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# Tutor profile: Chris D.

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Chris D.
Teacher for 12 years, Tutor for over a decade
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## Questions

### Subject:Physics (Newtonian Mechanics)

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Question:

A ball is thrown at a velocity of 12 m/s at an angle of 32 degrees from the horizontal. What are the ball's horizontal and vertical velocities?

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Chris D.

Newtonian physics problems are very commonly solved by visualizing the scenario into a free body diagram, which I cannot draw here. But if I could, what I would draw here would be a triangle with the 12.5 m/s written on the hypotenuse, and an "x" and "y" drawn to depict separating that velocity into the horizontal (x) and vertical (y) velocities. The 32 degree angle belongs between the hypotenuse and the "x" axis, as I've described it above. Since I know two pieces of information, the hypotenuse and the angle, using SOH CAH TOA to recall the trigonometric identities that will give me the formulas needed to solve for my unknown quantities. SOH gives me that the "sin 32 = O/H", and since the "opposite" side is y, that leads to "sin 32 = y/12", which can be rearranged into "y = 12 x sin32" = 6.36 m/s. CAH gives me that the "cos 32 = A/H", and since the "adjacent" side is x, that leads to "cos 32 = x/12", which can be rearranged into "x = 12 x cos 32" = 10.18 m/s.

### Subject:Basic Chemistry

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Question:

Mercury has a density of 13.5 g/mL. Determine the number of moles of mercury in 1.0 L of mercury.

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Chris D.

### Subject:Algebra

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Question:

4x + 24 = 36. Solve for x.

Inactive
Chris D.

My tutoring for a question like this depends on the student. I would typically ask if they've solved problems like this before. If they haven't, and/or it is apparent that this student needs more assistance or even a refresher on the lesson behind it, I actually work backwards. By that I mean that I have them approach this is a puzzle where x=? is the answer, and the puzzle has been created by someone who is trying to hide the answer by making the equation more difficult. So, let's begin by pretending we know what x is. Let's try x = 2. Since the final equation has a 4x and a "+ something", that means that the puzzle builder multiplied AND added to get to the final puzzle. Since these elements have to be added by the order of PEMDAS (which I would explain if the student doesn't know), multiplication is done BEFORE addition. This means that the puzzle maker multiplied by 4, which must be done to both sides. 4 times x gives 4x, and 4 times 2 gives 8, leaving "x = 2" to become "4x = 8". The puzzle maker then added 24, which, again, needs to be done to both sides. Adding 24 to 8 gives 32, making the new equation "4x + 24 = 32". Since the left side of the equation ("4x + 24") is exactly as it should be, my new equation is done, but does not add up to 36, which means the x=2 I started with is the wrong "answer". But building the equation up (backwards) like this, shows the student how the puzzle (or problem) can be built up using PEMDAS laws that do not change. Once they have this foundation, we are left with two options, guess and check (which is very time consuming), or undoing each step in reverse order, which is why PEMDAS must be done backwards while solving. ((If the student knew all of these foundational topics to begin with, I would start here)) Since you have to follow PEMDAS backwards, the addition is the last step, so must be undone first. Undoing addition is subtraction (the opposite function), so subtract 24 to undo ADDING 24. This must be done to both sides, so subtracting 24 from the left side undoes, or cancels out the addition of 24, leaving only the "4x", while subtracting 24 from 36 leaves 12. The new equation then becomes "4x = 12". Since there is no addition or subtraction in this new equation, we can move on to multiplication, where the x is being multiplied by 4. The opposite function of multiplication is division, so dividing both sides of the equation will "undo", or cancel out the multiplication of 4. Dividing 4x by 4 will leave only x, while dividing 12 by 4 leaves 3. So the new equation becomes "x = 3". When you have x by itself on one side, you have now solved for x, and do not need any more steps.

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