The number of integral points that lie exactly inside the square formed by lines x = 0, y=0, x= 10 and y= 10
Answers
Given:
A square made of the lines x = 0, y=0, x= 10 and y= 10.
To Find:
The number of integral points that lie exactly inside the square formed by lines .
Solution:
- Since the points should lie inside the square the points on the line cannot be considered.
- Therefore x values can belong to the following set.
- x ∈ { 1 , 2, 3, 4, 5, 6, 7, 8, 9} -> 9 elements
- Similarly, y values can belong to the following group.
- y ∈ { 1 , 2, 3, 4, 5, 6, 7, 8, 9} -> 9 elements.
Therefore the total number of integral points possible are 9 x 9 = 81.
Answer:
The relationship between current, charge and time is given as follows.
charge = current x time, that is, Q = It where,
charge is Q, it is measured in coulombs (C)
current is I, it is measured in amperes (A)
time is t, it is measured in seconds (s).
The relationship between electronic charge, charge and number of electrons are protons is given as follows.
charge = number of electrons or protons x electronic charge, that is Q = ne
where,
charge is Q, it is measured in coulombs (C)
number of electrons/protons is n, it is measured in numbers
electronic charge is e, it has a standard value = 1.6×10
−19
Coloumbs (C).
Equating both the above equations, that is,
It = ne we get,n=
e
I×T
=
1.6×10
−19
1×16
=10
20
.
Hence, number of electrons passing through a cross section of the filament in 16 seconds would be roughly 10
20
.