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# Tutor profile: Julie L.

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Julie L.
Mathematics Instructor for 17 Years
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## Questions

### Subject:Trigonometry

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Question:

Prove the following identity by showing justifying each step (you can assume knowledge of the sum and difference formulas for trigonometric functions): sin(2x)=2sin(x)cos(x)

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Julie L.

We will start on the left side of the equation and use the following steps to prove the identity: sin(2x) = sin( x + x) by the fact that multiplication is repeated addition = sin(x)cos(x) + cos(x)sin(x) by the sine of the sum of two angles formula = sin(x)cos(x) + sin(x)cos(x) by commutativity of multiplication = 2sin(x)cos(x) by repeated addition being the same as multiplication Thus, we have proven that sin(2x)=2sin(x)cos(x).

### Subject:Calculus

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Question:

Find an integral expression that represents the area under the curve f(x) = x^2 + 3 on the interval from [0,4]. Do not actually find the area.

Inactive
Julie L.

First, be sure the given function is positive (above the x-axis) on the given interval. We know that f(x) = x^2 + 3 represents a parabola opening up with a vertex of (0,3). So f(x) is positive on the [0,4] interval. Then we can represent the area under the curve of f(x) by setting up an integral and bounding it by 0 on the bottom, 4 on the top, placing the f(x) function in for the integrand and using dx as the differential. So the following would represent the area: Area = \int_{0}^{4}(x^2+3)dx

### Subject:Algebra

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Question:

A ball is dropped from the top of a 320 foot tall building. Determine the time, t, in seconds, at which the ball will hit the ground using the position function given by s(t) = -16t^2 + 320 (which is measured in feet).

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Julie L.

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