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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
Why you accept the definition of Empty set?
For reasons similar to those which explain why mathematicians accept the definition of zero as a number.
It provides an identity for unions of sets, provides for closure of sets under taking complements.
What is the angle formed by the hands of a clock at 1021?
I like your question. The hour hand is 10/60 from vertical, which reduces to 1/6. Converting to degrees (there are 360 degrees in a circle), would mean 1/6 of 360, resulting in 60. 21 minutes from vertical is 21/60, but since degrees are 6 times more than minutes, the product of 21 and 6 is 126. The clockwise angle is therefore 60 + 126 = 186.
Since 186 is larger the a straight line, one might also answer that the angle formed on the Southwest side of the two hands is 174 (360 - 186). There are two angles formed by the hands in the circle.
What numbers 1 and 55000 are divisible by 3?
There are 18,333 multiples of 3 between 1 and 55,000. They are 3,6,9,12 and keep adding three until you get to 54,999.
1000 grams = 1 kilogram so 198 g = 198/1000 kg = 0.198 kg. Simple!
How many corfficients does -3x3 plus x2 plus 17 plus 6x4 have?
- 3X3 + X2 + 17 + 6X4
Three. I will put the coefficients in parentheses.
(- 3 )X3 + (1)X2 + 17 + (6)X4
=========================( remember, 1 is always an implied coefficient )
What are a score or more mathematical facts about zero?
Zero is sometimes known as nought, nil or nothing
Zero is a number in its own right
Zero is the freezing point of water in Centigrade
Zero is an even number because it's between 2 odd integers
Zero reduces any number to 1 when raised by its power except itself
Zero is essential in the Hindu-Arabic numeral system
Zero tells us that there is a difference between 23 and 203
Zero is needed for positional place value purposes
Zero percent is 0%
Zero or any other integer is the beginning of a decimal number
Zero and 1 form the binary system
Zero is not a prime number
Zero is not a composite number
Zero 3 figure bearings are 000 which is North
Zero as a Roman numeral is N which in Latin is nihil meaning nil
Zero coordinates on the Cartesian plane are (0, 0) which is the origin
Zero it can be argued is the centre of infinity on the number line
Zero means an event will not happen in probability
Zero originated from the Indian subcontinent
Zero was used by the ancient Mayans but looked quite differently
Zero isn't needed in the ancient Roman numeral system because the positional place value of the numerals are self evident
QED by David Gambell
What are 26 geometrical properties each being in consecutive order of the alphabet?
Examples are as follows:-
Alternate angle
Bisector
Circumference
Diameter
Exterior angle
Face
Ground
Hexagon
Interior angle
Junction
Kite
Line segment
Mid-point
Nonagon
Octagon
Parallelogram
Quadrilateral
Rectangle
Square
Triangle
Undecagon
Vertex
Width
X- axis
Y-axis
Zone
* * * * *
You can look up these or more terms at the attached link.
Unfortunately, the browser used for posting questions is hopelessly inadequate for mathematics: it strips away most symbols. All that we can see is "...find Th and Th derivative of y - five cos (twox) ...". From that it is not at all clear what the missing symbols (operators) might be. I am guessing that you want the nth and (n+1)th derivatives of something like y = -5*cos(2x). I am also assuming that you are familiar with the chain rule for finding derivatives. Finally, this browser is also rubbish and I cannot show superscripts so I will use the ^ symbol to represent powers..
y = -5*cos(2x)dy/dx = -5*[-sin(2x)]*2 = 2*5*sin(2x) d^2y/dx^2 = 2*5*cos(2x)*2 = 2^2*5*cos(2x)d^3y/dx^3 = 2^2*5*[-sin(2x)]*2 = -2^3*5*sin(2x) d^4y/dx^4 = -2^3*5*cos(2x)*2 = -2^4*5*cos(2x) = 2^4*y
So,for n = 1, 5, 9 ... [n = 1 mod(4)]: d^ny/dx^n = 2^n*5*sin(2x) = 2^n*5*cos(pi/2 - 2x)for n = 2, 6, 10 ... [n = 2 mod(4)]: d^ny/dx^n = 2^n*5*cos(2x) = -2^n*y
for n = 3, 7, 11 ... [n = 3 mod(4)]: d^ny/dx^n = -2^n*5*sin(2x) = -2^n*5*cos(pi/2 - 2x)
for n = 4, 8, 12 ... [n = 0 mod(4)]: d^ny/dx^n = -2^n*5*cos(2x) = 2^n*y
q = k*r^3/(s*sqrt(t))
Why is a math variable a lowevercase letter?
Sometimes it is, sometimes it is not. There is no rule or even a convention, about it.
What is another set of values the helps describes variability in a data set?
The word "another" in the question implies that you already have one or more set of values in mind. However, you have not chosen to share that information. It is, therefore, impossible for me to know whether the answer that I suggest is already one that you know of or a new one.
The word "another" in the question implies that you already have one or more set of values in mind. However, you have not chosen to share that information. It is, therefore, impossible for me to know whether the answer that I suggest is already one that you know of or a new one.
The word "another" in the question implies that you already have one or more set of values in mind. However, you have not chosen to share that information. It is, therefore, impossible for me to know whether the answer that I suggest is already one that you know of or a new one.
The word "another" in the question implies that you already have one or more set of values in mind. However, you have not chosen to share that information. It is, therefore, impossible for me to know whether the answer that I suggest is already one that you know of or a new one.
It is 12 feet tall - as stated in the question!
Prime Factorization:
72= 2x2x2x3x3
44=2x2x11
GCF: 2x2 =4
LCM: 2x2x2x3x3x11=792
Nope. The Ancient Greeks were trying to find the ratio of circumference to area.
9729 is evenly divisible by 9. 9729 divided by 9 equals 1081.
What are the rules for integration?
There are a lot of rules for integration! Plus a lot of techniques!
Here is the power rule as a simple example.
int[Xn dx]
= (Xn + 1)/(n + 1) + C
( n does not equal - 1 )
