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Black_prince [1.1K]
3 years ago
10

I NEED YOUR HELP FAST!!!!

Mathematics
2 answers:
nekit [7.7K]3 years ago
6 0

Answer:

c. \:  {w}^{64}

Sorry if i get it wrong

vovangra [49]3 years ago
6 0
C. I believe, if I am wrong I’m sorry.
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Divide f(x) by d(x), and write a summary statement in the form indicated.
lukranit [14]
( x^4 - 4 x³ + 2 x² - 4 x + 1 ) : ( x² + 1 )   =  x² - 4 x + 1
- x^4             - x²
------------------------
          - 4 x³ + x² - 4 x
            4 x³        + 4 x
         -----------------------
                      x²  + 1
                   - x²   - 1
                ----------------
                   R ( x ) = 0
( x^4 - 4 x³ + 2 x² - 4 x + 1) =  ( x² + 1 ) ( x² - 4 x + 1 )
3 0
3 years ago
At a movie theater, 360 people can see a particular movie over a period of 3 hours. At this
Agata [3.3K]

Answer:233

Step-by-step explanation:cause i said so

7 0
3 years ago
Read 2 more answers
Prove or disprove (from i=0 to n) sum([2i]^4) <= (4n)^4. If true use induction, else give the smallest value of n that it doe
ddd [48]

Answer:

The statement is true for every n between 0 and 77 and it is false for n\geq 78

Step-by-step explanation:

First, observe that, for n=0 and n=1 the statement is true:

For n=0: \sum^{n}_{i=0} (2i)^4=0 \leq 0=(4n)^4

For n=1: \sum^{n}_{i=0} (2i)^4=16 \leq 256=(4n)^4

From this point we will assume that n\geq 2

As we can see, \sum^{n}_{i=0} (2i)^4=\sum^{n}_{i=0} 16i^4=16\sum^{n}_{i=0} i^4 and (4n)^4=256n^4. Then,

\sum^{n}_{i=0} (2i)^4 \leq(4n)^4 \iff \sum^{n}_{i=0} i^4 \leq 16n^4

Now, we will use the formula for the sum of the first 4th powers:

\sum^{n}_{i=0} i^4=\frac{n^5}{5} +\frac{n^4}{2} +\frac{n^3}{3}-\frac{n}{30}=\frac{6n^5+15n^4+10n^3-n}{30}

Therefore:

\sum^{n}_{i=0} i^4 \leq 16n^4 \iff \frac{6n^5+15n^4+10n^3-n}{30} \leq 16n^4 \\\\ \iff 6n^5+10n^3-n \leq 465n^4 \iff 465n^4-6n^5-10n^3+n\geq 0

and, because n \geq 0,

465n^4-6n^5-10n^3+n\geq 0 \iff n(465n^3-6n^4-10n^2+1)\geq 0 \\\iff 465n^3-6n^4-10n^2+1\geq 0 \iff 465n^3-6n^4-10n^2\geq -1\\\iff n^2(465n-6n^2-10)\geq -1

Observe that, because n \geq 2 and is an integer,

n^2(465n-6n^2-10)\geq -1 \iff 465n-6n^2-10 \geq 0 \iff n(465-6n) \geq 10\\\iff 465-6n \geq 0 \iff n \leq \frac{465}{6}=\frac{155}{2}=77.5

In concusion, the statement is true if and only if n is a non negative integer such that n\leq 77

So, 78 is the smallest value of n that does not satisfy the inequality.

Note: If you compute  (4n)^4- \sum^{n}_{i=0} (2i)^4 for 77 and 78 you will obtain:

(4n)^4- \sum^{n}_{i=0} (2i)^4=53810064

(4n)^4- \sum^{n}_{i=0} (2i)^4=-61754992

7 0
3 years ago
Divide using synthetic division -3 1 8 9 -18
agasfer [191]

Answer:

Step-by-step explanation:

-3   /   1    8    9    -18

              -3    -15   18

     _______________

        1      5     -6     0

The remainder here is 0 and the quoitient is 1x^2 + 5x - 6.

3 0
3 years ago
Is it possible for an x-intercept and a y-intercept to have no intercept
wel
<span>Not all functions will have intercepts</span>
5 0
3 years ago
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