Frank
Hello, this is Frank.
From today, I will introduce practical math concepts useful in global business. These are at a fundamental level, but I hope they will also help you in learning English alongside math.
This time, we tackle a problem involving derivatives and calculating the speed of a hydrofoil in still water.
Let’s start with my favorite topic, derivatives. As a humanities major, I chose a fundamental question. Why not give it a try?
【Questions】
(1) What is the derivative of \(y = x^{3} + 6\)?
(2) A hydrofoil goes 15 km upstream in 15 minutes. The speed of the stream is 5 km/h. What is the speed of the hydrofoil in still water?
Here are the solutions to the questions above.
【Answers】
(1) Using the formula \(\frac{d}{dx}(x^{n}) = nx^{n-1}\), we get:
\(\frac{d}{dx}(x^{3} + 6) = 3x^{2} + 0 = 3x^{2}\)
(2) “15 km upstream in 15 minutes” means the hydrofoil would cover 60 km in 1 hour.
Speed of the stream = 5 km/h.
∴ Speed of the hydrofoil in still water = 60 + 5 = 65 km/h.
How was that? I created these problems and solutions based on international math websites and textbooks, such as High School Math Revisited. Numbers, conditions, and explanations have been adjusted to ensure originality.
Stay tuned for future installments! b＾＾)
Learn more about Practical Math for Global Business b＾＾)
Reference: High School Math Revisited by Kazuo Takahashi, Nihon Jitsugyo Publishing
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