Mrs.Cats is making pancakes.She makes 30 pancakes to share equally amoug 5 people. How many pancakes does each person get?
2 answers:
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___________________________
◆ AREA RELATED TO CIRCLES ◆ ___________________________
As shown in the figure ,
Radius of circle = 5 cm
Side of square = 2 × (Radius of inscribed circle)
Side of square = 2 × 5 cm
Side of square = 10 cm = a
___________________________
Now ,
Area of shaded region = (Area of square) - ( Area of inscribed circle )
Area of shaded region =
Area of shaded region =
Area of shaded region = 100 - 78.571
◆ AREA RELATED TO CIRCLES ◆ ___________________________
As shown in the figure ,
Radius of circle = 5 cm
Side of square = 2 × (Radius of inscribed circle)
Side of square = 2 × 5 cm
Side of square = 10 cm = a
___________________________
Now ,
Area of shaded region = (Area of square) - ( Area of inscribed circle )
Area of shaded region =
Area of shaded region =
Area of shaded region = 100 - 78.571
Answer:
[a,b] divides n
Step-by-step explanation:
Let us denote the least common multiple of a and b [a,b]=m.
We want to prove that m divides n, where n is a multiple of a and b.
We suppose m does not divide n, then by the Division Theorem, there exists q and r integers such that:
(1) ... n=mq+r, where 0<r<m
As n is a multiple of a and b, there exists s and t integers such that:
sa=n and tb=n
Same thing happens to m as it is the least common multiple, there exists u and v such that:
ua=m and vb=m
So (1) has the following form:
n=mq+r ⇒ sa=uaq+r ⇒sa-uaq=r⇒(s-uq)a=r and
n=mq+r ⇒ tb=vbq+r ⇒ tb-vbq=r⇒ (t-vq)b=r
So r is a multiple of a and b, but r<m which is a contradiction as, m is the least common multiple of a and b. So this concludes the proof.
So this means that is and integer.
As m= vb, then is an integer, lets say
=v; and as m=ua, then
=u.
So v=
=a, so
divides a; on the other hand,
u=
=b, so
divides b. From this we can conclude that
is a common divisor of a and b.