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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
15,800. Do the math. I certainly shouldn't be doing it for you.
What are the lines at each side of a football field called?
what are the lines calledat each side of a football field called
What is the exact value of sin 405?
sin(405) = square root of 2 divided by 2 which is about 0.7071067812
How is a slope used in real life?
Virtually everywhere; in fact the entire notion of the derivative of a function is based on slope. Both slope and derivative have uses in real life, e.g. your position, speed and acceleration can be calculated using either. Or, you could find the derivative of a logistics curve (a curve that models population growth), etc.
Does a circle pass the vertical line test?
No. Because a vertical line will pass through two points on the graph.
What are two prime numbers whose sum is 42?
Split the number in half and make an equation adding the two together to make the desired amount. Unless the number that is half the total is prime, adjust the first number down by an amount to make it a prime number, then adjust the second one up by an equal amount and check whether it is also a prime number. If the second number is also a prime number, you have found two prime numbers that equal the desired amount. If not, adjust the first number down to another prime number, repeating the procedure above until you have two prime numbers.
If you split 42 in half, the result is 21. Take the equation 21 + 21 = 42. Since 21 is not prime, adjust the first number down to 19 which is the first prime number below 21. That means the other number would be 23, which is prime. So, you have two prime numbers that add up to 42 = 19 + 23.
The prime factorization of 42 is 2 x 3 x 7, so it has three factors that are prime: 2, 3, and 7.
23
Does a steep line always have a negative slope?
A line doesn't have a negative slope if it's steep or not. Possitive and negative slope is determined by the way it goes up or down. When you look at a line from the left to the right, if it gets higher as you get closer to the right, then it has a positive slope. On the other hand, if you also look at it from left to right and the line goes down as it nears the right side, it has a negative slope. If the line is horizontal, it has a slope of 0. If the line is vertical, it has no slope.
Can a function have a limit at every x-value in its domain?
Yes, that happens with any continuous function. The limit is equal to the function value in this case.
Yes, that happens with any continuous function. The limit is equal to the function value in this case.
Yes, that happens with any continuous function. The limit is equal to the function value in this case.
Yes, that happens with any continuous function. The limit is equal to the function value in this case.
Binomials are algebraic expressions of the sum or difference of two terms. Some binomials can be broken down into factors. One example of this is the "difference between two squares" where the binomial a2 - b2 can be factored into (a - b)(a + b)
Distance d = speed x time
With one hour head start the slower car traveled d= 55x1 = 55 miles
The faster car catches up when they have traveled same distance
d = 65t = 55t + 55
10t = 55
t = 5.5 hours
How many faces and edges of pyramid?
one face eight edges and five corners
* * * * *
The above answer is complete rubbish.
A pyramid is a generic term for three dimensional shapes which consist of an n-sided polygon (n > 2) as base and n triangular faces meeting at an apex above the base.
For any integer n>2, a pryramid with an n-polygonal base has:
n + 1 faces
n + 1 vertices and
2n edges.
What does symbolic mean in math?
In math, symbolic logic is simply expressing a mathematically logical statement through the use of symbols. For instance, one could always write down the phrase, "one plus one equals two," but using symbolic logic, that statement can be expressed much more succinctly as 1 + 1 = 2.
A better example is:
The indefinite integral of one divided by the quantity one minus the square of x with respect to x is equal to one half multiplied by the natural logarithm of the quotient of the quantities one plus x and one minus x with the constant of integration added to this result
Symbolically written, that statement is expressed as:
∫ [1/(1 - x2)] dx = ½ ln[(1 + x)/(1 - x)] + C,
which is a whole heck of a lot easier to write!
The median is Q2, if it is on the right side of the box, then then it is close to Q3 than it is to Q1. If the right line ( whisker) is longer than the left, it mean the biggest outlier is farther from Q3 than the smallest outlier is from Q1. All of this means the population from which the data was sampled was skewed to the right.
The dot-product of two vectors is the product of their magnitudes multiplied by
the cosine of the angle between them. The dot-product is a scalar quantity.
How do you find the perimeter and area of a irregular figure?
Divide the irregular figure into manageable pieces and work out their individual areas, sum the areas to that of the original figure.
Measure the perimeter.
Why is every singleton set in a discrete metric space open?
In a metric space, a set is open if for any element of the set we can find an open ball about it that is contained in the set. Well for the singletons in the discrete space, every other element is said to have a distance away of 1. So we can make a ball about the singleton of radius 1/2 ... this ball just equals that singleton since it contains only that element. So it is contained in the set. Thus the singleton set is open.
