So, F + V − E = 7 + 8 − 13 and the answer would be 2 which is the expected outcome. Another way to prove the formula does not work for all solids is to take a Icosahedron and connect 2 opposite corners. Joining both corners, the solid will be a Icosahedron but it is not a convex polyhedron. As the soild is not a convex polyhedron should not be 2. So, F + V − E = 20 + 11 − 30, getting the answer as 1 which proves the generalisation F + V − E = 2 does not work.
A polynomial has been completely factored only if all of its factors are linear or irreducible quadratic. Whenever polynomial are factored into only linear and irreducible quadratics, it has been factored completely since it can’t be factored further over real numbers. For example, when we have n degree polynomials as such function below: p(x) = axn + bxn-1 + ……k The Fundamental Theorem of Algebra will tell us that this n degree polynomials are going to have n-roots or in other way of seeing it, the n value of x will make the expression on the right to be equal to 0. 2. History of root finding The history of root finding dates back during the Islamic Golden Age.
1. INTRODUCTION Snowflakes, feathery ice crystals that typically display a delicate six-fold symmetry might be the most distinguished mathematical art in the world, from the center of the snowflake, to the outskirts of their anatomy. When inspected, one notices that the different limbs of the snowflakes are mathematically constructed of fractal triangles. With that said, the aim of my exploration is to generate an equation that will aid me in representing a snow flake of any size, in order to do so I would need to explore specific areas of mathematics such as: symmetry, graphical representations, sequences and series and many more. As a consequence I will be focusing on the mathematical concept of: fractal triangles, in order construct my
1.2.2 Rational numbers All the numbers that we use in our normal day-to-day activities are called Real Numbers. Real numbers are: Positive integers (1, 2, 3, 4, etc.) Fractions (1/2, 2/3, 1/4, etc). [The integers are really forms of fractions (1/1, 2/1, 3/1, etc.)] Negative numbers (-1, -3/4, etc.)
He determined that there was a finite amount of positive integers less than any given positive integer, which led to the proposition famously known as Fermat’s Last Theorem. In modern notation, this contends that if a, b and c are integers greater than 0, and if n is an integer greater than 2, then there are no solutions to the equation: an + bn = cn  . For instance, when n is equal to 1 or 2 there exists an infinite amount of integer solutions to the above equation. However, for n greater than or equal to 3, there are no natural numbers for which the statement is true. This equation could also be interpreted as a more general version of the Pythagorean Theorem, as both are concerned with the sums of squares of whole numbers.
Error of Kurtosis .468 .468 The table shows that the in the data set, the GPA variable is a left skewed distribution of -.053 and a left kurtosis of -.811. The final variable indicates that the left skewed distribution stands at -.334 and a left kurtosis of -.334. Section 3: Research Question, Hypotheses, and Alpha level Research Question: Is there a relationship between the performance at the GPA and the final? Null Hypothesis: There is no difference between the GPA performance and the final. On the Asymptomatic significance test, the significance level is 0.05.
There is no linear relationship between X and Y, and the best-fit line is a horizontal line going through the mean of all Y values. When R2 equals 1.0, all points lie exactly on a straight line with no scatter. Knowing X lets you predict Y perfectly. (http://www.graphpad.com/guides/prism/6/curve-fitting/index.htm?r2_ameasureofgoodness_of_fitoflinearregression.htm) In this graph the R2 value is 0.97 which can be rounded off to 1.0 which means that knowing X which in this case is the different concentrations of sodium thiosulfate, predicts the Y which is the time the time the solution turns cloudy resulting X not to be seen from the opening of the conical flask from a person’s eye
I had many fun experiences in 8th grade. Although I am very excited to move on to highschool, I will miss 8th grade as well. I learned many things in 8th grade. I learned a lot about U.S. history and I found physics very interesting. Algebra and Spanish, the two high school classes that I took this year were quite challenging but very rewarding.
It can be depicted with the usage of Cantor's diagonal argument that for any infinite list of numbers in the interval [0,1] number will always occur in [0,1] , that are not included in the list. An uncountable set is also, at times referred to as