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Tutor profile: Florence L.

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Florence L.
Civil Engineer
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Questions

Subject: SAT II Mathematics Level 2

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Question:

If $$ f(x) = \sqrt[3]{x^3+1}$$ what is $$ f^{-1}(2)$$?

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Florence L.
Answer:

This is a typical inverse function and substitution problem. The first step is to find the inverse function: $(f(x) = \sqrt[3]{x^3+1}$) First switch x with the inverse of x: $(x = \sqrt[3]{f^{-1}(x)^3+1}$) Now solve: $(x^3 = f^{-1}(x)^3+1$) $(x^3-1 = f^{-1}(x)^3$) $(\sqrt[3]{x^3-1} = f^{-1}(x)$) Now substitute x with 2 and solve: $(f^{-1}(2) = \sqrt[3]{2^3-1}$) $(f^{-1}(2) = \sqrt[3]{8-1}$) $(f^{-1}(2) = \sqrt[3]{7}$) $(f^{-1}(2) = 1.9$)

Subject: Trigonometry

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Question:

You're having a fun day in the park flying your kite. If the kite is at a height of 10 meters and is 8 meters horizontally away from you, how long is the string in meters?

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Florence L.
Answer:

This is a simple Pythagorean Theorem problem. The sides of the right triangle is 10 meters and 8 meters and the string connecting you to the kite is the hypotenuse. The Pythagorean Theorem provides the formula: $(c^2 = a^2 + b^2$) Plugging the number into the formula gives us: $(c^2 = 10^2 + 8^2$) and solving for c: $(c = \sqrt{10^2 + 8^2}$) $(c = \sqrt{100 + 64}$) $(c = \sqrt{164}$) $(c = 12.8$) Therefore, the kite string is 12.8 meters long.

Subject: Physics

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Question:

What is the difference between energy and power?

Inactive
Florence L.
Answer:

Energy takes many forms, i.e. Kinetic energy, Potential energy, etc., while power is just the rate of energy. General equation of energy is: Energy = Force x Displacement x cosine(theta) and general equation of power is: Power = Energy/time. The unit for energy is Joules while power takes on the unit of Watts.

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