Juliana S.

Vanderbilt Student with 6 Years of Tutoring

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Geometry

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Question:

If the diameter of a circle is 25 cm, what is the area in inches?

Juliana S.

Answer:

The first thing I would do is convert from cm to in. The conversion is 2.54 cm to 1 in, therefore, 25 cm approximately equals 7.87 in. The area for a circle is area = $$pi*r^{2}$$ where pi = 3.1415. This equation requires the radius, not the diameter. The diameter = 2* radius. Therefore, the radius is 3.937 in. When you plug in the radius the answer is approximately 48.69 $$in^{2}$$

Calculus

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Question:

Differentiate h(t) =$$t^{3}+t^{2}sin(2t)$$

Juliana S.

Answer:

To take the derivative you need to remember three rules. 1. When you have an exponent you take the exponent and it becomes the coefficient and then subtract one from the power f(x) = $$x^{2}$$ becomes f'(x) = $$2x^{1}$$ 2. The second rule you need to remember is about trig functions. The derivative of sin(x) is cos(x). 3. Lastly you need to remember the chain rule. If there is a function inside of a function you take the derivative of the outer function first and then multiply the derivative of of the inner function Applying these three rules the above function becomes h'(t) = $$2t^{2} + 2tsin(2t)+2t^{2}cos(2)$$

ACT

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Question:

28. If 2$$x^{2}$$ +6x = 36, what are the possible values of x? F. –12and 3 G.–6and3 H.–3and6 J. –3 and 12 K. 12 and 15

Juliana S.

Answer:

First, you should get all terms to one side of the equation in order to solve this quadratic formula. You can assign each coefficient to a letter in the quadratic formula a = 2 b = 6 c = -36 Next you can either try and factor or use the quadratic formula to solve. The quadratic formula is$$\frac{ -b(+ or - ) \sqrt{b^2-4ac}}{2a}$$ When you plug in the values above you should get G, -6 and 3.

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