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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 locus equidistant from ab which are 6 inches apart and also five inches away from a?

Points equidistant from AB lie on its perpendicular bisector. Points 5 inches from A lie on the circle with centre A and radius = 5 inches. You will have two points where the perp bisector and circle intersect.

What angle the gun can fire the maximum range?

Theoretically, ignoring air friction, 45 degrees. But that also depends on muzzle velocity. If you can fire a projectile at a speed great enough, it would become an orbiting 'satellite' if fired parallel to the ground.

How do you calculate the explicit formula and the nth term of the Fibonacci sequence?

(1/sq rt 5)((1+sq rt 5)/2)n - (1/sq rt 5)((1-sq rt 5)/2)n

This is based on the golden ratio (1+sq rt 5)/2) because the ratio of 2 Fibonacci terms approaches the golden ratio as the 2 terms used get larger. IE the ratio ot the 10th term to the 9th term is 55/34 = 1.61765 and the golden ratio is approx. 1.61803.

When using this formula if your calculator does not round, you will round to get the appropriate Fibonacci number.

How many grams does an empty water bottle have?

The answer depends on how big the bottle is and what material it is made of.

What is a statement that is always true forwards and backwards?

A bi-conditional statement can be true or false. If it is true, then both forward and backward statements are true. See Bi-conditional Statement


In English grammar

The statement, Love you! could be true too if said/written backward as You love!

What is the next number 2 7 26 101 400?

2 x 4 -1 =7

7 x 4 - 2 = 26

26 x 4 - 3 = 101

101 x 4 - 4 = 400

400 x 4 - 5 = 1600 - 5 = 1595

So, the next number is 1595

What is optimal feasible solution?

It is usually the answer in linear programming. The objective of linear programming is to find the optimum solution (maximum or minimum) of an objective function under a number of linear constraints. The constraints should generate a feasible region: a region in which all the constraints are satisfied. The optimal feasible solution is a solution that lies in this region and also optimises the obective function.

How do you prove that a finite set of points cannot have any accumulation points in a real analysis?

If you have a finite set of points (call them A1, A2, A3...), then you have a finite set of distances to the points.

So for any point B, simply pick a distance D that's smaller than the distance between B and A1, the distance between B and A2, and so on. (This is possible, since there a finite number of points.)

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Since there are no points within distance D of B (because this is how you chose D), point B can not be an accumulation point (because an accumulation point must have points within any given distance of it)

What is the sum of the square roots of 100 and 225?

The square root of 100 = 10

The square root of 225 = 15

The sum = 10 + 15 = 25

What is 48 over 110 simplified?

To simplify 48 over 110, you first need to find the greatest common divisor of the two numbers, which is 2. Divide both the numerator and the denominator by 2 to get 24 over 55. Therefore, 48 over 110 simplified is 24 over 55.

What is the pattern 1 3 9 27 81?

xi+1 = 3 xi

x1 = 1

x2 = 3 x 1 = 3

x3 = 3 x 3 = 9

x4 = 3 x 9 = 27

x5 = 3 x 27 = 81

Is infinity a prime or composite?

Infinity is not a number. It cannot be graphed nor placed onto a number line.

Infinity is an idea, a prospect.

So the answer is "none"

since Infinity isnt a number.

How do you say 900000000?

Nine Hundred Million or,

Nine Zero Zero Zero Zero Zero Zero Zero Zero, or

Nine followed by eight zeroes.

What does transform do?

Transformers are an important part in the electrical distribution network. They step up or step down electricity.