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kirill115 [55]
3 years ago
12

An arena is hosting a concert. At the most, the arena can hold 8,500 people. If tickets have already been sold to 6,900 people,

what is the highest number of tickets that can still be sold?
Mathematics
1 answer:
ElenaW [278]3 years ago
8 0

Answer:

Subtract 6,900 from 8,500 to get the highest number of tickets that can still be sold which is 1,600.

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Answer:

Step-by-step explanation:

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Consider the function ​f(x)equalscosine left parenthesis x squared right parenthesis. a. Differentiate the Taylor series about 0
dybincka [34]

I suppose you mean

f(x)=\cos(x^2)

Recall that

\cos x=\displaystyle\sum_{n=0}^\infty(-1)^n\frac{x^{2n}}{(2n)!}

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\cos(x^2)=\displaystyle\sum_{n=0}^\infty(-1)^n\frac{(x^2)^{2n}}{(2n)!}=\sum_{n=0}^\infty(-1)^n\frac{x^{4n}}{(2n)!}

which also converges everywhere (and we can confirm this via the ratio test, for instance).

a. Differentiating the Taylor series gives

f'(x)=\displaystyle4\sum_{n=1}^\infty(-1)^n\frac{nx^{4n-1}}{(2n)!}

(starting at n=1 because the summand is 0 when n=0)

b. Naturally, the differentiated series represents

f'(x)=-2x\sin(x^2)

To see this, recalling the series for \sin x, we know

\sin(x^2)=\displaystyle\sum_{n=0}^\infty(-1)^{n-1}\frac{x^{4n+2}}{(2n+1)!}

Multiplying by -2x gives

-x\sin(x^2)=\displaystyle2x\sum_{n=0}^\infty(-1)^n\frac{x^{4n}}{(2n+1)!}

and from here,

-2x\sin(x^2)=\displaystyle 2x\sum_{n=0}^\infty(-1)^n\frac{2nx^{4n}}{(2n)(2n+1)!}

-2x\sin(x^2)=\displaystyle 4x\sum_{n=0}^\infty(-1)^n\frac{nx^{4n}}{(2n)!}=f'(x)

c. This series also converges everywhere. By the ratio test, the series converges if

\displaystyle\lim_{n\to\infty}\left|\frac{(-1)^{n+1}\frac{(n+1)x^{4(n+1)}}{(2(n+1))!}}{(-1)^n\frac{nx^{4n}}{(2n)!}}\right|=|x|\lim_{n\to\infty}\frac{\frac{n+1}{(2n+2)!}}{\frac n{(2n)!}}=|x|\lim_{n\to\infty}\frac{n+1}{n(2n+2)(2n+1)}

The limit is 0, so any choice of x satisfies the convergence condition.

3 0
4 years ago
The Abs R Us bodybuilding club has an annual memebership fee of $414. You plan to visit 8 each month, how much is your cost per
Lisa [10]
Comment
There are 12 months in a year. He plans on visiting 8 times each month. 

Step One 
Find the number of visits per year.

<em>Givens</em>
Number of visits per month = 8
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Visits = # visits / month * number of months
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Step Two
<em>Calculate the cost / visit</em>
Total Cost = 414 visits.
Total Visits = 96

Cost / Visit = Total Cost / Total visits.
Cost / Visit = 414 / 96
Cost / Visit = 4.31 roughly.
4 0
4 years ago
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