1 Answer

Dmitriy Sintsov · Answer 1 · 2019-04-22T14:42:20+0000

Determine point A:

$y(x)=(10)/(2x+1)-2\\(10)/(2x+1)-2=0\implies x=2$

so A(2,0)

Find the function for the tangent:

(dy)/(dx)=-(-20)/((2x+1)^2)

the tangent function is a line

$y=ax + b = (dy)/(dx)|_A\cdot x + b\\$

(with slope being the derivative evaluated at point A(2,0))

(dy)/(dx)|_A=-(4)/(5) so a=-4/5.

Determine b by using what we know about A:

$y=-(4)/(5)x+b\\0=-(4)/(5)\cdot 2+b\implies b=(8)/(5)$

so the function is

$y = -(4)/(5)x+(8)/(5)\\5y + 4x = 8$

(i) this is demonstrated above

(ii) distance AC: we know A(2,0) and C(0,5/8), the distance is:

$\sqrt{(0-2)^2+((5)/(8)-0)^2}=√(281)/8\approx 2.1$

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