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Answer:

It is given that 4x + 10y= -26 is an equation of the tangent line to the graph of y=g(x) at x=16.

At x = 16, y = -9

=> g(16) = -9

4x + 10y = -26

=> y = -0.4x - 2.6

The slope of the line is -0.4

This implies that g'(16) = -0.4

For the curve defined by `y = (g(x))^2`

`dy/dx = 2*g(x)*g'(x)`

At x = 16, y = 81

`dy/dx = 2*(-9)*-0.4 = 7.2`

The equation of the tangent is `(y - 81)/(x - 16) = 7.2`

=> 10y - 810 = 72x - 1152

=> 72x - 10y - 342 = 0

=> 36x - 5y - 171 = 0

**The required tangent is 36x - 5y - 171 = 0**

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