# Tutor profile: Florence L.

## Questions

### Subject: SAT II Mathematics Level 2

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

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

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?

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

What is the difference between energy and power?

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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