[S2 Maths Topic: Graphs & Quadratic Equations] Optical illusions. They are a rare occurrence in Nature, and sometimes observed over deserts in the form of mirages, or the Brocken spectre when the sun casts your own shadow among moving clouds to name a few. But with the help of Physics (and Maths), we can recreate a "mirage" [Parabolic Ghost] of an object by placing it carefully between two special, non-Euclidean convex mirrors. A Do-It-Yourself mirage? How does it work? Professor Burkard Polster works out the mathematics behind the phenomenon so that you can try to make one yourself. (Hint: Some old flashlight heads have the perfect geometry to replicate the [y = x^2] shape depicted in the v

An adult can drink a bottle of juice in 27 days. In one day, a man can drink 1/27 of a bottle. An child can drink a bottle of juice in 54 days. In one day, a child can drink 1/54 of a bottle. To solve this, add up their rates: When you combine them together, 1/27 + 1/54 = 2/54 + 1/54 => 3/54 Simplify the answer: 3/54 => 1/18. If they both put their efforts into drinking from the same bottle, both an adult and a child can finish 1/18 of a bottle a day. So how many days would it take them to finish one bottle of juice? 1 ÷ 1/18 => 18/18 ÷ 1/18 = 18 days. It would take them a total of 18 days to finish the bottle of juice. Just remember, kids: All things in moderation, and don't force yourself

An adult can finish a bottle of juice in 27 days, whereas a child can finish it in 54 days. If they both drink out of the same bottle at their respective rates, how long will it take for the bottle to be emptied? (The answer will be revealed in our next post, what is yours?)