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Anirban D.

Your friendly maths tutor, engineer in Munich

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Trigonometry

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Question:

Solve the trigonometric equation for x: tan3x=1/tan2x.

Anirban D.

Answer:

Since 1/tanA = tan (π/2 − A), we can write the above equation as tan3x = tan(π/2 − 2x), 3x = (π/2 − 2x) + Kπ, since if tanA = tanB, then A = B + Kπ, where K= some integer 3x − (π/2 − 2x) = Kπ, 5x − π/2 = κπ, 5x = Kπ + π/2, x = Kπ/5 + π/10

Geometry

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Question:

A rectangular swimming pool has a length of 30 meters, a width of 10 meters, and an average depth of 2 meters. If a hose can fill the pool at a rate of 0.5 cubic meters per minute, how many hours will it take the hose to fill the pool?

Anirban D.

Answer:

Since the swimming pool is rectangular, we can find its volume as the length, width and height (depth) are already given. So, volume = length X width X height = 30 X 10 X 2 = 600 cubic meters Rate of filling the pool by the hose = 0.5 cubic meters per minute. Therefore, hours taken by the hose to fill the pool =(600 cubic meter)/ (0.5 cubic meters per minute) =600/0.5 minutes =6000/5 minutes =1200 minutes =1200/60 hours =20 hours

Algebra

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Question:

Two people are 14 miles apart and begin walking towards each other. Person A walks 3 miles per hour and Person B walks 4 miles per hour. How long will it take them to reach each other?

Anirban D.

Answer:

Total distance to be covered by walking= 14 miles Distance covered by A = lets say, d miles Then, distance covered by B = 14 - d miles. Both use the same amount of time to meet each other and lets refer that time as t hours. By the equation, speed X time = distance, we get: since speed of A is 3 miles/hour, equation for A: 3t = d...............................(1) Similarly, equation for B: 4t = 14 - d........................(2) Substituting the value of d from (1) to (2), 4t = 14 - 3t 4t + 3t = 14 7t = 14 t= 2 Therefore, it will take 2 hours for A and B to reach each other.

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