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Mathematical Analysis
Mathematical analysis is, simply put, the study of limits and how they can be manipulated. Starting with an exhaustive study of sets, mathematical analysis then continues on to the rigorous development of calculus, differential equations, model theory, and topology. Topics including real and complex analysis, differential equations and vector calculus can be discussed in this category.
2,575 Questions
How many electrons would fit in the universe?
somewhere around 4*10^184 planck cubes could fit in the obervable universe and those are a lot smaller than electrons. So that number would be somewhere between a googol and this number.
What is the difference between a 'dot product' and a 'cross product'?
Given two vectors, a and b, their dot product, represented as a ● b, is equal to their magnitudes multiplied by the cosine of the angle between them, θ, and is a scalar value.
a ● b = ║a║║b║cos(θ)
Cross Product:Given two vectors, a and b, their cross product, which is a vector, is represented as a X b and is equal to their magnitudes multiplied by the sine of the angle between them, θ, and then multiplied by a unit vector, n, which points perpendicularly away, via the right-hand rule, from the plane that a and bdefine.
a X b= ║a║║b║sin(θ)n
What are the intervals in a coordinate graph?
They depend on what is being graphed and in the level of detail of the information.
The S transform in circuit analysis and design is method for transforming the differential equations describing a circuit in terms of dt into differential equations describing a circuit in terms of ds. With t representing the time domain and s representing the frequency domain.
Usually the writing of the time domain equations for the circuit is skipped and the circuit is redrawn in the frequency domain first and the equations are taken directly from this transformed circuit. This is actually much simpler and faster than transforming the time domain equations of the circuit would be.
The S transform and Laplace transform are related operations but different; the S transform operates on circuits and describes how they modify signals, the Laplace transform operates on signals.
Is the union of disjoint sets is always the empty set?
No, only if both sets are empty. The intersection of disjoint sets is always empty.
How many inches is 2 feet and 6 inches?
2 feet = 2 feet x12 inches = 24 inches
24 inches + 6 inches = 30 inches
Yes.
You also need to know the business case, the cost of raw material, the production costs, the benefit to consumers, and about a hundred other factors.
You also will need to factor in new technology breakthroughs. In the 1980's, the desktop computers were less powerful than today's hand held calculators and cost well over $10,000.
However, if you just look around you, you will see how we have benefited from science and technology over the years. Don't you know, the cell phone is less than forty years old? And the first ones were big cumbersome suitcase phones. That is just one of hundreds of examples of scientific breakthroughs that are benefiting us today.
Loci of a point: -First, draw a point/dot anywhere -Then, decide the distance from the point to the other points (5cm) -Mark 5cm above the first point. -With your compass, place the sharp part on the first point, and the pencil on the second point. Draw a circle, and there! That's the loci of a point.
What is 15 over 9 in simplest form?
15/9=5/3
How: 15/9 divide top and bottom by a number
Number=3 15 divided by 3= 5
9 divided by 3= 3
What is 60 years of a century in decimal form?
60 years of a century in decimal form would be 0.60 of a century.
How far do you walk in a half hour at medium pace?
FYI I asked this question but I want to add that the half hour walk is on flat terrain, asphalt actually and I am 5'5" and 250 lbs (which is why I've been walking, usually longer but I'll take any walking I can get) if that factors in at all. Thanks for any help!
Time and a half pay on national holidays?
Most places do pay time and a half, some have a set amount of extra pay for holidays, while others pay at the same rate. There is no legal obligation for a private company to pay any kind of holiday pay, just a moral and social obligation.
Euler's dilemma is based on the seven bridges of Konigsberg. The question was could one start at one point and return there having cross each bridge once and only once. The answer, as Euler proved, was No.
This question has important consequences for graph theory and, later, for topology. A popular version of the dilemma was to draw figures without lifting pen from paper.
For more on the Bridges of Konigsberg, see the attached link.
