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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 distributive property when multiplying polynomials?
You just multiply the term to the polynomials and you combine lije terms
tissue paper covered in sticky tape and put newspaper over it and paint it white it could look like a bandage but it could hurt. Or you could get paper rip it into strips put it into a bucket add water and glue and cover it where you want it.
What is the definition of profit and loss in mathematics?
Profit:If the selling price(S.P.)of an article is greater than the cost price(C.P.), the difference between the selling price and cost price is called a profit.
loss:If the selling price (S.P.) of an article is less than the cost price(C.P.),the difference between the cost price and selling price is called loss.
What is Godel's incompleteness theory?
Gödel's incompleteness theorem was a theorem that Kurt Gödel proved about Principia Mathematica, a system for expressing and proving statements of number theory with formal logic. Gödel proved that Principia Mathematica, and any other possible system of that kind, must be either incomplete or inconsistent: that is, either there exist true statements of number theory that cannot be proved using the system, or it is possible to prove contradictory statements in the system.
What does 1.2 million dollars mean?
1.2 million dollars is 12 hundred thousand dollars. In other words, it is one million two hundred thousand dollars. ($1,200,000)
The government will get 522,659.55 of it in taxes , leaving you with 677,340.45.
The derivative of a function, df/dx, is to single variable calculus as the gradient of a function, ∇f, is to multivariable calculus.
If f is a function of three variables, x, y, and z, then the gradient of f is the vector function ∇f(x, y, z) = <∂f/∂x(x, y, z), ∂f/∂y(x, y, z), ∂f/∂z(x, y, z)>
All of the uses of derivatives in single variable calculus are analogous to the uses of gradients in multivariable calculus:
In single variable calculus the derivative tells us the instantaneous rate of change at some point, [x, f(x)]. In multivariable calculus, the gradient of a function tells us the instantaneous rate of change at some point, [x, y, f(x,y)], or if the function is of more than two variables, ∇f would tell us the instantaneous rate of change at a point [x, y, z, ….., f(x, y, z, ….)]. One Important difference in calculus of more than one variable is that a function can have many different rates of changes at one point. To understand why this is so, imagine that you are standing on a hilltop which is defined by a function of two variables f(x, y). The downward slope of the hill, the gradient, is different depending on the direction you look; to find the slope you need to specify a direction. This is why we take the 'directional derivative' which is simply the dot product of the gradient with a unit direction vector (the direction you are looking down the hill). For example suppose we want to find the instantaneous rate of change of the function f(x,y) = x2 + y2 at the point (2,1) in the direction of v = <0, 1>:
The directional derivative in the direction of v = ∇f(x, y) ◠<0,1>
= < ∂f/∂x(x, y, z), ∂f/∂y(x, y, z)> ◠<0,1> = <2x, 2y> ◠<0,1> = 2y evaluated at (2,1) = 2.
Let's continue our comparison of derivatives and gradients. In single variable calculus a derivative of a function is equal to zero at a maximum or minimum value of the function. This fact can be used in practical applications that require maximizing and minimizing functions of one variable. The same is said of the gradient in multivariable calculus. By setting the gradient of a multivariable function equal to zero, we can solve for the point of maximum or minimum values.
Yeah, that's valid, but it's almost always the worst possible way to go about solving a question. Any functions which are complicated enough to be worth showing have limits are usually too complicated to do it that way.
Is the saying best foot forward or best face forward?
I'm not certain, but when googling it seems like foot is more common. Both technically mean the same thing.
No. Logic deals with statements or values or reasoning, none of which are tangible objects or forces.
It means that whatever you have substituted is the solution of the given linear equation. Or you have substituted the equation in itself.
Giga is a prefix which means one billion. For example: 1 Gigapascal = 1 billion Pascals.
In a spreadsheet software such as Microsoft Excel or OpenOffice Calc, there is a Goal Seek tool (Under Data, What If Analysis for Excel; under Tools for OpenOffice), which allows you to try to find a value of a particular cell, which will give the desired value in a target cell. The target cell needs to contain a formula, whose value changes with the cell that you are adjusting.
How can you convert numeric data between different number systems using a floating point?
Here is an example: 3.1416, which is pi rounded to the nearest ten thousandth, converted to binary:
The highest power of 2 in the number is 2^1 (2), so we start with 1-. Subtracting 2 leaves 1.1416. The next power of 2 is 2^0 (1). The left over difference is greater than 1, so we have 11. so far. Subtracting 1 from the previous difference leaves 0.1416. The next power of 2 is 2^(-1), or 1/2. Our difference is less than 1/2, so our next bit (short for binary digit) is 0. So far we have 11.0. The next power of 2 is 2^(-2), or 1/4. Our difference is less than a quarter, so we have 11.00. Next is 2^(-3), or 1/8. Our difference is greater than an eighth, so we have 11.001 so far, and we subtract 0.125 from 0.1416, leaving 0.0166. That's less than 1/16, so we have 11.0010. It's also less than 1/32, so we're up to 11.00100. It's greater than 1/64, so we have 11.001001. 0.0166 - 0.015625 = 0.000975. That's less than 1/128 (so we have 11.0010010), it's less than 1/256 (11.00100100), it's less than 1/512 (11.001001000), it's less than 1/1024 (11.0010010000), but it's greater than 1/2048 (taking us to 11.00100100001). Subtracting 0.00048828125 leaves 0.00048671875. Subtracting 1/4096 and 1/8192 takes us to our original precision (one ten thousandth) and brings our number to 11.0010010000111. Since the next bit is also a 1, I will round the number up to 11.0010010001000. And there you have it: binary pi rounded to the 8192nds place.
Going from binary to decimal is easy: you just add together the powers of 2 for every place in the number that has a 1. There are 1's in the 2s place, in the 1s place, in the 8ths place, in the 64ths place and in the 1024ths place. 2 + 1 + 1/8 + 1/64 + 1/1024 = slightly more than 3.1416 (because we rounded up).
a model for multiplication problems, in which the length and width of a rectangle
represents the product.
Is the image of an open set under a continuous mapping need not be open?
f(x) = x^{2} is a continuous function on the set R of real numbers, and (-1, 1) is an open set in R, but f(-1, 1) = [0, 1), and [0, 1) is not an open set in R. So, f is not an open function on R.
How do you forecast room occupancy of hotel?
You create a statistical model using data for any variable that you think might affect room occupancy. Where direct data are not available, you could use proxies. Using these data you could carry out a multiple regression which would give you the best variables to use and an equation, using those variables, to forecast occupancy.
Some variables that may be of use:
Season
Number of hotels/room in town
Your prices, offers
Other hotels' prices
Your quality (star) rating
Customer satisfaction, your reputation
Location (your and others')
Amenities (your and others')
Special events - eg conferences, conventions
Advertising
Ties with airlines, car rental etc.
You create a statistical model using data for any variable that you think might affect room occupancy. Where direct data are not available, you could use proxies. Using these data you could carry out a multiple regression which would give you the best variables to use and an equation, using those variables, to forecast occupancy.
Some variables that may be of use:
Season
Number of hotels/room in town
Your prices, offers
Other hotels' prices
Your quality (star) rating
Customer satisfaction, your reputation
Location (your and others')
Amenities (your and others')
Special events - eg conferences, conventions
Advertising
Ties with airlines, car rental etc.
You create a statistical model using data for any variable that you think might affect room occupancy. Where direct data are not available, you could use proxies. Using these data you could carry out a multiple regression which would give you the best variables to use and an equation, using those variables, to forecast occupancy.
Some variables that may be of use:
Season
Number of hotels/room in town
Your prices, offers
Other hotels' prices
Your quality (star) rating
Customer satisfaction, your reputation
Location (your and others')
Amenities (your and others')
Special events - eg conferences, conventions
Advertising
Ties with airlines, car rental etc.
You create a statistical model using data for any variable that you think might affect room occupancy. Where direct data are not available, you could use proxies. Using these data you could carry out a multiple regression which would give you the best variables to use and an equation, using those variables, to forecast occupancy.
Some variables that may be of use:
Season
Number of hotels/room in town
Your prices, offers
Other hotels' prices
Your quality (star) rating
Customer satisfaction, your reputation
Location (your and others')
Amenities (your and others')
Special events - eg conferences, conventions
Advertising
Ties with airlines, car rental etc.
Why working capital is important and some ratio of working capital?
Working capital is a business's blood as well as the oxygen that gives your business its every breath. In other words, working capital is what keeps your business alive and functioning. Working capital is obviously very important. Have you noticed that your business's cash flow is not as steady as you wish? Has it become difficult to pay for your business's day-to-day expenses? If so, you might be in need of working capital.
