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Setler79 [48]
4 years ago
9

The figure shown is a rectangle. If you draw a new rectangle in which the dimensions are doubled, what is the relationship betwe

en the PERIMETERS of the two rectangles?
A) The perimeter of the new rectangle is twice that of the original rectangle.
Eliminate
B) The perimeter of the new rectangle is one-half that of the original rectangle.
C) The perimeter of the new rectangle is four times that of the original rectangle.
D) The perimeter of the new rectangle is one-fourth that of the original rectangle.

Mathematics
1 answer:
KATRIN_1 [288]4 years ago
7 0
the answer is A, sorry if you can't read it quite well

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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}+.....

as

                 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
4 years ago
Can someone help me with this. Will Mark brainliest.
Annette [7]
False hope that helps
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3 years ago
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PLZ HELP! I need to turn this in urgently <3
andriy [413]

Answer:

91

Step-by-step explanation:

This is a 180° line and it would be 180-89=91.

This isn't much but hope it helps .^.

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4 years ago
"What temperature is 23 degrees less than 8 degrees Fahrenheit?
Bumek [7]
-15 degrees Fahrenheit
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4 years ago
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What do the differences between the equation of a
EastWind [94]

Answer:

it tells u what color

Step-by-step explanation:

8 0
3 years ago
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