One root of the equation $3x^2 - 10x + 3 = 0$ is $\frac{1}{3}$. Find the other root.

Solve the given two equations and select the correct answer from the given options.
$I.$ $\sqrt{784} x + 1234 = 1486$
$II.$ $\sqrt{1089} y + 2081 = 2345$

Find the value of $x^{3}+y^{3}+z^{3}-3xyz$,when $x+y+z=16$ and $xy+yz+zx=78$.

If $x = \sqrt {1 + \sqrt {1 + \sqrt {1 + \dots \infty} } }$,then $x =$

$Quantity \, 1:$ Profit percent for a shopkeeper. The shopkeeper uses a faulty scale while buying cloth from a wholesaler. His scale measures $10 \%$ extra than the actual measurement. While selling,the shopkeeper gives $10 \%$ less and offers a discount of $10 \%$ to the customer.
$Quantity \, 2:$ Profit percent for a man who calculates his profit on the selling price. He marks up the cost of his item by $25 \%$ and then sells the item at a discount of $10 \%$.

Solve the given two equations and select the correct answer from the given options.
$I.$ $x = \sqrt{172}$
$II.$ $y^{2} - 29y + 210 = 0$