I was going through a JSTSE paper, When I found this question...
How many points (x,y) exist in the 1st quadrant such that x+y=7 ?
2 years, 7 months ago
The formula for the number of Natural numbers satisfying \(x + y = k\) is always \(k-1\).
So in this case k = 7 . Hence number of points are 6
This formula is just a observation based. Please verify it @Azhaghu Roopesh M @Krishna Ar @Sravanth Chebrolu
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Yes, I too think the same, but if the no. of points asked is in fractions or decimals there can be many . . .
What do you say @Rajdeep Dhingra ???
Mar 25, 2015
Going to class \(10\)
Well as this formula is valid only for natural numbers so the sum will also be a natural number.
If it is not specified natural number or k is a rational number with denominator \(\ne\) 1 then the answer is \(\infty\)
Exactly. Then this might have been included in the question . . .
If the number of points(x,y) are said to be only whole numbers(not decimals), then there are 6, they are:
\( (1,6),(2,5),(3,4),(4,3),(5,2) and (6,2) \)
If it is mentioned, including decimals, then it is infinite . . .
What do you say Azhaghu Roopesh M ???
@Sravanth Chebrolu Do (0,7) and (7,0) not lie in any quadrant? Coz the definition of the point in the 1st quadrant is x,y>0. Anyways.. If included, they should be 8 in number , eh. I think there is a typo.
Yeah it was a typo, I've changed it. And yes, I think what you said is also right, the points (7,0) and (0,7) lie on the axes not the quadrants.
Yeah , since the number 7 is quite small , we can count it out .
Exactly. Is there any formula for these kind of problems???
Look up the Generating Functions wiki here on B'ant . Anyway , I've got to go now, Bye :)
I guess there would have been more information provided. Most likely the question would have specified \(x,y\) to be integers.
But it has been said that x,y belong to the first quadrant , so automatically \(x,y \geq 0\)
Is this the exact same question ? If so , it is a simple question of Generating Functions
Generating functions? Are you sure? This is a JSTSE question, so its for classes 10 or below I think.
Well , I think any class 10 student has the ability to count the number of solutions manually , it's just that the method of Generating Functions works for finding solutions of the type :\(x+y = N\) or other types .
Not exactly below.. The maths questions were mainly Of class 10 level iincluding all AP, GP , Quadratics, Vieta's etc...