Use pictures to explain how to use the sum 13 to show how to add in any order
1 answer:
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4, 7 and 9 are mutually coprime, so you can use the Chinese remainder theorem.
Start with
Taken mod 4, the last two terms vanish and we're left with
We have , so we can multiply the first term by 3 to guarantee that we end up with 1 mod 4.
Taken mod 7, the first and last terms vanish and we're left with
which is what we want, so no adjustments needed here.
Taken mod 9, the first two terms vanish and we're left with
so we don't need to make any adjustments here, and we end up with .
By the Chinese remainder theorem, we find that any such that
is a solution to this system, i.e. for any integer
, the smallest and positive of which is 149.
Answer:
1222 billion dollars.
Step-by-step explanation:
To find the total increase from 1960 to 2010, we need to find the growth of each decade and sum them all:
In the period 1960-1970, we have x = 1, and the growth is:
In the period 1970-1980, we have x = 2, and the growth is:
The growth in the following 3 periods are:
So the total growth in the period 1960 - 2010 is:
Rounding to the nearest billion dollars, we have a total of 1222 billion dollars.