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Ask QuestionPosted by Balram Nagarfyhjjo To Touch-Me-Not 4 years, 4 months ago
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Posted by Aaaaa Student 4 years, 4 months ago
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Gaurav Seth 4 years, 4 months ago
We know that, Three lines are said to be concurrent, if they pass through a common point which also means that the point of intersection of any two lines always lies on the third line.
Now, the three given equations of line are:
2x + y − 3 = 0 ... (1)
5x + ky − 3 = 0 ... (2)
and 3x − y − 2 = 0 ... (3)
Firstly, we will solve the equations (1) and (3) and find out the value of x and y. The corresponding value of x and y will also satisfy the equation (2) as all the given lines are concurrent.
Therefore, on adding (1) and (3), we get
2x + y − 3 + 3x − y − 2 = 0
⇒ 5x - 5 = 0
⇒ x = 1
On putting value of x in (1), we get
2(1) + y − 3 =0
⇒ y - 1 = 0
⇒ y = 1
So, the point of intersection of two lines is (1, 1).
Now, this point will also satisfy the equation (2).
Therefore, on putting (x, y) = (1, 1) in (2), we get
5(1) + k(1) − 3 = 0
⇒ k + 2 = 0
⇒ k = - 2
Posted by Sanjeev Sharma 4 years, 4 months ago
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Kalki Kalki 4 years, 4 months ago
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⠀ 4 years, 4 months ago
For n = 1 ,
p(k) is true
Let for n = k ,p(k) is true
For n = k+1:
(k+1)(k+2)(k+3)
k(k+1)(k+2)(k+3)/k divisible by 6
So by mathematical induction , statement is true for all n€N
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Sakshi Jagtap 4 years, 4 months ago
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Yogita Ingle 4 years, 4 months ago
There are some sets that do not contain any element at all. For example, the set of months with 32 days. We call a set with no elements the null or empty set. It is represented by the symbol { } or Ø.
Some examples of null sets are:
The set of dogs with six legs.
The set of squares with 5 sides.
The set of cars with 200 doors.
The set of integers which are both even and odd.
Sajal Thakur 4 years, 4 months ago
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Har Har Mahadev 🙏 4 years, 4 months ago
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