It was fun to mess around with the arduino to find what changed the pitch and frequency of the siren. When we changed the value of 1000 in the tone value, the bigger the number, the higher the pitch was created. Also, multiplying sine by a larger number, the pitch would change too. Changing the delay would make the siren go for a longer period of time, or a shorter period of time, depending on the number. When the delay is longer it sounds more like an ambulance, but when it's shorter it can sound like a bunch of treefrogs. After awhile, it gets really annoying and all you hear for the next few hours is the high-pitched whine of the sirens. It's a great time. https://drive.google.com/a/slsharks.net/#shared-with-me
After making this unit circle, it made my life SO much easier on Kahoot. For example, if you needed to find the sine of 30 degrees, you look at the circle to where 30 is marked and look at the y-coordinate. To find the cosine of an angle, you have to find the angle and use the x-coordinate. Lastly, the tangent of an angle is equal to the sine (y-coordinate), divided by the cosine (x-coordinate). Having the number of degrees and the radians also makes it much easier to solve questions because you can just look at the unit circle and it has the the radians and degrees right next to eachother.
There are several different types of loans you can get when it comes to paying for college. There are private loans (from banks/credit unions), and government loans, which can be subsidized or unsubsidized. Government subsidized loans mean that you don't have to pay the 3.86% interest rate until after you graduate. Unsubsidized means that you pay interest while you are going to school, which is also set at 3.86%. A big advantage to government loans is that the interest rate is much lower than private loans, but the money is strictly for college use. When you get a private loan, the interest rate is higher, but can be used for more than one thing. If I were to get a $5000 subsidized loan for all 4 years of college, I would owe $20000 and have to pay 3.86% interest after I graduated. If I chose to pay off the loan in 10 years, the equation for this would be A= 20000( 1+.0386)^10. "A" would then equal $29,208.76 and when divided by the number of months in 10 years (120), would give me the amount of money I would pay my student loan back per month, $243.41.
After doing all the math, we discovered it would hypothetically take about 42 folds to reach the moon. This is unrealistic because it is hard to fold a normal paper more than 6 or 7 times. The stack would be SO extremely small that it would be hard to see!
A limit is the number that you approach from either the left or the right on a graph and get arbitrarily close to that number, but never reach it. A limit only exists if both sides of that limit are approaching the same number. For example, if F(x)= (x^2+x-6)/ (x-2), the function has a limit of two because the graph approaches 2 from either side and only comes arbitrarily close. They help explain points of discontinuity on a graph by showing what the function is approaching on both sides of the discontinuity. With all of this said, I strongly dislike limits.
There are a few connections between factors and zeros. Factors are the inverse of what the zeros. For example if the factor is (x+2)(x-3)(x-4), the zeros would be x=-2, x=3, and x=4. By using long division or synthetic division, we are able to find the zeros that aren't easy to find using the graphing technique by giving us a quadratic equation to solve. The degree of a polynomial actually gives you the number of the zeros you're looking for. f(x)=x^4-9x^3+18x^2+32x-96 shows us that we only need to find 4 zeros, and often when graphed, you can get the easy zeros first. The degree of the polynomial also gives us the number of factors there is going to be also. If there is 4 zeros, there is going to be 4 factors because they are inverse to eachother.
The graph looks this way due to the piecing together of three different functions. I had to find the equation of each of the lines before I graphed them to find the equation of the graph. y=-2x+2 is the equation for the line X < 0 or equal to zero also. If 0 < x < 2, then the equation for the quarter circle would be y= the square root of 4-x^2. The equation for the final part of the graph is y= (x-2)^2 if x > or equal to 2.
I think that the ball will not go in the hoop. It will most likely hit the back of the hoop and bounce back towards Mr. Cresswell.
Today in this activity, I found the inverse of y=x^2 by switching the x's and y's first. Then I took the square root of each side and was left with positive and negative square root of x. I took note that once I graphed both the positive and negative inverses of the equation, it looked like the function had been turned on its side. I didn't realize that that the inverse of the function was reflected over both the x and y axis. I also didn't think that folding the paper along the function y=x would make them line up almost exact. Although this function didn't have an inverse that was also a function, other functions can have inverses that are also functions. For example, the function y=x has an inverse that is also a function because it passes the vertical line test.
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