^^^^^^^^^^
That kinda makes sense lol. Still confuses me
Heres one for anyone to have a go at...
Solve the equation sin (x) = square root of 3 cos (x) for x (wierd symbol that i think means all elements of ) [- pie , pie], giving exact values in terms of pie
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Yup you're pretty much there!
e^2x = 6 - e^x
e^2x + e^x - 6 = 0
Let A = e^x
so A^2 + A - 6 = 0
A_______-2
A_______+3
So A = 2, or A = -3
But A = e^x
so e^x = 2 or e^x = -3
but e^x is always positive so discard the solution e^x = -3
now go with e^x = 2
and x = log_e(2)
:)
ahhhh thanks a bunch, i sat there trying to work it out in strange strange ways cos i totally didnt notice that it was quadratic. gar idiot. thanks for the explanation!
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^^^^^^^^^^^
That kinda makes sense lol. Still confuses me
Heres one for anyone to have a go at...
Solve the equation sin (x) = square root of 3 cos (x) for x (wierd symbol that i think means all elements of ) [- pie , pie], giving exact values in terms of pie
pie haha
yeh this was on the sample exam hey
sin (x) = root 3 x cos (x)
sin(x)/cos(x) = root3
tan(x) = root3
my problem here is that i dont know the exact values off by heart haha :oops:
but look it up in your text book
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^^^^^^^^^^^
That kinda makes sense lol. Still confuses me
Heres one for anyone to have a go at...
Solve the equation sin (x) = square root of 3 cos (x) for x (wierd symbol that i think means all elements of ) [- pie , pie], giving exact values in terms of pie
Divide both sides by cos(x) and you get....
tan(x)=square root 3
x = -2pi/3 and pi/3
EDIT:
Ah, too late
But exact values are very important for the exam, so you should learn them
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Ohh yehhh damn I should know that :@