Blog of Andrés Aravena
MSR:

Homework 5

16 March 2023. Deadline: Thursday, 23 March, 10:00. by Andrés Aravena, Ph.D.

1. Drake’s equation

In 1961 the scientist Francis Drake proposed the following formula to estimate the number of alien civilizations that can contact us

\[N = R_* \cdot f_\mathrm{p} \cdot n_\mathrm{e} \cdot f_\mathrm{l} \cdot f_\mathrm{i} \cdot f_\mathrm{c} \cdot L\]

where

Drake made the following estimations

Please use interval arithmetic to find the smallest and largest value of \(N\) under this model.

2. Cost of a tuna can (without the tuna)

If you want to store food in a tin container, you need to make the container. The cost of making a can depends on how much material is required.

How much material is needed to make a tuna can? Please use interval arithmetic to find the interval containing the true value of the area of the can’s surface. The relevant formulas are \[S_1 = π r^2 = \frac{π}{4}D⋅D\\ S_2 = H⋅L = H⋅D⋅π\] where the diameter \(D\) is 85.5mm ± 0.05mm and the height \(H\) is 36.5mm ± 0.05mm.

What are the units of \(S_1\) and \(S_2\)?

3. How much tuna can be stored in a tuna can?

Once you have the can, you can put tuna inside. lease use interval arithmetic to find the interval containing the true value of the can’s volume. The relevant formula is \[V=H⋅S_1 = H\cdot \frac{π}{4}D⋅D\]

What are the units of \(V\)?

4. If the tuna can grows

We want to store twice as much tuna on the can. How much material do you need?

What is the cheapest way to store tuna?

Deadline: Thursday, 23 March, 10:00.

Originally published at https://anaraven.bitbucket.io/blog/2023/msr/homework05.html