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2 years ago

What is the distance (3,9) and (12,21)

Mathematics

2 answers:

VMariaS [17]2 years ago

7 0

6 and 8 I think I’m not sure

eimsori [14]2 years ago

4 0

d = 15.

The easiest way to calculate the distance between two point in the space is usign the equation d = √(x₂-x₁)²+(y₂-y₁)².

The distance between the points (3, 9) and (12, 21) is:

d = √(12-3)²+(21-9)² = √(9)²+(12)² = √81+144 = √225 = 15

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Answer:

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Step-by-step explanation:

A mathematical induction consists in only 2 steps:

First step: Show the proposition is true for the first one valid integer number.

Second step: Show that if any one is true then the next one is true

Finally, if first step and second step are true, then the complete proposition is true.

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First step: using and replacing n=2 (the first valid integer number >1)

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As the result is an integer number, so the first step is true.

Second step: using any next number, $n+1$ , let it replace

$2*(n+1)^3+3*(n+1)^2+(n+1)\\2*(n^3+3*n^2+3*n+1)+3*(n^2+2*n+1)^2+(n+1)\\2*n^3+6*n^2+6*n+2+3*n^2+6*n+3+n+1\\(2*n^3+3*n^2+n)+(6*n^2+12*n+6)$

As the First step is true, we know that

$2*n^3+3*n^2+n$ $=6*k$ ,

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$6*k+6*(n^2+2*n+1)\\6*[k+(n^2+2*n+1)]$

Finally

$\frac{6*[k+(n^2+2*n+1)]}{6} =k+(n^2+2*n+1)$

where the last expression is an integer number

So the second step is true, and the complete proposition is True

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