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(A) Given the equation: $z = a^{2} x^{3} y^{1/2}$.Since $a$ is a constant,its relative error $\frac{\Delta a}{a} = 0$.The relative error in $z$ is giv

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$18$

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(A) Given the equation: $z = a^{2} x^{3} y^{1/2}$.Since $a$ is a constant,its relative error $\frac{\Delta a}{a} = 0$.The relative error in $z$ is given by: $\frac{\Delta z}{z} = 3 \left( \frac{\Delta x}{x} ight) + \frac{1}{2} \left( \frac{\Delta y}{y} ight)$.To find the percentage error,multiply by $100$:$\frac{\Delta z}{z} 	imes 100 = 3 \left( \frac{\Delta x}{x} 	imes 100 ight) + \frac{1}{2} \left( \frac{\Delta y}{y} 	imes 100 ight)$.Given $\frac{\Delta x}{x} 	imes 100 = 4\%$ and $\frac{\Delta y}{y} 	imes 100 = 12\%$.Substituting the values: $\frac{\Delta z}{z} 	imes 100 = 3(4\%) + \frac{1}{2}(12\%) = 12\% + 6\% = 18\%$.

For $z = a^{2} x^{3} y^{1/2}$,where $a$ is a constant. If the percentage error in the measurement of $x$ and $y$ are $4\%$ and $12\%$,respectively,then the percentage error for $z$ will be $........... \%$.

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