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Pre-Calc Blog

If you took out $20,000 in student loans, and were able to pay $125.99 a month, you could pay your loans off in 20 years, assuming the loans were either direct subsidized or direct unsubsidized. In total, you would end up paying $30,237.60. The interest rate I used for this post was 4.45%, but if I had used another interest rate, the total amount of money you'd pay would either increase or decrease, depending on if he rate was higher or lower than the one used. It was surprising to me that it can take 20 years to pay off $20,000, even if you're paying $126 a month. I knew that loans took a long time to pay off, but I guess I never really knew how long. Interest rates also make a bigger difference that I had thought. I hadn't realized that they would beef the price up so much. This project definitely changed my views on loans. I will certainly be careful when taking out loans, because they can take a while to pay off.

Factors and Zeros and very closely connected. You can even say that factors are basically zeros! Division helps us to factor polynomials by allowing us to remove the easy-to-find zeros, the ones you can get from the graph. You can then use synthetic division to find the more hidden zeros (and thus find the factors). The degree of the polynomial helps us to find the zeros of the polynomial because the number of zeros matches the highest degree of the polynomial! This is a good way to find the factors of the polynomial, as the factors are essentially the zeros!

Even functions are functions in which f(x) is equal to f(-x). They have y-axis symmetry. Odd functions are functions in which f(-x) is equal to -f(x). They have origin symmetry. Both functions have a form of symmetry, but the type depends on whether the function is even or odd. You can check algebraically (does f(x) equal f(-x), f(-x) equal -f(x), or neither). You can also check graphically (y-axis symmetry, origin symmetry, or neither). Function families that are even are parabolas and lines. One that is odd is cubed root.I don't really have any questions from this assignment. It all more or less makes sense to me.

My predictions were fairly close to the actual graph, however there were obviously some discrepancies, as you can see. As to what reasoning lead me to my graph predictions, all I can say was I looked at the angle and made my best guess.The zeros of the graph represent the point then the skateboard is no longer moving in the air. In all three graphs, the zeros are all obviously in the same place at the start (0,0), and when they finish, they are very close to the same spot as each other, too. The maximums and minimums vary, because the ramps are different heights, and thus the skateboard will have a different trajectory.The graphs rise the fastest when the skateboard is approaching the top height of its jump, as this is when its height is increasing the quickest. It is falling the fastest as it finishes its height climax, as this is when its height is decreasing the quickest.​'

​"Every morning, during summer camp, the youngest boy scout has to hoist a flag to the top of a flag pole."

​Graph A would mean that the boy scout is raising the flag at a steady rate. Graph B would mean that he raises the flag quickly at first, but more slowly as time goes on. Graph C means that the boy scout raised the flag at a non-constant rate, sometimes going more quickly than others. Graph D shows that the boy scout raises the flag slowly at first, and then more quickly as time goes on. Graph E shows that he raises the flag slowly, then very quickly, then slowly again. Graph F would mean that the boy scout raised the flag the length of the pole all at once. Graph A seems to be the most realistic of the six, because as time goes on, the flag goes up. Raising a flag doesn't seem to be a very challenging thing to do, so it seems most likely that he would do so at a constant rate over time. He could have realistically raised the flag as B, C, D, or E show as well, but graph A seems to be the most logical. The least realistic graph would be F. That graph shows that the flag has essentially been teleported to the top of the pole. It shows that the boy scout has raised he flag to the top in no time, which is impossible.