Matt R.

Vanderbilt graduate 3.7 GPA

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Basic Chemistry

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Question:

What are the number of moles of CO2 which contains 16 g of oxygen?

Matt R.

Answer:

Carbon has a molar mass of 12g, and O2 has a molar mass of 32g. So, one mole of O2 has 32 grams. The question asks for 16g. Since 16 is half of 32, we know we have half of one mole. So the answer is .5 moles.

ACT

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Question:

If the hypotenuse of a right triangle is 10 inches long and one of its legs is 5 inches long, how long is the other leg?

Matt R.

Answer:

Using the Pythagorean theorem, a^2+b^2=c^2 we can easily solve for this question. A and B represent the two legs of the triangle and C represents the hypotenuse A^2= 5x5= 25 C^2= 10x10=100 So substituting in we have 25+b^2= 100 b^2= 75 So we take the square root of 75 and the answer is. b=5√3

Algebra

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Question:

Solve for y in: 2y+5= -3y-10

Matt R.

Answer:

In order to solve for y in the equation above, we must first get the variable y alone on one side of the equation. In order to do this, we will want anything with a y in it on one side, and anything without a y on the other side. To do this we will bring -3y to the other side of the equals sign. When any number or variable (y) crosses the equals sign, it changes signs. So -3y becomes a positive 3y. So now we have 2y+3y+5= -10. Combine the y values. 5y+ 5= - 10. Now since we want the y alone, we will bring the 5 to the other side. Remember that the sign changes so 5 becomes -5. So we have, 5y= -10 - 5. We know that -10-5 is -15. So we have 5y= -15. We don't want 5y's we want 1y. So we ill divide 5y by 5 and -15 by 5. The answer is y= -3. Note that most teachers will not say bringing -3y across the equals sign, they will say, add 3y to both sides and subtract 5 from each side. I can teach using both methods, however, thinking about the equals sign as a sign changer has sped math up for me and allows for much quicker solutions. This extra speed will be a huge advantage in more advanced math classes like calculus. I will adjust my method of teaching based on the individual student, and how he/she likes to work.

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