A board 109 cm long has to be cut into two pieces so that the longer part is 10 cm more than twice as long as the shorter part.
1 answer:
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Answer:
3n² + 5n - 2
Step-by-step explanation:
<u>Given sequence</u>:
6, 20, 40, 66, 98, 136, ...
Calculate the <u>first differences</u> between the terms:
As the first differences are not the same, calculate the <u>second differences:</u>
As the <u>second differences are the same</u>, the sequence is quadratic and will contain an n² term.
The <u>coefficient</u> of the n² term is <u>half of the second difference</u>.
Therefore, the n² term is: 3n²
Compare 3n² with the given sequence:
The second operations are different, therefore calculate the differences <em>between</em> the second operations:
As the differences are the same, we need to add 5n as the second operation:
Finally, we can clearly see that the operation to get from 3n² + 5n to the given sequence is to subtract 2.
Therefore, the nth term of the quadratic sequence is:
3n² + 5n - 2
Answer: Hence, there are approximately 48884 integers are divisible by 3 or 5 or 7.
Step-by-step explanation:
Since we have given that
Integers between 10000 and 99999 = 99999-10000+1=90000
n( divisible by 3) =
n( divisible by 5) =
n( divisible by 7) =
n( divisible by 3 and 5) = n(3∩5)=
n( divisible by 5 and 7) = n(5∩7) =
n( divisible by 3 and 7) = n(3∩7) =
n( divisible by 3,5 and 7) = n(3∩5∩7) =
As we know the formula,
n(3∪5∪7)=n(3)+n(5)+n(7)-n(3∩5)-n(5∩7)-n(3∩7)+n(3∩5∩7)
Hence, there are approximately 48884 integers are divisible by 3 or 5 or 7.