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The curve C has equation
y = arsinh (x3), x ≥ 0.
The point P on C has x-coordinate √2.
(a) Show that an equation of the tangent to C at P is
y = 2x - 2 √2 + In(3+ 2√2).
The tangent to C at the point Q is parallel to the tangent to Cat P.
(b) Find the x-coordinate of Q, giving your answer to 2 decimal places.
For the supply and demand functions below find the value of xe where equilibrium occurs. D(x) = -2x+275 and S(x) = 3x+150.
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The number of motor vehicles deaths increased by 13.75 times from 1912 to 2003. There were 39,525 more deaths in 2003 than in 1912. Find the number of motor vehicle deaths in each of the two years.
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