Thanks for sharing the secrets of learning math. I am sure this would really help students not only to score good marks but also for better understanding of math.
Practice, sharing and discussion with others is fruitful in learning math or any other subject.
Practice—> Improves skills and understanding of concepts
Sharing—> Enhances knowlegdge
Discussion—> Interesting and innovative way to explore new things….
If you are talking about ordinary lines and ordinary geometry, then parallel lines do not meet. Now the basic plane doesn’t have a point called “infinity”, it only consists of points describable by pairs of coordinates ( x ,y ).
For example, the line x = 1 and the line x = 2 do not meet at any point, since the x coordinate of a point cannot be both 1 and 2 at the same time
Two lines moving in the same direction on a plane will never meet at a finite set of coordinates
I can think of two things that might be confusing this issue. The first has to do with perspective drawing. In perspective drawing (imagine standing on straight railroad tracks that are going off into the distance), parallel lines appear to intersect.
The other thing that you may be thinking about is that in some non-Euclidean geometry, parallel lines are not the same distance apart the whole time .
Hi Sureshbala, That’s right ! Thanks for the explanation.
I would like to share alternate way :
Find the number of cases in which none of the digits show a ‘6’.
i.e. all three dice show a number other than ‘6’, 5 * 5 *5 = 125 cases.
Total possible outcomes when three dice are thrown = 216.
The number of outcomes in which at least one die shows a ‘6’ = Total possible outcomes when three dice are thrown – Number of outcomes in which none of them show ‘6’.
= 216 – 125 = 91.
The required probability = 91 / 216
Letters can be arranged in 4 ! Ways , that is, 4×3 x 2×1 ways = 24 ways
(Since letter can be put into first envelope in 4 ways, in second envelope letter can be put in 3 ways, letter can be put into third envelope in 2 ways, letter can be put into fourth envelope in 1 way)
Probability that only one letter will be put into the envelope with its correct Address = 4/24 =1/6
( Four possibilities are:
1. first letter will be put into the envelope with it’s Correct address and rest three are incorrect
2. Second letter will be put into the envelope with its Correct address and rest three are incorrect
3. Third letter will be put into the envelope with its correct address and rest three are incorrect
4. Fourth letter will be put into the envelope with its correct address and rest three are incorrect )
9 ^ 99 (9 to the power of 99) which calculates out as
9 * 9 * 9 * 9 * 9 * 9 * 9 ... and so on 99 times.The correct answer, however, if you extend the idea even further ends up as…
9 ^ 9 ^ 9 (9 to the 9th power of 9).
Work out the second and third powers first ( 9 * 9 * 9 * 9 * 9 * 9 * 9 * 9 * 9 = 387420489. ) We can therefore restate
the sum as 9387420489 which works out as…. very very big indeed.
Hi,
This is the right answer. It’s a good idea to show image. : )
Well, you are right it is undefined. But the question is, if it could be defined, what “should” it be? 0 or 1?
I think, the answer should be 1.
Could you suggest why it should be “1” before I give arguments to suport my answer.
Infinity is not a number; it’s an idea. In mathematics, “infinity” is the useful concept of a process with no end and is often used in contexts where it is treated as if it were a number (i.e., it counts or measures things: “an infinite number of terms”).
It is often mistakenly thought to be the largest number or a place on the real number line.
Instead, it is the idea of a limit, as in the expression x approaches to infinity, which suggests that the variable x increases without bound.Answer: 64
If there are 32 tangent lines, then there are 64 unbounded regions. It is not very difficult to visualize that each tangent line drawn creates two unbounded regions.
The man pics 7 flowers initially dipped them in lake and get doubled, that is 14 flowers. Then he offered 8 flowers in temple 1 and left with 6 flowers. He dipped remaining 6 flowers in lake to get 12 flowers and offers 8 flowers in temple 2. Now, he is left with 4 flowers dipped them in lake and gets 8 flowers which he offered in temple 3. So he offers 8 flowers in each temple.
Yes, we can also prove the fact 0.99…. = 1 by using sum of geometric series.
9 * 10 ^ -1 + 9 * 10 ^ -2 + ..... + 9 * 10 ^ – inf approaches to 1.
The series is in G.P and
Common difference ( r) = (9/100) / (9/10) =1/10
In GP, Sum to infinity = a/ (1-r)
Here a = 9/10 and r = 1/10=> S inf = (9/10) / 1- (1/10)
= (9/10) / (9/10)= 1Think, another solution may be…..
He planted 3 trees at the corners of an equilateral triangle. He built a mound in the middle and planted the 4th on the top of the mound so that it was the same distance from the other 3 trees. (on the points of a tetrahedron.)
