Final answer:
These problems involve using proportions and scale factors in mathematical scenarios such as scale drawings and similar triangles. The questions require converting actual sizes to scaled sizes and vice versa. Understanding these concepts is essential for solving problems related to scale and proportionality.
Step-by-step explanation:
The situations presented involve applying proportions and scale factors to calculate unknown lengths and heights, which is a concept typically encountered in mathematics.
In the case of the superheroes, similar triangles are used to determine the relationship between The Wasp and Ant-Man's heights and their shadows. Then the same proportional relationship is used to figure out Spider-Man's shadow length.
To solve Jonah's spider drawing problem, we need to calculate the scale factor and apply it to the actual length of the spider's body. Since the scale is 0.5 cm = 4 mm, and the actual length of the spider is 16 mm, we convert this to the scale of the drawing.
To find the length of the spider's body in a new drawing that's half the size of the original, the scale factor is halved. Alyssa's classroom problem also requires understanding of scale factor, as she needs to convert actual dimensions to a scaled-down size in a drawing.
For the circular fountain problem, if the scale drawing has a diameter of 3 cm and we need the actual diameter, we must know the scale used to make the drawing. Without this scale, we cannot determine the actual diameter.
In the example with the intelligent ant, the scenario is analogous to Hubble's Law, indicating that objects (ants in this case) move away from each other at speeds proportional to their distances—similar to galaxies in the expanding universe.