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Effectus [21]
1 year ago
6

Find all the frist differnce and explian your answer

Mathematics
2 answers:
Sever21 [200]1 year ago
8 0

Answer: No this is not a linear function as the y values have different first differences.

Step-by-step explanation:

First we look at the x values. We start off and look at the second x value and subtract the first x value from it (That would be 1-0) and that equals to 1. Then we look at the third x value and subtract the second x value from it (2-1) and that equals to 1. Then we look at the fourth x value and subtract the third x value from it (That would be 3-2) and that is 1. Next we look at the fifth x value and subtract the fourth x value from it (That would be 4-3) and that is 1.

Now we look at the y values and do the same thing as with the x values. We start off and look at the second y value and subtract the first y value from it (That would be 1-0) and that equals to 1. Then we look at the third y value and subtract the second y value from it (4-1) and that equals to 3. Then we look at the fourth y value and subtract the third y value from it (That would be 9-4) and that is 5. Next we look at the fifth y value and subtract the fourth y value from it (That would be 16-9) and that is 7.

Even though the x values all have the same first differences, the y values do not and so this cannot be a linear function.

I hope this helps. Tell me if something doesn't make sense.

svet-max [94.6K]1 year ago
7 0

Answer:

No, it is a quadratic relation.

Step-by-step explanation:

Work out the first differences between the given y-values:

0 \underset{+1}{\longrightarrow} 1 \underset{+3}{\longrightarrow} 4 \underset{+5}{\longrightarrow} 9 \underset{+7}{\longrightarrow} 16

As the first differences are <u>not the same</u>, this is <em>not </em>a <u>linear relation</u>.

Work out the second differences:

1 \underset{+2}{\longrightarrow} 3\underset{+2}{\longrightarrow}5\underset{+2}{\longrightarrow}7

As the second differences are the same, the relation is quadratic and will contain an x² term. The coefficient of x² is always half of the second difference.  As the second difference is 2, the coefficient of x² is one.

\begin{array}{|c|c|c|c|c|c|}\cline{1-6}x & 0 & 1 & 2 & 3 & 4\\\cline{1-6}x^2 & 0 & 1 & 4 & 9 & 16\\\cline{1-6}\end{array}

Comparing x² with the given y-values, we can see that no further operation is needed.  Therefore, the relation is quadratic and the equation is y=x^2.

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z=5\left(\cos \left(\dfrac{3\pi}{2}\right)+i\sin \left(\dfrac{3\pi}{2}\right)\right)

Step-by-step explanation:

If a complex number is z=a+ib, then the trigonometric form of complex number is

z=r(\cos \theta +i\sin \theta)

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It can be rewritten as

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\theta=\dfrac{3\pi}{2}

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z=5\left(\cos \left(\dfrac{3\pi}{2}\right)+i\sin \left(\dfrac{3\pi}{2}\right)\right)

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