The Fibonacci Sequence refers to the sequence of numbers in which each number is equal to the sum of the two previous numbers. This sequence is used in several movies, including Pi by Darren Aronofsky and The Da Vinci Code by Dan Brown.
Asymptotes and holes are equations in which the line on a graph gets very close to a specific line without touching it. Both asymptotes and holes make the bottom of a fraction 0 to find the line on the graph. However, asymptotes do not cancel out the top of the fraction, where holes are pieces of the equation that are the same on the top and bottom of the fraction. These cancel out and create a gap in the line on the graph.
To reduce the square root of 500 using Mr. Kelly's method, the first step is using the half-box containing the number 500. Then the smallest number that goes into 500 is placed outside the half-box, which 500 is divided by. the new number is placed in a new half-box, and this process continues until the number 1 is reached. Next, each pair of numbers is circled. In this case, there is a pair of 2's and a pair of 5's, with one 5 left over. The two pairs are multiplied together to get 10, which is placed out to the front of the answer. The unpaired number, 5, is placed inside the square root symbol, giving us the answer of 10 square roots of 5. This method works because it can always be multiplied out to receive an accurate answer and is a simple way to reduce square roots. For math purposes this answer is better than a calculator because calculator answers completely solve the equation and you're left with a long decimal number. However, this is very useful when looking for a concrete number, such as in science class.
To find the inverse of a function, the X's and Y's in and equation trade places. To verify that two functions are inverse, you solve the equations. An example of an inverse that is a function is
X^y*X^z=X^yz is sometimes true. For instance, if y=3 and z=5, the answer would be X^8 because the exponents are added together. However, if y and z equal 2, added and multiplied together they equal 4. Therefore, this equation is only true if the numbers are the same when adding and multiplying them together.
Quadratic equations are equations in the format ax^2+bx+c. Ax^2 represents the quadratic term, bx represents the linear term, and c is the constant term. The graphs for these equations will always look like a U or an upside-down U.
One way to solve quadratic equations is by graphing. Taking the equation x^2+6x+8 and plugging it in give two solutions, -2 and -4, as shown by the graph below. Another way to solve quadratic equations is by factoring. Using the same equation, we must find two numbers that can be multiplied together to equal 8 and added together to equal 6. (x+2)(x+4) can be foiled out to check the work, and it equals our original equation. Because this equation is assumed to be set equal to 0, to find what x equals each parenthesis must be set equal to 0. If the first one, x+2, is equal to zero, then subtracting 4 from each side will result in one answer. When x+4=0, x=-4. The third way to solve quadratic equations is by completing the square. Using the same equation, we first subtract 8 from each side. Then, to complete the square, divide the 6 by 2. Take the quotient, square it, and add the number to each side. Now our equation(x^2+6x+9=-8+9) can be factored out. (x+3)^2=1. Square root each side to get rid of the exponent. Taking the square root of a variable makes it either plus or minus the number, so the equation is x+3=(+or-)1. Now the equation can easily be solved. x+3=1. Subtract 3 from each side and x=-2. In x+3=-1, subtract 3 from each side to get x=-4. The final method is solving using the equation x=-b(+or-) the square root of b^2-4(a)(c) all over 2a. If a=1, b=6, and c=8, then the equation is x=-6(+or-) the square root of 36-4(1)(8) all over 2(1). Simplify to get x=-6(+or-) the square root of 4 all over 2. The square root of 4 is 2. Everything in the equation is divisible by 2. x=-3(+or-)1. x=-3+1 is -2 and x=-3-1 is -4. To factor the equation x3+3x2-54x, only two steps need to be taken. First, each term is divided by x to reduce the number of variables, and x is placed out front of the equation, which now looks like this: x(x2+3x-54). The second step factors the equation further. We're trying to get two numbers that can be multiplied together to equal negative 54 and be added together to equal 3. These two numbers are -6 and 9. Now our equation is as follows: x(x-6)(x+9). We can distribute and FOIL our solution to check our answer. Factoring and solving are related because they're both taking an equation and breaking it down to get a more simple answer. Solving and equation includes factoring. Boom. I'm out.
1. When a positive number is added, the line starts higher on the y axis.
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April 2015
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