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aleksandr82 [10.1K]
3 years ago
5

Find the absolute maximum value for the function f(x) = x2 – 3, on the interval [–4, 0) U (0, 3].

Mathematics
1 answer:
BigorU [14]3 years ago
7 0
13 will be the answer. Plug in -4 into the equation
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I need help with this its a bit easy will mark brainlist
LenKa [72]

Answer:

First box: y/x = 38/2 = 19

Second box: y/x = 57/3 = 19

Third box: y/x = 76/4 = 19

Constant of proportionality = 19

Equation: y = 19x

8 0
3 years ago
Read 2 more answers
Which expressions are equivalent to 64’1Check all that apply.
erastovalidia [21]

Answer: a,c,f (4^3, 8^2, 2^6)

Step-by-step explanation:

8 0
3 years ago
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
PLEASE HELP!
Kitty [74]
You can reword the two equations as:

-5x-y=15 (Divide original value by 3)
-2x+6y=6

Then use elimination to find x:

-30x-6y=90 (Multiply by 6 to get y values to be same to cancel out)
-2x+6y=6

You're left with:

-32x=96. Which can then be solved to find x which is -3.

Then plug back in 

-2x+6y=6

Now to: -2(-3)+6y=6.

Which reduces to 6+6y=6. So y=0.



To graph them, just reword the equations (yes once again) so that y is in front.

y=-5x-15 and y=(1/3)x+1






8 0
3 years ago
What is the slope of the line passing through (-2, 4) and (3,-4) ​
mariarad [96]
hold on i will send in the comments i’m working on it rn
5 0
3 years ago
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