anonymous
  • anonymous
the equation of the line tangent to the curve y=kx+8/k+x at x= -2 is y=x+4. what is the value of k?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
check your question , possibly a typo
anonymous
  • anonymous
no, thats it word for word
anonymous
  • anonymous
y= (k+1)x +(8/k) ( eqn of the "curve" , even though its a line )

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anonymous
  • anonymous
the only way to have a tangent to a line , is for the tangent to be the line
anonymous
  • anonymous
so (k+1)x +(8/k) = x+4
anonymous
  • anonymous
now we are told they are a tangent at x=-2, so we could sub x=-2 into the above to find k , but we could also sub any value of x we like , these lines have to be the same for all x
anonymous
  • anonymous
but ill just sub x=-2 -2(k+1) + 8/k = 2 -2k(k+1) +8 = 2k -2k^2 -2k -2k +8 =0 -2k^2 -4k+8 =0 -2(k^2 +2k -4) =0
anonymous
  • anonymous
k^2 +2k -4 =0
anonymous
  • anonymous
how did you get that function?
anonymous
  • anonymous
(k+1)^2 = 5 k +1 = +-sqrt(5) k = -1+-sqrt(5)
anonymous
  • anonymous
not an answer
anonymous
  • anonymous
well your teacher is stupid
anonymous
  • anonymous
i doubt that you dont even know what the equation of the line tangent is
anonymous
  • anonymous
this is a question from an ap test so there are no typos
anonymous
  • anonymous
lol was the curve \[y=kx + \frac{8}{k+x}\] y =
anonymous
  • anonymous
if it was................ :|
anonymous
  • anonymous
use brackets when you are writting fractions on the net :|
anonymous
  • anonymous
put the kx on top also
anonymous
  • anonymous
sorry? didnt know
anonymous
  • anonymous
lol
anonymous
  • anonymous
y=(kx+8)/k+x
anonymous
  • anonymous
With the given info, one finds the tangent vector of the curve to be <1, -1> and the point of tangency to be (-2, 2). You can find k by plugging in (-2, 2).

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