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Rosie R.
8 years of tutoring math, one year away from my BS in Mathematics at Marquette University, and full of passion for helping others.
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Question:

I have a math test coming up on Friday (it is currently Monday). I don't feel prepared but I don't know where to even start studying. What do I do?

Rosie R.

Calculus
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Question:

What is optimization? And why does the derivative help with optimization problems?

Rosie R.

Optimization is a very practical application of calculus. We use it to design running tracks with the least amount of material that still meet the correct criteria. We use it to fit the full 12 ounces of soda in a can using the least amount of aluminum possible. Optimization is essentially making the most out of the bare minimum criteria. We learned previously that derivatives give the instantaneous slope of a graph. If the derivative is zero, we know the graph has leveled off and is likely changing directions. Previously we learned how to check if the point where the derivative is zero is a local maximum or minimum. Finding this max or min by taking the derivative of provided/derived mathematical models allows us to find dimensions or data regarding the best way to approach a situation.

Algebra
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Question:

I am given two equations and I need to determine if the two lines will intersect at any given point. If they intersect, I need to determine where they will cross paths. Where do I start? How can I check my work?

Rosie R.

To determine if two lines cross, you need to begin by finding their slopes. The slope of a line is the "m" in the point-slope equation: y = mx + b. If you are given an equation that fits the point-slope form, then you can determine the slope that way. For instance, in the equation, y = 2x + 3, the slope is 2. You may have to do some rearranging, for instance, if you have 10y = 20x + 3, you will have to divide everything by 10 in order to isolate y. If you are not given an equation, and you are simply given two points, you can calculate the slope. First decide which point is plotted further to the left. This will be your x1 and y1 values. The point furthest to the right will be your y2 and y1 values. The slope is rise (y-values; rise and y kind of rhyme, if that helps) over run (x-values). Calculate by doing (y2-y1)/(x2-x1). Once you determine the slopes, it is time to figure out if they are the same. If the slopes are the same numerical value, the lines are parallel and will never intersect. There is an exception. If the lines are exactly the same, they intersect at every point. If they are different, then set both equations equal to each other. For instance, y = 2x +3 and y = 4x + 9 can be rewritten as 4x + 9 = 2x + 3, and x = -3. This is the x-value where they intersect. Take x=-3 and plug it into either equation to figure out what the y-component of the intersection is.

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