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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
What is the probability that you will win if you buy one of 200 raffle tickets to win a television?
The odds are 1 in 200. The probability of winning is 0.005.
What is formula of differentiation?
The answer by Broad Way covers a very narrow range of situations. If f(x) is a function of x then the derivative of f(x) and this is defined asthe limit, as h tends to 0, of [f(x+h) - f(x)] / h, if it exists.
In graph form, [f(x + h) - f(x)] / h is the gradient of f(x) between the points at which the abscissa are x and x+h. As x+h comes closer and closer to x (ie as h tends to 0) the ratio tends to the gradient of the tangent to the curve f(x) at the point x.
Is the complement of a set is the set of all things that are in the set true or false?
false, because the complement of a set is the set of all elements that are not in the set.
What are 2 ways that you can multiply 18 x 34?
There are many ways and these depend on your fluency with number and their inter-relations.
For example, since I know that 17^2 = 289 so I would do
18*34 = (17+1)*(2*17) = 2*17^2 + 2*17 = 2*289 + 2*17 = 2*(289+17) = 2*306 = 612. Of course, I would not go through all those steps but they are shown there so that you may be able to follow.
An alternative would be to multiply 18 by 4 and 30 and then to sum the answers:
18*4 = 72, 18*30 = 540 and so the answer is 72+540 = 612.
This is equivalent to 18*34 = 18*(30 + 4)
Yet another method, attributed to Euclid is to halve the smaller number and double the other, ignoring halves, and keep going until the smaller number reaches 1.
18 ... 34
9 ... 68
4 ... 136
2 ... 272
1 ... 544
Then add together the larger numbers for which the left hand number is odd. Thus 68 + 544 = 612.
How do you calculate water volume in cylindrical tank while it's slant edge is rest on horizontal?
Volume = Area of cross section x height
Why zero divided by zero is not 1?
A division is the answer to a multiplication problem. For example:
(number) = 6 / 3
is the answer to:
2 times (number) = 6
What number do you have to replace here? There is exactly one solution, namely the number 3.
1 / 0 is equivalent to:
(number) times 0 = 1.
This has no solution.
0 / 0 is equivalent to:
(number) times 0 = 0
This has infinitely many solutions; any real number will work. However, in both cases (non-zero divided by zero, and zero divided by zero), it has been shown that dividing by zero causes lots of errors (for example, you can "prove" that 0 = 1; meaning, you can "prove" almost anything, if you carelessly divide by zero). Therefore, division by zero is usually not considered an acceptable operation, especially in pure mathematics.
What does it mean when people say you divided by zero?
It means that your not making any sense? Cause you can't divide a number by zero.
What are the factors and prime factors of 500 without the number 5 in it?
factors of 500 without 5- 1, 2, 4, 10, 20, 100
prime factors of 500 without 5 - 2, 2
What is mathematical phrase for a circle?
You can define a circle as the locus (set) of all points equidistant from a given point.
What is 2 over 3 times 2 over 3?
4/9. Get yourself 9 pennies. Now divide those into 3 equal parts. Remove one of those parts [1/3] and mix the remaining pennies [2/3] up. Now take those pennies and divide it into 3 equal parts. Remove one part [1/3 of those pennies]. You now have 4 pennies out of the original (9 pennies.) What is the rule that you could have used to come up with the answer without using pennies?
Play around with 12 pennies and do some fraction multiplications. See why there are so many old measuring systems based on the number 12 and not 10.
How are potential and mass related?
All matter has mass which is essentially a constant. Potential is a form of energy which a body may (or may not have) by virtue of its position or state and is often based on some arbitrary reference level.
What is the answer to the problem -24-25?
When you subtract a number from a negative number, the resulting answer answer is only more negative. To phrase the problem in words, what value is 25 less than negative 24?
So your answer is -49
How is discover the separations of variables?
I firmly believe that most brilliant ideas come from people just playing with things.
"Hmmm... what happens if I assume that the solution is in this form..."
When you subtract one square number from another the answer is 12 what are those numbers?
It is: 16-4 = 12
What is 52 with an exoponet of -3 simplified to?
Use the definition of negative exponents: that's the same as 1 divided by (52 to the power 3).
The measurements make for a very steep slide with a gradient of nearly 3.3! Anyway, given these measurements, the bottom of the slide needs to be attached approx 25.6 inches from the bottom of the tower.
If surface area is 624square meters how many 10cm by 10cm tiles are needed to cover surface?
1 cm = .01m so were looking at 624 sq. m covered by blocks with area .01 sq. m. Divide 624 by .01 and you get 62400 tiles.
How many meters cubed are in one foot cubed?
1 ft = 0.3048 m
1 ft3 = 1 ft x 1 ft x 1 ft
= 0.3048 m x 0.3048 m x 0.3048 m
≈ 0.0283 m3
What represents thefffffffffffff difference between two equal fractions A 1 B 1 half C 1 fourth D 0?
Choose D. Anything minus itself equals zero.
