Solve the following equations: 1) 2^x x 9^y = 5184; 2) Evaluate (1.2)/((0.0415)2) + 5sqrt(0.976) using tables. Round to 3 decimal places.

The equation is $2^x \times 9^y = 5184$.
We know that $9 = 3^2$. So, the equation becomes $2^x \times (3^2)^y = 5184$, which simplifies to $2^x \times 3^{2y} = 5184$.

So, $5184 = 2^6 \times 81$.
Now, factorize 81:

So, $81 = 3^4$.
Therefore, $5184 = 2^6 \times 3^4$.

Comparing $2^x \times 3^{2y} = 2^6 \times 3^4$:
For the base 2: $x = 6$
For the base 3: $2y = 4 \implies y = \frac{4}{2} \implies y = 2$

The values are $\boxed{x=6, y=2}$.

Rounding to three decimal places:

The area of a triangle is given by:

where $a$ and $b$ are the lengths of two sides, and $C$ is the angle included between those sides.

Given:
$PQ = 5 \text{ cm}$
$QR = x^2 \text{ cm}$
$\angle PQR = 30^\circ$
Area $= 20 \text{ cm}^2$

We know that $\sin(30^\circ) = \frac{1}{2}$.

Multiply both sides by 4:

Divide both sides by 5:

Take the square root of both sides. Since $x$ represents a length (part of $QR = x^2$), it must be positive.

The value of $x$ is $\boxed{4}$.