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What is general equation?
A general equation typically refers to a mathematical expression that represents a relationship between variables. It can take various forms depending on the context, such as linear equations, quadratic equations, or differential equations. The general equation aims to encapsulate a wide range of specific cases or instances within its framework, often allowing for the derivation of particular solutions by substituting specific values for the variables.
What does all solutions mean when solving an algebraic equation?
It means that some equations can have more than one solution, and that you are supposed to find all of them. For example, equations with polynomials tend to have more than once solution; thus, x squared = 25 is satisfied both for x = 5, and for x = -5.
Can linear equations have more than one solutions?
No, a linear equation in two variables typically has one unique solution, which represents the intersection point of two lines on a graph. However, if the equation represents the same line (as in infinitely many solutions) or if it is inconsistent (no solutions), then the type of solutions can vary. In general, a single linear equation corresponds to either one solution, no solutions, or infinitely many solutions when considering the same line.
What is general solution to a trigonometric equation?
The general solution to a trigonometric equation provides all possible angles that satisfy the equation. For example, for equations involving sine or cosine, the general solutions can often be expressed in the form ( x = n \cdot 2\pi + \theta ) or ( x = n \cdot 2\pi - \theta ) for sine, or ( x = n \cdot 2\pi + \theta ) for cosine, where ( n ) is any integer and ( \theta ) is a specific angle solution. This reflects the periodic nature of trigonometric functions, allowing for infinitely many solutions based on the periodic intervals.
What equations will have a graph with a slope of negative 3?
That will depend on what equations but in general if it has a slope of -3 then it will have a down hill slope
How many solutions does the nonlinear system of equations graphed below have?
2
What is general equation?
A general equation typically refers to a mathematical expression that represents a relationship between variables. It can take various forms depending on the context, such as linear equations, quadratic equations, or differential equations. The general equation aims to encapsulate a wide range of specific cases or instances within its framework, often allowing for the derivation of particular solutions by substituting specific values for the variables.
What does all solutions mean when solving an algebraic equation?
It means that some equations can have more than one solution, and that you are supposed to find all of them. For example, equations with polynomials tend to have more than once solution; thus, x squared = 25 is satisfied both for x = 5, and for x = -5.
Can linear equations have more than one solutions?
No, a linear equation in two variables typically has one unique solution, which represents the intersection point of two lines on a graph. However, if the equation represents the same line (as in infinitely many solutions) or if it is inconsistent (no solutions), then the type of solutions can vary. In general, a single linear equation corresponds to either one solution, no solutions, or infinitely many solutions when considering the same line.
What is general solution to a trigonometric equation?
The general solution to a trigonometric equation provides all possible angles that satisfy the equation. For example, for equations involving sine or cosine, the general solutions can often be expressed in the form ( x = n \cdot 2\pi + \theta ) or ( x = n \cdot 2\pi - \theta ) for sine, or ( x = n \cdot 2\pi + \theta ) for cosine, where ( n ) is any integer and ( \theta ) is a specific angle solution. This reflects the periodic nature of trigonometric functions, allowing for infinitely many solutions based on the periodic intervals.
How can you determine the number of solutions for an equation?
In general, you cannot: it all depends on the domain.x + 2 = 0 has no solutions is the set of positive integers but does have one if the domain is the integers.2x - 3 = 0 has no solutions if the domain is integers, but there is one solution if the domain is the rationals.x2 - 2 = 0 has no solutions if the domain is the rationals but there are two solutions if the domain is the reals.x2 + 2 = 0 has no solutions if the domain is the reals but there are two solutions if the domain is the complex numbers.Cos(x) = 1 has no solutions if the domain is (0, 360) but two solutions for the domain [0, 360].
What is the difference between general reference sources and special reference sources?
differentiate general reference sources and special reference sources with example
What equations will have a graph with a slope of negative 3?
That will depend on what equations but in general if it has a slope of -3 then it will have a down hill slope
Where can someone get information about eCommerce Solutions?
One can get some useful general information about e-commerce solutions from Wikipedia. If one is looking to buy e-commerce software then one could get information about e-commerce solutions from the website called CS-Cart, for example.
What will form electrolyte solutions in water when ionized?
Any ionized chemical will cause water to become electrically conductive. In general, salts are the best example.
Do relativity equations hold true for normal conditions?
Yes. In the limit where the velocity difference between two observers gets ever closer to zero, the equations of spacial relativity reduce to the Newtonian equations. Indeed, if this were not true, then special relativity would be *wrong*. Similarly, general relativity gives the same answers as Newtonian gravity for the cases in which Newtonian gravity applies.
What is the first step in solving a system of nonlinear equations by substitutions?
In general, a system of non-linear equations cannot be solved by substitutions.
