We know that when an integer n is divided by 5. there is a remainder in {0.1,2,3,4}. That is.
there Is an integer 1 so that n = 5q + r. where r {0.1,2,3,4). By considering four cues, show that
if n is not a multiple of 5, then n2 is not a multiple of 5. Note that if n is not a multiple of 5, then
the remainder r {1.2.3.4}.
Solution
case - 1:
n = 5q+1 , where q is an integer
squaring on both sides
=> n2 = (5q+1)2 = 25q2 + 10q + 1
=> n2 = 5(5q2 + 2q) + 1
Hence n2 is not multiple of 5 as it leaves remainder 1 if divided by 5
case - 2:
n = 5q+2 , where q is an integer
squaring on both sides
=> n2 = (5q+2)2 = 25q2 + 20q + 4
=> n2 = 5(5q2 + 4q) + 4
Hence n2 is not multiple of 5 as it leaves remainder 4 if divided by 5
case - 3:
n = 5q+3 , where q is an integer
squaring on both sides
=> n2 = (5q+3)2 = 25q2 + 30q + 9
=> n2 = 5(5q2 + 6q + 1) + 4
Hence n2 is not multiple of 5 as it leaves remainder 4 if divided by 5
case - 4:
n = 5q+4 , where q is an integer
squaring on both sides
=> n2 = (5q+4)2 = 25q2 + 40q + 16
=> n2 = 5(5q2 + 8q + 3) + 1
Hence n2 is not multiple of 5 as it leaves remainder 1 if divided by 5
So,we can say that if n is not a multiple of 5,then n2 is not a multiple of 5.
Post Exam Fun(da) Intra UEM General Quiz 2024 - Prelims q&a.pdf
We learned about was finding the slope (or slant) of a linear equat.pdf
1. We learned about was finding the slope (or slant) of a linear equation in an applied problem, in a
graph or with two points, and in an equation. Specifically for applied problems, we looked at an
example of a roof, of a road, and of a wheelchair ramp.
Think about examples in your everyday life (personal, work, school, etc.) where slope is
relevant. Describe at least one example of slope in the real world in detail, with the relevant math
behind it.
(Note, your example must be original.)
Solution
During my commute to school, I must cover a distance of 30 km per hour on average in order not
to be late for class.
This distance is represented by the linear equation: d = 30t, where d is the distance in km and t is
the time in hours.
The slope of the line is important in this case since it represents my average speed, 30 km/hr, that
I must maintain in order not to be late.
