In the year 2003 a company made 8.8 million in profits. For each consecutive year after that their profits increased by 6%. How
1 answer:
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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.
The average rate of change for the height of the plant measured in centimeters per day between day 0 and day 20 is 1.32 cm per day.
<h3>What is average height?</h3>The average height is the ratio of change in height of the plant and the time taken taken for that change.
Given is the height of a plant in centimeters is modeled as a function of time, in days.
For day 0, the height is 18cm and the height for day 20 is 42 cm, then the average height change is
height per day = 42 - 18/ 20 -0
height per day = 1.2 cm/day
Thus, the average height of plant is 1.2 cm/day.
Learn more about average height.
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