bar (E)=sqrt (((Delta bar (m))/(m))^2+((delta bar (h))/(h))^2+((2bar (D))/(bar (D)))^2)(sqrt {((0.049)/(70509))^2+(frac {0.087){1

$\bar {E}=\sqrt {(\frac {\Delta \bar {m}}{m})^{2}+(\frac {\delta \bar {h}}{h})^{2}+(\frac {2\bar {D}}{\bar {D}})^{2}}{\sqrt {(\frac {0.049}{70509})^{2}+(\frac {0.087}{1}}$<br /><br />To solve this problem, we need to calculate the numerator and denominator separately and then take the square root of the ratio.<br /><br />First, let's calculate the numerator:<br />$\sqrt {(\frac {\Delta \bar {m}}{m})^{2}+(\frac {\delta \bar {h}}{h})^{2}+(\frac {2\bar {D}}{\bar {D}})^{2}}$<br /><br />Given that $\Delta \bar {m} = 0.049$, $m = 70509$, $\delta \bar {h} = 0.087$, and $h = 1$, we can substitute these values into the equation:<br />$\sqrt {(\frac {0.049}{70509})^{2}+(\frac {0.087}{1})^{2}+(\frac {2\times 0.049}{70509})^{2}}$<br /><br />Simplifying the equation, we get:<br />$\sqrt {(\frac {0.049}{70509})^{2}+0.087^{2}+(\frac {0.098}{70509})^{2}}$<br /><br />Next, let's calculate the denominator:<br />$\sqrt {(\frac {0.049}{70509})^{2}+(\frac {0.087}{1})^{2}}$<br /><br />Simplifying the equation, we get:<br />$\sqrt {(\frac {0.049}{70509})^{2}+0.087^{2}}$<br /><br />Now, we can calculate the numerator and denominator separately and then take the square root of the ratio:<br />$\bar {E}=\sqrt {\frac {(\frac {0.049}{70509})^{2}+0.087^{2}+(\frac {0.098}{70509})^{2}}{(\frac {0.049}{70509})^{2}+0.087^{2}}}$<br /><br />Simplifying the equation, we get:<br />$\bar {E}=\sqrt {1+\frac {(\frac {0.098}{70509})^{2}}{(\frac {0.049}{70509})^{2}+0.087^{2}}}$<br /><br />Therefore, the final answer is:<br />$\bar {E}=\sqrt {1+\frac {(\frac {0.098}{70509})^{2}}{(\frac {0.049}{70509})^{2}+0.087^{2}}}$