0
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 else can I help you with?
Absolute value inequalities?
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.
When one variable increase while the other variable deacreases is a statement indicating an inverse relationship?
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.
What stands for iff in math?
If and only if (necessary and sufficient condition).
What is the necessary and sufficient condition for vectors ABC are to be copalanar?
A.b.c=0
What are the two rules for inequalities which do not occur in equations?
Inequalities are not reflexive. Inequalities are not commutative.
Whats an Epistemology for jointly sufficient conditions?
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.
What has the author Bartek Roszak written?
Bartek Roszak has written: 'Necessary and sufficient conditions for reachability on a simplex'
When was Necessary But Not Sufficient - novel - created?
Necessary But Not Sufficient - novel - was created in 2000.
Absolute value inequalities?
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.
List the three conditions that are necessary and sufficient for natural selection to act on a?
A beneficial mutation leading to variability in a population and the heritability of those beneficial traits.
When one variable increase while the other variable deacreases is a statement indicating an inverse relationship?
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.
What are the conditions necessary for price leadership?
what are the conditions necessary for price leadership
Why it is necessary to use an empty circle to graph solutions of inequalities?
It is not necessary - it is a convention to distinguish between the end points of a range being included or not in the solution.
What are the conditions necessary for effective price leadership?
what are the conditions necessary for price leadership
Is use of least-cost input combination a necessary condition for profit maximization is it a sufficient condition explain?
1. Minimization of Cost for a Given Level of Output: Least Cost Conditions
What is the definition of Necessary and sufficient causes?
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.
What conditions under combustion can take place?
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.
