Simplify: 1.a) (34 x 3⁻²)/33, 1.b) Express 0.00032 in standard form, 2.a) Expand and simplify: (2x-3)(x+5)-(x-4)2

The simplified expression is $\boxed{\frac{1}{3}}$.

1.b) Express 0.00032 in standard form:
To express a number in standard form, we move the decimal point until there is one non-zero digit to its left.

It was moved 4 places to the right.

The number in standard form is $\boxed{3.2 \times 10^{-4}}$.

2.a) Expand and simplify: $(2x - 3)(x + 5) - (x - 4)^2$

Remember to distribute the negative sign to all terms in the second expansion.

The expanded and simplified expression is $\boxed{x^2 + 15x - 31}$.

2.b) Factorise completely: $3x^2 - 11x - 4$
We are looking for two numbers that multiply to $3 \times (-4) = -12$ and add up to $-11$. These numbers are $-12$ and 1.

The completely factorised expression is $\boxed{(x - 4)(3x + 1)}$.

2.c) Solve: $4x^2 - 9 = 0$
This is a difference of squares, $a^2 - b^2 = (a-b)(a+b)$, where $a = \sqrt{4x^2} = 2x$ and $b = \sqrt{9} = 3$.

The solutions are $\boxed{x = \frac{3}{2} \text{ or } x = -\frac{3}{2}}$.

3. Solve:
$3x + 2y = 17 \quad \text{(Equation 1)}$
$2x - y = 4 \quad \text{(Equation 2)}$
We will use the elimination method.

The solutions are $\boxed{x = \frac{25}{7}, y = \frac{22}{7}}$.

4. Two similar cones have radii 3 cm and 9 cm.
Let $r_1 = 3$ cm (smaller cone) and $r_2 = 9$ cm (larger cone).

4.a) Find the scale factor.
The scale factor $k$ is the ratio of corresponding linear dimensions. We'll use the ratio of the larger radius to the smaller radius.

The scale factor is $\boxed{3}$.

4.b) If the smaller cone has volume 40 cm$^3$, find the volume of the larger cone.
For similar solids, the ratio of their volumes is the cube of the scale factor.
Let $V_1$ be the volume of the smaller cone and $V_2$ be the volume of the larger cone.

The volume of the larger cone is $\boxed{1080 \text{ cm}^3}$.

4.c) If the slant height of the smaller cone is 5 cm, find that of the larger cone.
For similar solids, the ratio of their corresponding linear dimensions (like slant height) is equal to the scale factor.
Let $l_1$ be the slant height of the smaller cone and $l_2$ be the slant height of the larger cone.

The slant height of the larger cone is $\boxed{15 \text{ cm}}$.

5. A cylindrical water tank has radius 7 m and height 10 m.
Given: $r = 7$ m, $h = 10$ m.

5.a) Find its volume.
The formula for the volume of a cylinder is $V = \pi r^2 h$.

The volume of the tank is $\boxed{490\pi \text{ m}^3}$.

5.b) Find its total surface area.
The formula for the total surface area of a cylinder is $A = 2\pi r h + 2\pi r^2$.

The total surface area of the tank is $\boxed{238\pi \text{ m}^2}$.

5.c) If water costs KSh 50 per cubic meter, find the cost to fill the tank.
Cost to fill the tank = Volume $\times$ Cost per cubic meter.
Using the volume from 5.a):

If we use $\pi \approx 3.14159$:

The cost to fill the tank is $\boxed{24500\pi \text{ KSh}}$ (or approximately $\boxed{\text{KSh } 76969.36}$).