Factorize completely: x2 - 2xy2 + y4 13. Solve for y given that y is acute and (3y - 50^) = (2y + 10^)

The expression $x^2 - 2xy^2 + y^4$ is in the form of a perfect square trinomial, $a^2 - 2ab + b^2 = (a-b)^2$.

In this case, $a = x$ and $b = y^2$.

The completely factorized expression is:

13. Solve for y given that y is acute and $\sin(3y - 50^\circ) = \cos(2y + 10^\circ)$

We can rewrite the right side of the equation:

Now the equation is $\sin(3y - 50^\circ) = \sin(80^\circ - 2y)$.
For $\sin A = \sin B$, we have two general cases:
Case 1: $A = B + 360^\circ n$
Case 2: $A = 180^\circ - B + 360^\circ n$
Since y is acute, we will consider the primary solutions.

This value is acute ($0^\circ < 26^\circ < 90^\circ$).

This value is not acute.

Therefore, the acute value for y is:

14. A solid consists of a cone and a hemisphere. The common diameter of the cone and the hemisphere is 10 cm, and the slanting height of the cone is 12 cm. Calculate correct to two decimal places the surface area of the solid.

Common diameter = 10 cm.
Radius ($r$) = $\frac{10 \text{ cm}}{2} = 5$ cm.
Slanting height of the cone ($l$) = 12 cm.

The solid is formed by joining a cone and a hemisphere at their circular bases. Therefore, the total surface area of the solid is the sum of the curved surface area of the cone and the curved surface area of the hemisphere.
Total Surface Area = Curved Surface Area of Cone + Curved Surface Area of Hemisphere.

Curved Surface Area of Cone = $\pi r l$
Curved Surface Area of Hemisphere = $2 \pi r^2$

Total Surface Area = $\pi (5 \text{ cm})(12 \text{ cm}) + 2 \pi (5 \text{ cm})^2$
Total Surface Area = $60 \pi \text{ cm}^2 + 2 \pi (25 \text{ cm}^2)$
Total Surface Area = $60 \pi \text{ cm}^2 + 50 \pi \text{ cm}^2$
Total Surface Area = $110 \pi \text{ cm}^2$

Using $\pi \approx 3.14159265...$
Total Surface Area = $110 \times 3.14159265$
Total Surface Area $\approx 345.5751915$ cm$^2$

Rounding to two decimal places:
Total Surface Area $\approx 345.58$ cm$^2$

The surface area of the solid is: