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lina2011 [118]
2 years ago
5

K^2+8k-9=0 can you help me solve with showing work

Mathematics
2 answers:
givi [52]2 years ago
7 0
Using the PSN method:

P = -9
S = 8
So N = 9,-1

Using 9 and -1 in the original equation gives:

k^2+9k-k-9=0
\\k(k+9)-1(k+9)=0
\\(k-1)(k+9)

\\\\k=1,-9
erastova [34]2 years ago
5 0
K² + 8k - 9 = 0
k = <u>-8 +/- √(8² - 4(10)(-9))</u>
                   2(1)
k = <u>-8 +/- √(64 + 360)</u>
                   2
k = <u>-8 +/- √(424)
</u>               2<u>
</u>k = <u>-8 +/- 20.59126028
</u>                     2<u>
</u>k = <u>-8 + 20.59126028</u>    k = <u>-8 - 20.59126028
</u>                    2<u />                                    2<u>
</u>k = <u>12.5912608</u>             k = <u>-20.5912608
</u>              2    <u /><u />                                 2<u>
</u>k = 6.2956304<u />                k = <u />-10.2956304<u>
</u>
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Answer:

The explicit formula

a_n = 3 +0.25 (n-1)

The recursive formula

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a_n = a_ {(n-1)} +0.25     if n>1

Step-by-step explanation:

If a sequence is arithmetical then the difference between any of its consecutive terms will be constant

3, 3.25, 3.5, 3.75,

3.25-3 = 0.25\\\\3.5-3.25 = 0.25\\\\3.75 -3.5 = 0.25

The difference between the consecutive terms remains constant so the sequence is arithmetic.

The explicit formula for an arithmetic sequence is:

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d = 0.25

a_1 is the first term of the sequence.

a_1 = 3

So

a_n = 3 +0.25 (n-1)

Finally, the recursive formula is:

a_1 = 3\\\\a_n = a_ {(n-1)} +0.25

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2 years ago
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