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(B) Given the transformation of axes by shifting the origin to $(h, 5)$,the relations are $x = X + h$ and $y = Y + 5$.Substituting these into the equa

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$13$

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(B) Given the transformation of axes by shifting the origin to $(h, 5)$,the relations are $x = X + h$ and $y = Y + 5$.Substituting these into the equation $y = x^3 - 9x^2 + cx - d$:$Y + 5 = (X + h)^3 - 9(X + h)^2 + c(X + h) - d$$Y + 5 = (X^3 + 3hX^2 + 3h^2X + h^3) - 9(X^2 + 2hX + h^2) + cX + ch - d$$Y = X^3 + (3h - 9)X^2 + (3h^2 - 18h + c)X + (h^3 - 9h^2 + ch - d - 5)$Comparing this with $Y = X^3$,the coefficients of $X^2$ and $X$ must be zero,and the constant term must be zero:$1) 3h - 9 = 0 \Rightarrow h = 3$$2) 3h^2 - 18h + c = 0$ $\Rightarrow 3(9) - 18(3) + c = 0$ $\Rightarrow 27 - 54 + c = 0$ $\Rightarrow c = 27$$3) h^3 - 9h^2 + ch - d - 5 = 0$ $\Rightarrow 27 - 9(9) + 27(3) - d - 5 = 0$ $\Rightarrow 27 - 81 + 81 - d - 5 = 0$ $\Rightarrow d = 22$Now,calculate $\left(d - \frac{c}{h}\right) = 22 - \frac{27}{3} = 22 - 9 = 13$.

By shifting the origin to the point $(h, 5)$ by the translation of coordinate axes,if the equation $y=x^3-9x^2+cx-d$ transforms to $Y=X^3$,then $\left(d-\frac{c}{h}\right)=$

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