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3 years ago

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Mathematics

2 answers:

wlad13 [49]3 years ago

6 0

Answer:

$19.80

Step-by-step explanation:

Each pack of organic milk costs $3.96 dollars.

Mandy buys five of them.

Multiply 3.96 by 5.

$3.96*5=19.8$

Mandy spent $19.80 in all on his purchase.

Brums [2.3K]3 years ago

4 0

answer:

$19.80

Step-by-step explanation:

$3.96 x 5 = 19.80

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SOLUTION We observe that f '(x) = -1 / (1 + x2) and find the required series by integrating the power series for -1 / (1 + x2).

Ann [662]

Answer:

Required series is:

$\int{\frac{-1}{1+x^{2}} \, dx =-x+\frac{x^{3}}{3}-\frac{x^{5}}{5}+\frac{x^{7}}{7}+.....$

Step-by-step explanation:

Given that

$f'(x) = -\frac{1}{1 + x^{2}}$ ---(1)

We know that:

$\frac{d}{dx}(tan^{-1}x)=\frac{1}{1+x^{2}}$ ---(2)

Comparing (1) and (2)

$f'(x)=-(tan^{-1}x)$ ---- (3)

Using power series expansion for $tan^{-1}x$

$f'(x)=-tan^{-1}x=-\int {\frac{1}{1+x^{2}} \, dx$

$= -\int{ \sum\limits^{ \infty}_{n=0} (-1)^{n}x^{2n}} \, dx$

$= -\sum{ \int\limits^{ \infty}_{n=0} (-1)^{n}x^{2n}} \, dx$

$=-[c+\sum\limits^{ \infty}_{n=0} (-1)^{n}\frac{x^{2n+1}}{2n+1}]$

$=C+\sum\limits^{ \infty}_{n=0} (-1)^{n+1}\frac{x^{2n+1}}{2n+1}$

$=C-x+\frac{x^{3}}{3}-\frac{x^{5}}{5}+\frac{x^{7}}{7}+.....$

$tan^{-1}(0)=0 \implies C=0$

Hence,

$\int{\frac{-1}{1+x^{2}} \, dx =-x+\frac{x^{3}}{3}-\frac{x^{5}}{5}+\frac{x^{7}}{7}+.....$

7 0

3 years ago

Tickets to the school dance cost $3.00 in advance or $5.00 at the door. There were a total of 184 tickets sold, raising $688. Ho

GenaCL600 [577]

Answer: They sold 68 tickets at the door
688-920= -2x= -232
2x=232/2=116
184-116=68

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3 years ago

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Anna11 [10]

The answer is 589,918
Take 652203 and subtract 62,285 from that and you get 589,918

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3 years ago

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Andrej [43]

Answer:

dont click that link report it

Step-by-step explanation:

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3 years ago

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Rus_ich [418]

No they are not all rational numbers

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