Posted by ILias
1. The problem statement, all variables and given/known data
consider two conditions x2-3x-10 < 0 and |x-2| < A on a real number x, where A is positive real number
(i) find the range of values of A such that |x-2| < A is a necessary condition for x2-3x-10 < 0
(ii) find the range of values of A such that |x-2| < A is a sufficient condition for x2-3x-10 < 0
2. Relevant equations
3. The attempt at a solution
what is necessary and sufficient condition? I tried googling but found nothing about it...
thanks
Well, the first step is to solve the equality x2-3x-10= 0. You will get two solutions. Then you will have to think about what makes the inequality true. The necessary condition is the one that is required to make the statement true: "For Hot Dogs to taste good, they must have mustard". The sufficient condition is the one that says if the condition is met, the statement is true, "As long as hot dogs have mustard, hot dogs are good." The necessary and sufficient condition that if that condition is met, by necessity, the statement is true "only hot dogs that have mustard are good (necessity) and if they have mustard they need nothing else to be good (sufficiency)".
What's your question? To solve an absolute value inequality, knowledge of absolute values and solving inequalities are necessary. Absolute value inequalities can have one or two variables.
No. That condition is necessary but not sufficient.No. That condition is necessary but not sufficient.No. That condition is necessary but not sufficient.No. That condition is necessary but not sufficient.
A set of two or more inequalities is known as a system of inequalities. This system consists of multiple inequalities that involve the same variables and can be solved simultaneously to find a range of values that satisfy all conditions. Solutions to a system of inequalities are often represented graphically, where the feasible region indicates all possible solutions that meet all the inequalities. Such systems are commonly used in linear programming and optimization problems.
If and only if (necessary and sufficient condition).
A.b.c=0
An epistemology for jointly sufficient conditions involves the understanding of how knowledge is acquired through a combination of conditions that, when taken together, are sufficient to justify a belief. It focuses on the relationship between these conditions in establishing the reliability and validity of knowledge claims. This approach emphasizes the importance of considering all relevant factors to support the justification of knowledge.
Bartek Roszak has written: 'Necessary and sufficient conditions for reachability on a simplex'
Necessary But Not Sufficient - novel - was created in 2000.
What's your question? To solve an absolute value inequality, knowledge of absolute values and solving inequalities are necessary. Absolute value inequalities can have one or two variables.
A beneficial mutation leading to variability in a population and the heritability of those beneficial traits.
No. That condition is necessary but not sufficient.No. That condition is necessary but not sufficient.No. That condition is necessary but not sufficient.No. That condition is necessary but not sufficient.
A set of two or more inequalities is known as a system of inequalities. This system consists of multiple inequalities that involve the same variables and can be solved simultaneously to find a range of values that satisfy all conditions. Solutions to a system of inequalities are often represented graphically, where the feasible region indicates all possible solutions that meet all the inequalities. Such systems are commonly used in linear programming and optimization problems.
what are the conditions necessary for price leadership
It is not necessary - it is a convention to distinguish between the end points of a range being included or not in the solution.
1. Minimization of Cost for a Given Level of Output: Least Cost Conditions
A necessary cause is a condition that, by and large, must be present for the effect to follow. A sufficient cause, in contrast, is a condition that more or less guarantees the effect in question.
Combustion can take place under conditions of sufficient heat (ignition temperature), fuel, and oxygen. The heat initiates the reaction, fuel provides the substance to burn, and oxygen serves as the oxidizing agent. These conditions are necessary to sustain the combustion process.