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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 does 2d in maths mean?

2d means 2 dimensional or flat figures. If you are dealing with algebra or graphing, it would mean X and Y coordinates only, not Z.

What might be the advantages of using the archival method?

to storge the method in until a later day .tat way it give the man time to think about what is being said before answering the question.

What is the relation between ordinary differentiation and partial differentiation?

in case of partial differentiation ,

suppose a z is a function of x and y

so in partial differentiation of z w.r.t x all other variables except x are considered to be constant

but on the contrary in differentiation process they are not considered as constant unless stated .

Why do most Americans put a much higher value on looks than on intellect?

That is a generalization that is not neccessarily true. This is an assumption that everyone feels, acts, or thinks the same. Not everyone puts a higher value on looks. In today's society, people who place a higher value on looks are the ones that were never taught any better. I personally would much rather spend time with someone who uses their brain than with someone who is easy to look at.

What is the minimum number of guesses needed to find a specific number if you are given the hint higher or lower for each guess you make?

Assuming that you want to discount luck (if not, the answer would be 1), and that the guesser always guesses the median of the remaining range, the answer would be the (ceiling of the log(base 2) of the count of numbers in the range). If the log(base 2) is an exact integer, add 1.

Example 1, pick a number between 1 and 9. There are 9 numbers in the range, so the log(base2) of 9 is ~3.16. The ceiling of that is 4. Do not add 1 for a final answer of 4.

The full range is 1,2,3,4,5,6,7,8,9. The median is 5

First guess is 5. Higher - 6,7,8,9 is remaining range. 7 and 8 are the median numbers

Second Guess is 8. Lower - 6,7 is the remaining range. 6 and 7 are the median numbers.

Third guess is 7. Lower - 6 is the remaining range. 6 is the median number

Fourth guess is 6. Correct.

Example 2, pick a number between 1 and 16. There are 16 numbers in the range, so the log(base 2) of 16 is 4. The ceiling of 4 is 4. Add the 1 because the Log(base 2) is an integer, for a final answer of 5.

Full range is 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16. The median numbers are 8 and 9.

First Guess is 9. Lower - 1,2,3,4,5,6,7,8 is the remaining range. 4 and 5 are the median numbers

Second Guess is 4. Higher - 5,6,7,8 is the remaining range. 6 and 7 are the median numbers.

Third Guess is 6. Higher - 7,8 is the remaining range. 7 and 8 are the median numbers.

Fourth Guess is 7. Higher - 8 is the remaining range. 8 is the median.

Fifth guess is 8. Correct

Both of these examples show worst case scenarios. A "lucky guess" will reduce the number of guess needed, possibly all the way to 1.

Note: I do realize that to a math purist, in the examples where I said that the median numbers were x and y, the correct answer is that the median number is between x and y. Since I can not guess the number between the two numbers, I am bending the definition of median to treat the two bordering numbers as the median when the strict definition would list the median as being between those two numbers.

How do you cal 15 percent?

Calculating percentages is easy enough when you get the hang of it but here's a simple method that requires little to no thinking; I'll divide the process in easy steps:

1. Round up your bill to the nearest even dollar amount. An example of this would be to round a 27.59$ check total to 28$.

2. Take the 28$ (the amount of the rounded number) and divide that number by two. In our case, 28$/2 is 14$.

3. Add the two numbers together (in our case, 28+14 --> 42) and add a zero to it. 42 becomes 420.

4. Convert the result from Step 3 (the 420) to dollars/cents by placing a decimal in front of the last two numbers. In our case, 4.20$.

This is roughly 15% of the original 27.59$. And that's all there is. Of course, there are multiple methods to attaining the 15%, some that are less lengthy, but this one is most likely the easier one out of them all.

Mean 5 minutes longer than half the time?

Placing a question mark at the end of a phrase does not make it a sensible question. Try to use a whole sentence to describe what it is that you want answered.

How much drop PER FOOT needed for 300' of pipe?

Drop per foot doesn't care about length of run, it depends on pipe size. Pipe larger than 2" needs only 1/8" per foot (37.5" fall for 300'), 2" and smaller needs 1/4" per foot (75" fall for 300')

What is averaging principle?

In a perturbed system, writing the equations of motion in a form where the contribution of fast variables is replaced by their average on the corresponding invariant torus.

What part of a circle does the arrow represent when it is in the middle?

it represents the radius because radius is half the diameter and diameter is across the whole circle

What are the measurements for a 7ft pool tableSpecifically the baulk line D circle.?

For a 7-foot pool table, the baulk line is typically located 29 inches from the head cushion. The D circle, which is centered on the baulk line, has a diameter of 11.5 inches. This means the radius of the D circle is 5.75 inches, with the center point of the D positioned at the midpoint of the baulk line.

Why discrete Fourier transform is used in digital signal processing?

The Discrete Fourier Transform (DFT) is used in digital signal processing to analyze the frequency content of discrete signals. It converts time-domain signals into their frequency-domain representations, enabling the identification of dominant frequencies, filtering, and spectral analysis. By efficiently transforming data, the DFT facilitates various applications, including audio and image processing, communication systems, and data compression. Its computational efficiency is further enhanced by the Fast Fourier Transform (FFT) algorithm, making it practical for real-time processing tasks.