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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
Prime Factorization of:
41 = 41
26 = ........2 x 13
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LCM=41 x 2 x 13 = 1066
Will painting the glass covering a coil of PVC pipe with black paint reduce the heating efficiency?
The glass covering on what?
How many cubic meter of gas when compressed makes one kilo gram by weight?
Depends on the density of the gas.
What does it integers mean in algebra?
Counting numbers are 1,2,3....
If you include 0 and the opposites .... -3,-2,-1, 0,1,2,3 .... this creates the integers.
Integers do not include decimals or fractions.
Is every real number a whole number?
No. Real numbers are equivalence classes of cauchy sequences of rational numbers, which in turn are equivalence classes of pairs of integers (or whole numbers). Examples of real numbers that are not rational and therefore not integer are sqrt(2) and pi. Examples of real numbers that are rational but not integer are 1/2 and 13/17.
How many ways can you make twelve cents with coins?
There are several countries that use cents as a minor currency unit and they use different coinage. It is, therefore, not possible to answer the question without knowing which country it refers to.
What property of multiplaction allows you to break a problem into partial products?
distributive property, and substitution property.
EX: 42 x 20 = (40 + 2) x 20 = (40 x 20) + (2 x 20)
What shapes can an triangle be divided?
By a single straight line only into triangles or quadrilaterals.
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))
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 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!
