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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

Which side of the football field is the strong side?

Football Field Strong SideThe term "strong side" generally refers to the offensive team formation and not the field itself. In an unbalanced formation with more offensive players on one side of the center than the other, the side with more players is considered the "strong side." The extra man is usually the tight end and with a right-handed quarterback, he will normally line up on the right side of the line. Hence, the right side of the offensive team's line is usually the "strong side."

Some offensive systems designate the strong side as the side which is farthest from the sideline; for example, if the ball is on the right hashmark, strong side is on the left side of the ball, and vice versa. This is more often used in Canadian football, as with 12 players on the field a balanced formation is possible.

Why is it important to know the reverse process of multiplication?

To cross-check that a multiplication is correct as for example if 7*8 = 56 then the reverse process of division must be correct as 56/7 = 8 or 56/8 = 7

How do you factor 5x2 -4?

That doesn't factor neatly. Applying the quadratic equation, we find two real solutions:

(0 plus or minus 2 times the square root of 5) divided by 5.

x = 0.89442719

x = -0.89442719

If you had an x in there, it would come out nicer. 5x2 + x - 4 = (x + 1)(5x - 4)

What is deterministic and probabilistic system?

In my understanding the probabilistic is a system that you can predict but no 100% like deterministic system. In other words the result is randomness i.e it can have many different results instead of single results.

What are the applications of calculus?

Many, many applications. Calc is the basis of all higher math, for one. It's used intensively by scientists, engineers, economists, and computer programmers to name a few. Calculus attempts to model the natural world, so any profession that attempts to model natural phenomena can and should use calculus.

Fourier transform of unit step function?

we proceed via the FT of the signum function sgn(t) which is defined as:

sgn(t) = 1 for t>0 n -1 for t<0

FT of sgn(t) = 2/jw where w is omega n j is iota(complex)

we actually write unit step function in terms of signum fucntion : n the formula to convert unit step in to signum function is

u(t) = 1/2 ( 1 + sgn(t) )

As we know the FT of sgn(t) we can easily compute FT of u(t).

Hope i answer the question

How mycosis multiply?

Mycosis, or fungal infections, multiply through a process called sporulation where fungal spores are released and spread to new environments. These spores can survive in various conditions and can germinate into new fungal cells when they find a suitable environment with the necessary nutrients and moisture. Additionally, some fungi can also reproduce through budding or fragmentation of hyphae.

How can you express the concentration of a substance mathematically?

In chemistry, the concentration of a substance in solution is determined by molarity, which is symbolized by "M". This indicates the number of moles of a substance dissolved in one liter of a solvent (usually water).

For example:

- 1 mole of sodium chloride = 58 grams

- If 116 grams of sodium chloride are dissolved in 1 liter of water, then that solution is a 2-molar (2 M) solution of sodium chloride.

- If 232 grams of sodium chloride are dissolved in 1 liter of water, then that solution is a 4-molar (4 M) solution of sodium chloride.

How many triangles are there within a nonagon?

if you need to know how many triangles are in a polygon ... just take the number of its sides and subtract for example.

nonagon has 9 sides so it will be 9-2=7

so, a nonagon has 7 triangles

What are the advantages of the finite element method?

Models Bodies of Complex Shape

- Can Handle General Loading/Boundary Conditions

- Models Bodies Composed of Composite and Multiphase Materials

- Model is Easily Refined for Improved Accuracy by Varying

Element Size and Type

Difference between fourier series and z-transform?

Laplace = analogue signal

Fourier = digital signal

Notes on comparisons between Fourier and Laplace transforms:

The Laplace transform of a function is just like the Fourier transform of the same function, except for two things. The term in the exponential of a Laplace transform is a complex number instead of just an imaginary number and the lower limit of integration doesn't need to start at -∞. The exponential factor has the effect of forcing the signals to converge. That is why the Laplace transform can be applied to a broader class of signals than the Fourier transform, including exponentially growing signals. In a Fourier transform, both the signal in time domain and its spectrum in frequency domain are a one-dimensional, complex function. However, the Laplace transform of the 1D signal is a complex function defined over a two-dimensional complex plane, called the s-plane, spanned by two variables, one for the horizontal real axis and one for the vertical imaginary axis. If this 2D function is evaluated along the imaginary axis, the Laplace transform simply becomes the Fourier transform.

How many cubic yards are in a sidewalk that's 48in wide by 40ft long by 3.5 in thick?

1 cubic foot = 1,728 cubic inches

1 cubic yard = 27 cubic feet = 46,656 cubic inches

1 ft = 12 inches

40 ft = 480 inches

Volume of the walk = (48" x 480" x 3.5") = 80,640 cubic inches = 1.7284 cubic yard (rounded)

How many times can 50 go into 1400?

1400/50

Cancel down by '10'

Hence

140/5

5)140 = 28 The answer.