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Nicholas C.

Math tutor at Kumon learning center for a full school year.

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Pre-Calculus

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Question:

Simplify this, [(Tan(x) * Cos(x))/(Sin(x))] - Cos^2 (x)

Nicholas C.

Answer:

So, Tan(x) = Sin(x)/Cos(x) (Sin(x)/Cos(x) * Cos(x)) = Sin(x) Sin(x) / Sin(x) = 1 And using the Pythagorean identity of Sin^2 (x) + Cos^2 (x) = 1 we find that the remaining 1 - Cos^2 (x) is equal to a final simplified answer of Sin^2 (x)

Calculus

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Question:

If a 13 foot ladder whose base is sliding away from a wall at a rate of 3 feet per second and the top of the ladder is 12 feet off the ground, at what rate is the ladder sliding down the wall?

Nicholas C.

Answer:

First, it is known that with the Pythagorean Theorem here, a^2 + b^2 = c^2. Then, we plug in what we do know to the equation: a^2 + b^2 = 13^2 because the distance staying constant here is that of the length of the ladder, the hypotenuse. Then we take the derivative of that equation which makes it 2a * dA/dt + 2b * dB/dt = 0. Then plug in 12 for a since that is the distance from the ground and use the Pythagorean Theorem to find that b = 25^2 = 5 and also plug in the rate of the ladder sliding away from the wall 2 * 12 * dA/dt + (2 * 5 * 3) = 0, then simplifying 24 * dA/dt + 30 = 0 and solving for dA/dt, dA/dt = -30/24 = -15/12. This number means that the ladder is sliding down the wall at 15/12 feet per second at the moment that the base of the ladder is 5 feet away from the wall.

Algebra

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Question:

If the number a is multiplied by 5 and summed with 4 to equal 39, what number is a?

Nicholas C.

Answer:

5a + 4 = 39 5a = 35 a = 7

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