Step 1: Exploring potential utility objects.
- Old tyres can be creatively repurposed into functional objects, such as:
- Furniture (chairs, tables, swings).
- Playground equipment (climbing structures, jungle gyms).
- Decorative or practical planters.
- Artistic installations using recycled tyres.
Step 2: Conceptualizing the design. - Select an object that maximizes the use of tyre shapes.
- Utilize different tyre sizes and arrangements for structural stability.
- Maintain a balance between functionality and aesthetics.
Step 3: Illustrating the design.
- Provide a clear front-view sketch of the object.
- Include annotations to describe the integration of tyres.
- Apply texture and shading to enhance realism.
Let $ a_0, a_1, ..., a_{23} $ be real numbers such that $$ \left(1 + \frac{2}{5}x \right)^{23} = \sum_{i=0}^{23} a_i x^i $$ for every real number $ x $. Let $ a_r $ be the largest among the numbers $ a_j $ for $ 0 \leq j \leq 23 $. Then the value of $ r $ is ________.
A temperature difference can generate e.m.f. in some materials. Let $ S $ be the e.m.f. produced per unit temperature difference between the ends of a wire, $ \sigma $ the electrical conductivity and $ \kappa $ the thermal conductivity of the material of the wire. Taking $ M, L, T, I $ and $ K $ as dimensions of mass, length, time, current and temperature, respectively, the dimensional formula of the quantity $ Z = \frac{S^2 \sigma}{\kappa} $ is: