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Differential Equations
A differential equation, unlike other mathematical equations, has one or more of its unknowns undergoing a continual change. These equations mathematically describe the most significant phenomena in the universe, including Newtonian and quantum mechanics, waves and oscillators, biological growth and decay, heat, economics, and general relativity. Please direct all concerns about these intricate and all-encompassing equations here.
523 Questions
What is an example of constant rate of change?
A constant rate of change is anything that increases or decreases by the same amount for every trial. Therefore an example could be driving down the highway at a speed of exactly 60 MPH. If your speed doesn't change you are driving at a constant rate. Here's another: your cell phone company charges you $0.55 for every minute you use. The rate that you are charged always stays the same so it is a constant rate of change. Anything that goes up by X number of units for every Y value every time is a constant rate of change.
What is the rules in multiplying polynomials?
If there is subtracting terms in either polynomial, change them to adding a negative. Each term in the first polynomial is multiplied by each term in the 2nd polynomial, then add all the resulting terms together (taking into account the signs of the resulting multiplications), simplify by combining like powers of the variable.
This is basically what you are doing when you multiply 2 numbers by hand, example: 997 x 42 = 41874
997
x 42
----- First you mutiply 2 x 7 = 14, put the 4 carry the 1, etc.
Imagine instead (4x + 2)(9x2 + 9x + 7) = 2*7 + 2*9*x + 2*9*x2 + (4*x)*7 + (4*x)*(9*x) + (4*x)*(9x2) = 14 + 46x + 54x2 + 36x3
For x = 10 --> 14 +460 + 5400 + 36000 = 41874.
In computational complexity theory, Cook's theorem, also known as the Cook–Levin theorem, states that the Boolean satisfiability problem is NP-complete. That is, any problem in NP can be reduced in polynomial time by a deterministic Turing machine to the problem of determining whether a Boolean formula is satisfiable.
Simultaneous equations: x/3 -y/4 = 0 and x/2 +3y/10 = 27/5
Multiply all terms in the 1st by 12 and in the 2nd equation by 10
So: 4x -3y = 0 and 5x +3y = 54
Add both equations together: 9x = 54 => x = 6
Solutions by substitution: x = 6 and y = 8
How do you solve first order partial differential equation y2p - xyq x(z-2y)?
The Answers community requires more information for this question. Please edit your question using words eg "plus", "divide", "equals" because the browser used for posting questions rejects most mathematical symbols.
What are the physical significance of Maxwell's equations?
As per my knowledge,Maxwell's equations describes the relations between changing electric and magnetic fields. That means time varying electric field can be produced by time varying magnetic field and time varying magnetic field can be produced by time varying electric field.
Application of differential equation in chemistry?
The rate at which a chemical process occurs is usually best described as a differential equation.
Why are there fifty-two cards in a normal pack-?
The reason why there are fifty-two cards in a normal pack is because there are 4 suits with 13 cards in each suit.
How do you calculate quantity?
It depends on what is being calculated? Basically, a collection of something is counted as 1, 2, 3, and so on, to give a total. A simple instance is in counting loose two pence (UK) coins: piles of two pence coins are stacked in tens, then the piles are counted as 10, 20, 30, and so on. Or if there are 34 piles of 10 coins, then 34 x 10 = 340 pence (£3.40).
What do the letters mean in algebraic equations?
The letters in most algebraic equations mostly represent the value of the number or often at times the gradient.
What are the applications of impulsive differential equation in day today life?
If you happened to know impulsive differential equations and there was an outbreak of swine flu, bird flu, zombie bumblebees, etc., and there was a method to treat them (and you knew about it), then you *could* tell how likely it is that the treatment would be effective, and how long that would take. That could affect your stock portfolio, or whether or not you want to leave the house or answer the door because it's worth quarantining yourself away from disease... which could also just make you look like a crazy person because even if *you* can tell using impulsive differential equations that we're all doomed, your neighbors probably don't.
What is an example of a Rate of Change related to zoology?
The population of a species over a period of time will change according to some rate of change.
What is an example of a positive rate of change?
a car going from stoplight to next intersection accelerates at a positive rate of velocity change
How do you convert second order differential equations to first order differential equations?
You can't convert a second order DE to first order except in special cases (like an ODE with y'' and y' but no y terms).
HOWEVER, you can convert a second order ODE into a systemof first order ODEs:
Assume it is of the form f(x, y, y', y'') = 0, where y(x) is the solution.
1) Let u1 = y and u2 = y'
2) Substitute y'' for u2', y' for u2, and y for u1 to get eq1
3) u2 = u1' is eq2.
eq1 and eq2 are a system of two first-order ODEs which represent the same problem.
What is IVP in differential equations?
Initial Value Problem.
A differential equation, coupled with enough initial conditions for there to be a unique solution.
Example:
y'' - 6y = exp(x) ; y'(0) = y(0) = 0
What are the four Maxwell's equation?
Gauss's law: Electric charges produce an electric field. Gauss's law for magnetism: There are no magnetic monopoles. Faraday's law: Time-varying magnetic fields produce an electric field. Ampère's law: Steady currents and time-varying electric fields produce a magnetic field.
Which number is a solution of the inequality 10.6 b?
The answer to this question is 14. The reason why is becasue 14 is greater than 14
