Mary drew a parallelogram on a grid. One side of the parallelogram passed through point (1,4) with a gradient of 1/2. Determine the equation of the line and the co-ordinates of the x-intercept of the line.

Given point $(x_1, y_1) = (1, 4)$ and gradient $m = \frac{1}{2}$.

$$y - 4 = \frac{1}{2}(x - 1)$$

$$2(y - 4) = 1(x - 1)$$ $$2y - 8 = x - 1$$

$$2y = x - 1 + 8$$ $$2y = x + 7$$ $$y = \frac{1}{2}x + \frac{7}{2}$$

The final answer is $\boxed{y = \frac{1}{2}x + \frac{7}{2}}$.

Substitute $y=0$ into the equation of the line.

$$0 = \frac{1}{2}x + \frac{7}{2}$$

$$-\frac{7}{2} = \frac{1}{2}x$$

Multiply both sides by 2:

$$-7 = x$$

The x-intercept is $(-7, 0)$.
The final answer is $\boxed{(-7, 0)}$.

$$A = \pi r^2 + \pi r l$$

where $r$ is the base radius and $l$ is the slant height.

$$A = \pi (4.2 \text{ cm})^2 + \pi (4.2 \text{ cm})(20 \text{ cm})$$ $$A = \pi (17.64 \text{ cm}^2) + \pi (84 \text{ cm}^2)$$ $$A = 17.64\pi \text{ cm}^2 + 84\pi \text{ cm}^2$$ $$A = (17.64 + 84)\pi \text{ cm}^2$$ $$A = 101.64\pi \text{ cm}^2$$

Using $\pi \approx 3.14159$:

$$A \approx 101.64 \times 3.14159$$ $$A \approx 319.3982 \text{ cm}^2$$

Rounding to two decimal places:

$$A \approx 319.40 \text{ cm}^2$$

The final answer is $\boxed{319.40 \text{ cm}^2}$.

The formula for the volume of a sphere is $V_{sphere} = \frac{4}{3}\pi r^3$.
Given radius of sphere $r = 1.5 \text{ cm}$.

$$V_{sphere} = \frac{4}{3}\pi (1.5 \text{ cm})^3$$ $$V_{sphere} = \frac{4}{3}\pi (3.375 \text{ cm}^3)$$ $$V_{sphere} = 4.5\pi \text{ cm}^3$$

The volume of water displaced is equal to the volume of the sphere. This displaced volume causes a rise in the water level in the cylindrical tin.
The volume of the cylindrical rise is $V_{rise} = \pi R^2 h$, where $R$ is the radius of the tin and $h$ is the rise in water level.
Given radius of tin $R = 1.8 \text{ cm}$.

$$V_{rise} = \pi (1.8 \text{ cm})^2 h$$ $$V_{rise} = \pi (3.24 \text{ cm}^2) h$$

$$V_{sphere} = V_{rise}$$ $$4.5\pi = 3.24\pi h$$

Divide both sides by $\pi$:

$$4.5 = 3.24 h$$ $$h = \frac{4.5}{3.24}$$ $$h \approx 1.3888... \text{ cm}$$

$$h \approx 1.4 \text{ cm}$$

The final answer is $\boxed{1.4 \text{ cm}}$.