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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 do the numbers 68 77 59 95 86 1094 have in common?

They are all part of a larger set of numbers defined by the pattern of adding nine to the previous number in ascending order.

Is a ratio the same as division?

No. A ratio is calculated using division but they are not the same thing.

What are the limitations of operation research?

  • Dependence on an Electronic Computer: O.R. techniques try to find out an optimal solution taking into account all the factors. In the modern society, these factors are enormous and expressing them in quantity and establishing relationships among these require voluminous calculations that can only be handled by computers.
  • Non-Quantifiable Factors: O.R. techniques provide a solution only when all the elements related to a problem can be quantified. All relevant variables do not lend themselves to quantification. Factors that cannot be quantified find no place in O.R. models.
  • Distance between Manager and Operations Researcher: O.R. being specialist's job requires a mathematician or a statistician, who might not be aware of the business problems. Similarly, a manager fails to understand the complex working of O.R. Thus, there is a gap between the two.
  • Money and Time Costs: When the basic data are subjected to frequent changes, incorporating them into the O.R. models is a costly affair. Moreover, a fairly good solution at present may be more desirable than a perfect O.R. solution available after sometime.
  • Implementation: Implementation of decisions is a delicate task. It must take into account the complexities of human relations and behaviour.

How big is 16mm x 14mm?

1.Solve for Area

A = length x width

A = 16mm x 14mm

A = 224(mm x mm)

A = 224 mm2 [square millimeters]

2. Convert from metric or SI(System International) to English.

224 mm2 = 2.24 cm2

[10 mm = 1 cm] [1o mm x 10 mm = 1cm x 1cm]

100 mm2 = 1cm2

{(1cm2/1oo mm2 )}

dividing by 1cm2/100 mm2 removes the mm2 because mm/mm = 1 making the unit cm2.

224mm2/100 mm2 = 2.24 cm2

Using a conversion chart: square cm x 0.155 changes value to square inches.

2.24 x 0.155 = 0.3472 in2

Place a quarter on a ruler to visualize 1 square inch,or place the quarter in the corner of a piece of paper as close to the top + side of the paper without going off, make 1 cut parallel to top edge below coin and another cut parallel to side edge on the other side of the coin,

set the ruler over the square piece so that the end closest to the one is even with any edge with the top of the ruler across the middle.

The left edge of square is 0 and the other edge should end about the large mark next to the 1.

The mark in the middle is the half-way point between 0 and 1.

Half-way between 0 and 1/2 is 1/4, between 1/2 and 1 is 3/4.

If you keep this up until there are 32 equal sections between 0 and 1 you can then count 11 of these of 11/32 of an inch and color either side of this mark. The smaller area is about 0.3472 in2 [ 11/32 in2 is 0.34375 in2

about the size of 16mm x 14mm!

What is the next number in the pattern 98 72 77 49 54 and 20?

Using the rule

Un = (-134n5 + 2335n4 - 15280n3 + 46295n2 - 64356n + 37020)/60 for n = 1, 2, 3, ...

the next number is -531.

What is tweleve plus the product of 9 and a number?

Product means multiply by.

Lets call our "any number" x

12 + 9 * x is normally written as 9x + 12

Is 3.3166247903554 a rational number?

No, it is irrational because the decimal goes on without repeating.

What times what equals 599?

Well, isn't that a happy little math problem you've got there! Let's see, to find two numbers that multiply to 599, we can break it down into its factors. After a bit of painting and calculating, we find that 23 times 26 equals 599. Just like painting a beautiful landscape, sometimes it just takes a few brushstrokes to reveal the answer.

How did you pronounce mixed number?

An example of a mixed number is: three and three quarters which is 3 and 3/4

What does the millions place mean?

The millions place of a base-ten number is the position of the seventh digit left of the decimal point.