Maths-
General
Easy
Question
In the equation above, c is a constant. If the equation has infinitely many solutions, what is the value of c ?
Hint:
Hint:
Infinitely many solutions of an equation means that the equation is true for any value of the variable. In other words, when we put any value of x in the equation, we get a statement which is always true, (example 0 =0 ). Here, to find the value of c, we simplify the given equation. As the equation is true for every value of x, we put x=1 to find the value of c.
The correct answer is:
The given equation is
Expanding the terms of the above equation, we get
Simplifying the equation,
It is given that this equation has infinitely many solutions, so it must be true for all values of x.
We cannot put x=0 in the equation because then both the right hand side and the left hand side will be 0 and the term containing c will vanish.
Particularly, the above equation is true for x = 1
So,
Thus, we get that for 
, equation has infinitely many solutions.
The correct option is B)
Note:
As the equation is true for all values of x, we could have put x equal to any other number instead of 1, and we would get the same result. If we put x=1 in the first step as well, we would get the same value for x
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In mathematics, a survey is a technique for gathering data that involves posing a series of questions to participants to learn more about their attitudes and behaviors. It is the most typical and affordable method of data collection.
For example, Knowledge of consumer purchasing patterns can be used to understand product demand better and increase sales.
Types of Survey Methods
The procedure for gathering data is referred to as the survey method. Different approaches can help you get the extra information or insights you're looking for. Below is a list of some popular techniques.
Online Survey
Paper Survey
Telephonic Survey
Face-to-Face Interview
A polling agency recently surveyed 1,000 adults who were selected at random from a large city and asked each of the adults, “Are you satisfied with the quality of air in the city?” Of those surveyed, 78 percent responded that they were satisfied with the quality of air in the city. Based on the results of the survey, which of the following statements must be true?
I. Of all adults in the city, 78 percent are satisfied with the quality of air in the city.
II. If another 1,000 adults selected at random from the city were surveyed, 78 percent of them would report they are satisfied with the quality of air in the city.
III. If 1,000 adults selected at random from a different city were surveyed, 78 percent of them would report they are satisfied with the quality of air in the city.
Maths-General
In mathematics, a survey is a technique for gathering data that involves posing a series of questions to participants to learn more about their attitudes and behaviors. It is the most typical and affordable method of data collection.
For example, Knowledge of consumer purchasing patterns can be used to understand product demand better and increase sales.
Types of Survey Methods
The procedure for gathering data is referred to as the survey method. Different approaches can help you get the extra information or insights you're looking for. Below is a list of some popular techniques.
Online Survey
Paper Survey
Telephonic Survey
Face-to-Face Interview
