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Advocard [28]
3 years ago
7

If the pattern of the first 6 letters in CIRCUSCIRCUSCIRCUS… continues, what is the pattern’s 500 letter?

Mathematics
2 answers:
tangare [24]3 years ago
8 0

Answer:

I (capital i).

Step-by-step explanation:

We have the pattern:

CIRCUSCIRCUSCIRCUS...

The word "CIRCUS" repeats indefinitely.

And we want to find the 500th letter.

Note that CIRCUS repeats after every 6th letter. So, it will repeat and go back to C after 6 letters, 12 letters, 18 letters, and so on...

Note that 500 is the same as:

500=83(6)+2

So, 500 letters will be the word CIRCUS repeated 83 times plus 2 extra letters.

So the first 83 iterations won't matter as it'll just repeat. We only need to focus on the remaining letters.

After 500 letters, we will have reiterated CIRCUS 83 times for a total of 498 letters and we will start back at C at the 499th letter.

So, our 500th letter will be the letter after (the first) C, or I.

Our 500th letter is I (capital i).  

And we're done!

UkoKoshka [18]3 years ago
8 0

Answer:

I have to agree to the point with this other person

Step-by-step explanation:

The letter would be I (i)

for the exact reason they gave

couldn't have explained it better.

You should mark that person brainliest. I know i would.

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3 years ago
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Let F⃗ =2(x+y)i⃗ +8sin(y)j⃗ .
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Answer:

-42

Step-by-step explanation:

The objective is to find the line integral of F around the perimeter of the rectangle with corners (4,0), (4,3), (−3,3), (−3,0), traversed in that order.

We will use <em>the Green's Theorem </em>to evaluate this integral. The rectangle is presented below.

We have that

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                  P(x,y) = 2(x+y) \quad \wedge \quad Q(x,y) = 8\sin y

Let's calculate the needed partial derivatives.

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Thus,

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Now, by the Green's theorem, we have

\oint_C F \,dr = \iint_D (Q_x-P_y)\,dA = \int \limits_{-3}^{4} \int \limits_{0}^{3} (-2)\,dy\, dx \\ \\\phantom{\oint_C F \,dr = \iint_D (Q_x-P_y)\,dA}= \int \limits_{-3}^{4} (-2y) \Big|_{0}^{3} \; dx\\ \phantom{\oint_C F \,dr = \iint_D (Q_x-P_y)\,dA}= \int \limits_{-3}^{4} (-6)\; dx = -6x  \Big|_{-3}^{4} = -42

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