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Doss [256]
3 years ago
10

What is x times y with the exponent 2?

Mathematics
1 answer:
Citrus2011 [14]3 years ago
8 0
When to add exponents<span>, when to multiply </span>exponents<span>. Same ... Two factors of </span>x<span> -- </span>x2<span> -- </span>times<span> five factors of </span>x<span> -- </span>x5<span> -- </span>times<span> one factor of </span>x, .... (2x3y4)5<span> = </span>25x15y<span>20</span>
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Find the nth term of the sequence 7,25,51,85,127​
olya-2409 [2.1K]

Let <em>a </em>(<em>n</em>) denote the <em>n</em>-th term of the given sequence.

Check the forward differences, and denote the <em>n</em>-th difference by <em>b </em>(<em>n</em>). That is,

<em>b </em>(<em>n</em>) = <em>a </em>(<em>n</em> + 1) - <em>a </em>(<em>n</em>)

These so-called first differences are

<em>b</em> (1) = <em>a</em> (2) - <em>a</em> (1) = 25 - 7 = 18

<em>b</em> (2) = <em>a</em> (3) - <em>a</em> (2) = 51 - 25 = 26

<em>b </em>(3) = <em>a</em> (4) - <em>a</em> (3) = 85 - 51 = 34

<em>b</em> (4) = <em>a </em>(5) - <em>a</em> (4) = 127 - 85 = 42

Now consider this sequence of differences,

18, 26, 34, 42, …

and notice that the difference between consecutive terms in this sequence <em>b</em> is 8:

26 - 18 = 8

34 - 26 = 8

42 - 34 = 8

and so on. This means <em>b</em> is an arithmetic sequence, and in particular follows the rule

<em>b</em> (<em>n</em>) = 18 + 8 (<em>n</em> - 1) = 8<em>n</em> + 10

for <em>n</em> ≥ 1.

So we have

<em>a </em>(<em>n</em> + 1) - <em>a </em>(<em>n</em>) = 8<em>n</em> + 10

or, replacing <em>n</em> + 1 with <em>n</em>,

<em>a</em> (<em>n</em>) = <em>a</em> (<em>n</em> - 1) + 8 (<em>n</em> - 1) + 10

<em>a</em> (<em>n</em>) = <em>a</em> (<em>n</em> - 1) + 8<em>n</em> + 2

We can solve for <em>a</em> (<em>n</em>) by iteratively substituting:

<em>a</em> (<em>n</em>) = [<em>a</em> (<em>n</em> - 2) + 8 (<em>n</em> - 1) + 2] + 8<em>n</em> + 2

<em>a</em> (<em>n</em>) = <em>a </em>(<em>n</em> - 2) + 8 (<em>n</em> + (<em>n</em> - 1)) + 2×2

<em>a</em> (<em>n</em>) = [<em>a</em> (<em>n</em> - 3) + 8 (<em>n</em> - 2) + 2] + 8 (<em>n</em> + (<em>n</em> - 1)) + 2×2

<em>a</em> (<em>n</em>) = <em>a</em> (<em>n</em> - 3) + 8 (<em>n</em> + (<em>n</em> - 1) + (<em>n</em> - 2)) + 3×2

and so on. The pattern should be clear; we end up with

<em>a</em> (<em>n</em>) = <em>a</em> (1) + 8 (<em>n</em> + (<em>n</em> - 1) + … + 3 + 2) + (<em>n</em> - 1)×2

The middle group is the sum,

\displaystyle 8\sum_{k=2}^nk=8\sum_{k=1}^nk-8=\frac{8n(n+1)}2-8=4n^2+4n-8

so that

<em>a</em> (<em>n</em>) = <em>a</em> (1) + (4<em>n</em> ² + 4<em>n</em> - 8) + 2 (<em>n</em> - 1)

<em>a</em> (<em>n</em>) = 4<em>n</em> ² + 6<em>n</em> - 3

4 0
3 years ago
5. When y varies directly with x, the value of y = -2 when x = 4. What is the value of y when x = 8?
zmey [24]

Answer:

-4

Step-by-step explanation:

if y = -2 then x = 4

what is y when x = 8

\frac{ - 2}{x}  =  \frac{4}{8}  \\  - 16 = 4x \\ x =  - 4

7 0
2 years ago
Asap help 100 points
gregori [183]

Answer:

(4x + 2)° = (6x -10)°

4x + 2 = 6x - 10

4x -6x = -10 -2

-2x = -12

x = <u>-</u><u>12</u>

-2

x = 6°

7 0
3 years ago
Read 2 more answers
Solve the compound inequality, then correctly fill in the blanks below.<br> -3 2-5 &lt;2<br> I
lesantik [10]

Answer:

hold my picolr

Step-by-step explanation:

7 0
3 years ago
Angle A and B are supplementary. Angle a has a measure of 80. What is the measure of angle B? The measure of angle B is
ololo11 [35]
Well when two angles are supplementary they equal 180.
So if angle A is 80 degrees then that would mean that angle B equals 100 degrees. 


Hope This Helped :) 



4 0
3 years ago
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